More about the lattice of all possible theories
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John F Sowa
Jan 16, 2016, 5:00:54 PM1/16/16
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I received an offline note about generalization and specialization.
-------- Forwarded Message --------
Subject: Offlist - adding primitives to be more general
Anonymous
> Perhaps I'm missing something, but it appears Matthew is correct
> that adding more primitives does not necessarily make a system more
> specialized, in the sense of being more restricted. Arguably, adding
> primitives can make a system more general.
This is a matter of logic. A more general statement (or theory)
is true in a wider range of cases (possible worlds) than a more
specialized statement (or theory).
If you have a theory T with axioms t1,...,tN and you add another t,
it becomes more specialized. It says more, but it is true in a subset
of the cases (or worlds) as the previous theory.
> Consider a system that has primitives related to only a single sense,
> e.g. smell. Then add primitives for another sense, e.g. sight. The
> resulting system is more general - it can perceive aspects of a
> situation that are more complex than before
Now you're talking about systems instead of theories. Every system
that has both smell and sight is in the intersection of those that
have smell and those that have sight. That's a smaller set.
> Likewise, if we restrict a system to just a single spatial dimension,
> it is less general than if we add primitives for two or three spatial
> dimensions, and less general than if we add primitives for a temporal
> dimension.
Look at the theories: you can define a theory T of N dimensional
space for any N. That wouldn't say much about any particular N, but
it would contain axioms that are true for any possible value of N.
If you add an axiom that says N=1, that specializes T to a specific
theory for just the special case of N=1. It would contain every
theorem of T, but it would also contain many theorems that are
limited to just a linear space. If you add an axiom to T that
says N=2, you get a different specialized theory for flat spaces.
Now suppose you want a theory for linear, flat, or solid geometry.
You can add all the axioms for N=1, 2, or 3 to the axioms for any N.
That gives you the conjunction of a general theory (any N) with a
disjunction of three different specializations.
> Suppose we have primitives for only a single domain, e.g. corporations,
> and then add primitives for another domain, e.g. governments. The
> resulting system can be more general, as well as more specialized.
You will get a general theory of organizations and a conjunction
of a disjunction (corporations or governments).
Summary: If you delete an axiom from a theory, the resulting theory
will be true of more systems, but it will say less about each.
The most general theory (no axioms) says nothing about everything.
The most specialized theory (all possible axioms) is inconsistent;
therefore, it says everything about nothing.
John
-------- Forwarded Message --------
Subject: Offlist - adding primitives to be more general
Anonymous
> Perhaps I'm missing something, but it appears Matthew is correct
> that adding more primitives does not necessarily make a system more
> specialized, in the sense of being more restricted. Arguably, adding
> primitives can make a system more general.
This is a matter of logic. A more general statement (or theory)
is true in a wider range of cases (possible worlds) than a more
specialized statement (or theory).
If you have a theory T with axioms t1,...,tN and you add another t,
it becomes more specialized. It says more, but it is true in a subset
of the cases (or worlds) as the previous theory.
> Consider a system that has primitives related to only a single sense,
> e.g. smell. Then add primitives for another sense, e.g. sight. The
> resulting system is more general - it can perceive aspects of a
> situation that are more complex than before
Now you're talking about systems instead of theories. Every system
that has both smell and sight is in the intersection of those that
have smell and those that have sight. That's a smaller set.
> Likewise, if we restrict a system to just a single spatial dimension,
> it is less general than if we add primitives for two or three spatial
> dimensions, and less general than if we add primitives for a temporal
> dimension.
Look at the theories: you can define a theory T of N dimensional
space for any N. That wouldn't say much about any particular N, but
it would contain axioms that are true for any possible value of N.
If you add an axiom that says N=1, that specializes T to a specific
theory for just the special case of N=1. It would contain every
theorem of T, but it would also contain many theorems that are
limited to just a linear space. If you add an axiom to T that
says N=2, you get a different specialized theory for flat spaces.
Now suppose you want a theory for linear, flat, or solid geometry.
You can add all the axioms for N=1, 2, or 3 to the axioms for any N.
That gives you the conjunction of a general theory (any N) with a
disjunction of three different specializations.
> Suppose we have primitives for only a single domain, e.g. corporations,
> and then add primitives for another domain, e.g. governments. The
> resulting system can be more general, as well as more specialized.
You will get a general theory of organizations and a conjunction
of a disjunction (corporations or governments).
Summary: If you delete an axiom from a theory, the resulting theory
will be true of more systems, but it will say less about each.
The most general theory (no axioms) says nothing about everything.
The most specialized theory (all possible axioms) is inconsistent;
therefore, it says everything about nothing.
John
Patrick Cassidy
Jan 17, 2016, 2:47:19 PM1/17/16
to ontolo...@googlegroups.com
It appears that John is describing the mathematical set-theoretic sense of "general" here.
It seems from John's definition that the most "general" theory would be something like:
"something exists"
I think that practical knowledge engineers consider "general" to mean "generally useful" in which case an ontology with more primitives would be one that is more generally useful, i.e. "general". It covers more cases, and, with proper editing, can be made as small and efficient as is required for any specific application.
I am always interested in learning what people consider as "primitives" and would welcome any (preferably offline) suggestions for inclusion in that exalted category. The five senses are already on hand in my current list.
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
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It seems from John's definition that the most "general" theory would be something like:
"something exists"
I think that practical knowledge engineers consider "general" to mean "generally useful" in which case an ontology with more primitives would be one that is more generally useful, i.e. "general". It covers more cases, and, with proper editing, can be made as small and efficient as is required for any specific application.
I am always interested in learning what people consider as "primitives" and would welcome any (preferably offline) suggestions for inclusion in that exalted category. The five senses are already on hand in my current list.
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
>All contributions to this forum by its members are made under an open
>content license, open publication license, open source or free software
>license. Unless otherwise specified, all Ontolog Forum content shall be
>subject to the Creative Commons CC-BY-SA 4.0 License or its successors.
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Matthew West
Jan 18, 2016, 6:53:06 AM1/18/16
to ontolo...@googlegroups.com
Dear Pat C,
I am always interested in learning what people consider as "primitives" and would welcome any (preferably offline) suggestions for inclusion in that exalted category. The five senses are already on hand in my current list.
[MW>] Some time ago now I did some work on data integration architectures and came up with a pragmatic approach to identifying missing primitives, when you were trying to integrate a new system into an existing integration environment with a particular set of primitives. The paper that resulted can be found here:
http://www.matthew-west.org.uk/publications/IIDEASforPDTEurope.pdf
It was developed into an ISO standard (ISO 18876).
This will probably go some way to explaining why I don't think there is a limited number of primitives that can define everything else (unless you are talking about some particular closed world).
Regards
Matthew West
Information Junction
Mobile: +44 750 3385279
Skype: dr.matthew.west
matthe...@informationjunction.co.uk
http://www.informationjunction.co.uk/
https://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire, SG6 2SU.
I am always interested in learning what people consider as "primitives" and would welcome any (preferably offline) suggestions for inclusion in that exalted category. The five senses are already on hand in my current list.
http://www.matthew-west.org.uk/publications/IIDEASforPDTEurope.pdf
It was developed into an ISO standard (ISO 18876).
This will probably go some way to explaining why I don't think there is a limited number of primitives that can define everything else (unless you are talking about some particular closed world).
Regards
Matthew West
Information Junction
Mobile: +44 750 3385279
Skype: dr.matthew.west
matthe...@informationjunction.co.uk
http://www.informationjunction.co.uk/
https://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire, SG6 2SU.
Ed Lowry
Jan 18, 2016, 9:19:42 AM1/18/16
to ontolo...@googlegroups.com
Matthew
In looking for primitives, I suggest you consider "Toward Perfect Information Microstructures" at
http://users.rcn.com/eslowry/tpim.pdf . At present, students everywhere are taught how to arrange
pieces of information by educators who are unaware of pieces of information that are well designed
to be easily arranged. Students may end up giggling about that performance for a long time.
Ed Lowry
In looking for primitives, I suggest you consider "Toward Perfect Information Microstructures" at
http://users.rcn.com/eslowry/tpim.pdf . At present, students everywhere are taught how to arrange
pieces of information by educators who are unaware of pieces of information that are well designed
to be easily arranged. Students may end up giggling about that performance for a long time.
Ed Lowry
John F Sowa
Jan 18, 2016, 4:52:53 PM1/18/16
to ontolo...@googlegroups.com
Dear Pat C, Matthew, and Ed L,
PC
of metalanguage for talking about ontology.
We need some version of logic to represent formal ontologies.
The logical issues about combining and relating ontologies are
more important than any words (or symbols) in the metalanguage.
When we add primitives to an ontology, we are always adding a new
theory -- i.e., those definitions and axioms that specify the
new primitives. That new theory may be added in various ways:
1. Conjunction (AND operator) at the top level. This adds more
information about more kinds of things that may be used together.
Therefore, it enables sentences that use the ontology to talk
about more kinds of things and processes and all possible
combinations and interactions of them.
2. Disjunction (OR operator) at the top level. This adds more
information as in #1, but users must make a choice to use
one or the other.
3. Conjunction or disjunction at a lower level (AKA microtheory).
This adds more information, but only to the branch of the
ontology at the level immediately above it.
In terms of logic, conjunction (p & q) always reduces the number
of cases (possible worlds or applications) to the intersection
of those for which p is true and those for which q is true. You
can say more about that intersection, but you leave out some cases.
Disjunction (p | q) increases the number of cases to which the
theory may be applied, but you can't use the terminology of
both theories (except in the intersection for which p&q is true).
PC
about these issues. Are you adding them by AND or by OR? Are they
added at the top level? Or do they presuppose some levels above?
For example, the distinction of living or non-living presupposes
some theory about physical objects and processes, geometry, etc.
MW
> environment with a particular set of primitives:
> http://www.matthew-west.org.uk/publications/IIDEASforPDTEurope.pdf
I described above. I agree that there is no limit to the number of
primitives, especially when you get into the details at the lower
levels of any large engineering design.
And when you're trying to relate independently developed systems,
you need a conjunction of the theory that specifies the interfaces
with a disjunction of the primitives of each system.
EL
> for primitives ... consider "Toward Perfect Information Microstructures" at http://users.rcn.com/eslowry/tpim.pdf
for constructing a wide range of things. In fact, that's one reason
why LEGO has become a child's toy that some adults never stop playing
with. A important prerequisite, which LEGO also illustrates, is the
need for standard interfaces for connecting the building blocks.
The same principle applies to software design. The rapid adoption
rate of the WWW resulted from a good combination of two general and
flexible standards for connecting independently developed systems:
http and html. Tim Berners-Lee deserves a lot of credit for adopting
and adapting previously successful interfaces (Apple's HyperCard and
the ISO standard for SGML, which evolved from IBM's GML).
But the WWW also has some serious problems: Tim B-L was designing
a system for physicists to distribute research papers. He had not
anticipated the security issues required for selling products,
handling sensitive information, and keeping out the bad guys.
John
PC
> I think that practical knowledge engineers consider "general" to mean
> "generally useful" in which case an ontology with more primitives
> would be one that is more generally useful, i.e. "general". It covers
> more cases, and, with proper editing, can be made as small and
> efficient as is required for any specific application.
Ambiguities in the word 'general' are only relevant to the choice
> "generally useful" in which case an ontology with more primitives
> would be one that is more generally useful, i.e. "general". It covers
> more cases, and, with proper editing, can be made as small and
> efficient as is required for any specific application.
of metalanguage for talking about ontology.
We need some version of logic to represent formal ontologies.
The logical issues about combining and relating ontologies are
more important than any words (or symbols) in the metalanguage.
When we add primitives to an ontology, we are always adding a new
theory -- i.e., those definitions and axioms that specify the
new primitives. That new theory may be added in various ways:
1. Conjunction (AND operator) at the top level. This adds more
information about more kinds of things that may be used together.
Therefore, it enables sentences that use the ontology to talk
about more kinds of things and processes and all possible
combinations and interactions of them.
2. Disjunction (OR operator) at the top level. This adds more
information as in #1, but users must make a choice to use
one or the other.
3. Conjunction or disjunction at a lower level (AKA microtheory).
This adds more information, but only to the branch of the
ontology at the level immediately above it.
In terms of logic, conjunction (p & q) always reduces the number
of cases (possible worlds or applications) to the intersection
of those for which p is true and those for which q is true. You
can say more about that intersection, but you leave out some cases.
Disjunction (p | q) increases the number of cases to which the
theory may be applied, but you can't use the terminology of
both theories (except in the intersection for which p&q is true).
PC
> I am always interested in learning what people consider as "primitives"
That's fine. But when you add new primitives, you need to be clear
about these issues. Are you adding them by AND or by OR? Are they
added at the top level? Or do they presuppose some levels above?
For example, the distinction of living or non-living presupposes
some theory about physical objects and processes, geometry, etc.
MW
> a pragmatic approach to identifying missing primitives, when you
> are trying to integrate a new system into an existing integration
> environment with a particular set of primitives:
> http://www.matthew-west.org.uk/publications/IIDEASforPDTEurope.pdf
>
> This will probably go some way to explaining why I don't think there
> is a limited number of primitives that can define everything else
> (unless you are talking about some particular closed world).
The diagrams in that paper illustrate the conjunctions and disjunctions
> This will probably go some way to explaining why I don't think there
> is a limited number of primitives that can define everything else
> (unless you are talking about some particular closed world).
I described above. I agree that there is no limit to the number of
primitives, especially when you get into the details at the lower
levels of any large engineering design.
And when you're trying to relate independently developed systems,
you need a conjunction of the theory that specifies the interfaces
with a disjunction of the primitives of each system.
EL
> for primitives ... consider "Toward Perfect Information Microstructures" at http://users.rcn.com/eslowry/tpim.pdf
> students everywhere are taught how to arrange pieces of information
> by educators who are unaware of pieces of information that are well
> designed to be easily arranged.
I agree that modular designs with reusable parts are very effective
> by educators who are unaware of pieces of information that are well
> designed to be easily arranged.
for constructing a wide range of things. In fact, that's one reason
why LEGO has become a child's toy that some adults never stop playing
with. A important prerequisite, which LEGO also illustrates, is the
need for standard interfaces for connecting the building blocks.
The same principle applies to software design. The rapid adoption
rate of the WWW resulted from a good combination of two general and
flexible standards for connecting independently developed systems:
http and html. Tim Berners-Lee deserves a lot of credit for adopting
and adapting previously successful interfaces (Apple's HyperCard and
the ISO standard for SGML, which evolved from IBM's GML).
But the WWW also has some serious problems: Tim B-L was designing
a system for physicists to distribute research papers. He had not
anticipated the security issues required for selling products,
handling sensitive information, and keeping out the bad guys.
John
Patrick Cassidy
Jan 18, 2016, 6:52:40 PM1/18/16
to ontolo...@googlegroups.com
Matthew,
Thanks for the reference:
https://d2024367-a-62cb3a1a-s-sites.googlegroups.com/site/drmatthewwest/publications/IIDEASforPDTEurope.pdf?attachauth=ANoY7co59i8tiUPNl5Vb91v4doYA5Ybcq8tVzbNtouK1IkjGqN4ptD3prQrXg-yP1hdw5pCeIc4M5VJXXWEBBnHlfQOBAV8q9OWzQcy5z57yRS55-9t9lo3O62zPp0VPlXhQtH7ON-OoiYmJw3xplclxp5ZBNIcq6ydqcOPhtDpXgEJ9Dyz8bxemvHVkLPFIByi6GM7WftJufUZgeWhcBBYkZo4eZyLYDRfERdd7x5sonDWLbyKzKu0Sj6EZHWQ_NvQV3xaAAH4e&attredirects=0
That paper on IIDEAS is a good summary of the general tactic of integration via a foundation ontology ("integration model"). Is there a citation I can use (other than the URL link) to its published version?
The conclusion that the number of primitives is unlimited, however, does not follow from the experience of integrating a few domains and then noticing that new primitives are needed for another new domain. The number of primitives may be finite, if for no other reason than that the number of concepts that people learn over a lifetime is finite. It remains to be determined how large the number is.
Even assuming that adding new domains to be integrated will inevitably lead to a requirement for *some* new primitives, there are practical reasons to try to identify some inventory of primitives that will handle a very large number of domains. Minimizing the need for supplementation of the foundation ontology, allows elements in domains linked to the foundation ontology to be specified in sufficient logical detail to be unambiguous and more easily related to other applications elements. Trying to identify such a good starting foundation ontology has been a primary goal of the COSMO ontology effort.
But having a complete set of primitives isn't necessary for the approach to be useful, since new primitives added for new applications will in general be irrelevant to pre-existing linked applications, which can continue to interoperate without the new primitives,, as they did before the addition.
As to specific primitives, I gather from reading that paper that ISO 15926-2 should contain a good sample of primitives. Is there an easy way to distinguish the primitives from the derived concepts?
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
>-----Original Message-----
>From: ontolo...@googlegroups.com [mailto:ontolog-
Thanks for the reference:
https://d2024367-a-62cb3a1a-s-sites.googlegroups.com/site/drmatthewwest/publications/IIDEASforPDTEurope.pdf?attachauth=ANoY7co59i8tiUPNl5Vb91v4doYA5Ybcq8tVzbNtouK1IkjGqN4ptD3prQrXg-yP1hdw5pCeIc4M5VJXXWEBBnHlfQOBAV8q9OWzQcy5z57yRS55-9t9lo3O62zPp0VPlXhQtH7ON-OoiYmJw3xplclxp5ZBNIcq6ydqcOPhtDpXgEJ9Dyz8bxemvHVkLPFIByi6GM7WftJufUZgeWhcBBYkZo4eZyLYDRfERdd7x5sonDWLbyKzKu0Sj6EZHWQ_NvQV3xaAAH4e&attredirects=0
That paper on IIDEAS is a good summary of the general tactic of integration via a foundation ontology ("integration model"). Is there a citation I can use (other than the URL link) to its published version?
The conclusion that the number of primitives is unlimited, however, does not follow from the experience of integrating a few domains and then noticing that new primitives are needed for another new domain. The number of primitives may be finite, if for no other reason than that the number of concepts that people learn over a lifetime is finite. It remains to be determined how large the number is.
Even assuming that adding new domains to be integrated will inevitably lead to a requirement for *some* new primitives, there are practical reasons to try to identify some inventory of primitives that will handle a very large number of domains. Minimizing the need for supplementation of the foundation ontology, allows elements in domains linked to the foundation ontology to be specified in sufficient logical detail to be unambiguous and more easily related to other applications elements. Trying to identify such a good starting foundation ontology has been a primary goal of the COSMO ontology effort.
But having a complete set of primitives isn't necessary for the approach to be useful, since new primitives added for new applications will in general be irrelevant to pre-existing linked applications, which can continue to interoperate without the new primitives,, as they did before the addition.
As to specific primitives, I gather from reading that paper that ISO 15926-2 should contain a good sample of primitives. Is there an easy way to distinguish the primitives from the derived concepts?
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
>-----Original Message-----
>From: ontolo...@googlegroups.com [mailto:ontolog-
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Matthew West
Jan 19, 2016, 5:39:46 AM1/19/16
to ontolo...@googlegroups.com
Dear Pat C,
Matthew,
Thanks for the reference:
https://d2024367-a-62cb3a1a-s-sites.googlegroups.com/site/drmatthewwest/publications/IIDEASforPDTEurope.pdf?attachauth=ANoY7co59i8tiUPNl5Vb91v4doYA5Ybcq8tVzbNtouK1IkjGqN4ptD3prQrXg-yP1hdw5pCeIc4M5VJXXWEBBnHlfQOBAV8q9OWzQcy5z57yRS55-9t9lo3O62zPp0VPlXhQtH7ON-OoiYmJw3xplclxp5ZBNIcq6ydqcOPhtDpXgEJ9Dyz8bxemvHVkLPFIByi6GM7WftJufUZgeWhcBBYkZo4eZyLYDRfERdd7x5sonDWLbyKzKu0Sj6EZHWQ_NvQV3xaAAH4e&attredirects=0
That paper on IIDEAS is a good summary of the general tactic of integration via a foundation ontology ("integration model"). Is there a citation I can use (other than the URL link) to its published version?
[MW>] This is the reference to the paper:
West, Matthew; Fowler, Julian The "IIDEAS" architecture and integration methodology for integrating enterprises PDT Days 2001 (2001)
Even assuming that adding new domains to be integrated will inevitably lead to a requirement for *some* new primitives, there are practical reasons to try to identify some inventory of primitives that will handle a very large number of domains. Minimizing the need for supplementation of the foundation ontology, allows elements in domains linked to the foundation ontology to be specified in sufficient logical detail to be unambiguous and more easily related to other applications elements.
[MW>] Yes, our experience with ISO 15926 is that there is a substantial body that once established is reused by most domains. However, each domain brings something distinctive.
But having a complete set of primitives isn't necessary for the approach to be useful, since new primitives added for new applications will in general be irrelevant to pre-existing linked applications, which can continue to interoperate without the new primitives,, as they did before the addition.
[MW>] If only that were true. One of the problems of integration is that many domains overlap to a large extent with other neighbouring domains. However, far from having the same concepts, they take a rather different perspective on what are essentially the same underlying things. This requires identifying an underlying view that supports each. This is what the picture of successive integrations in the paper illustrates.
As to specific primitives, I gather from reading that paper that ISO 15926-2 should contain a good sample of primitives. Is there an easy way to distinguish the primitives from the derived concepts?
[MW>] Nearly everything in ISO 15926 is a primitive. Only things that are specifically identified as an the intersection of other entity types or classes would be non-primitive.
Matthew,
Thanks for the reference:
https://d2024367-a-62cb3a1a-s-sites.googlegroups.com/site/drmatthewwest/publications/IIDEASforPDTEurope.pdf?attachauth=ANoY7co59i8tiUPNl5Vb91v4doYA5Ybcq8tVzbNtouK1IkjGqN4ptD3prQrXg-yP1hdw5pCeIc4M5VJXXWEBBnHlfQOBAV8q9OWzQcy5z57yRS55-9t9lo3O62zPp0VPlXhQtH7ON-OoiYmJw3xplclxp5ZBNIcq6ydqcOPhtDpXgEJ9Dyz8bxemvHVkLPFIByi6GM7WftJufUZgeWhcBBYkZo4eZyLYDRfERdd7x5sonDWLbyKzKu0Sj6EZHWQ_NvQV3xaAAH4e&attredirects=0
That paper on IIDEAS is a good summary of the general tactic of integration via a foundation ontology ("integration model"). Is there a citation I can use (other than the URL link) to its published version?
West, Matthew; Fowler, Julian The "IIDEAS" architecture and integration methodology for integrating enterprises PDT Days 2001 (2001)
The conclusion that the number of primitives is unlimited, however, does not follow from the experience of integrating a few domains and then noticing that new primitives are needed for another new domain. The number of primitives may be finite, if for no other reason than that the number of concepts that people learn over a lifetime is finite. It remains to be determined how large the number is.
[MW>] I agree it is likely the number is finite, but I would argue that you can never be certain you have found all of them. To say that you would have to be able to show that there was no other perspective or nothing new that could possibly be discovered or invented.
Even assuming that adding new domains to be integrated will inevitably lead to a requirement for *some* new primitives, there are practical reasons to try to identify some inventory of primitives that will handle a very large number of domains. Minimizing the need for supplementation of the foundation ontology, allows elements in domains linked to the foundation ontology to be specified in sufficient logical detail to be unambiguous and more easily related to other applications elements.
But having a complete set of primitives isn't necessary for the approach to be useful, since new primitives added for new applications will in general be irrelevant to pre-existing linked applications, which can continue to interoperate without the new primitives,, as they did before the addition.
As to specific primitives, I gather from reading that paper that ISO 15926-2 should contain a good sample of primitives. Is there an easy way to distinguish the primitives from the derived concepts?
John F Sowa
Jan 19, 2016, 12:59:50 PM1/19/16
to ontolo...@googlegroups.com
Dear Matthew and Pat C,
PC
or even the universe can store all of them. But when anyone sets an
upper limit, someone else finds an application that needs a larger one.
Do you remember when Bill Gates said that no personal computer would
ever need more than 640K bytes?
From
http://www.oxforddictionaries.com/words/how-many-words-are-there-in-the-english-language
> The Second Edition of the 20-volume Oxford English Dictionary contains
> full entries for 171,476 words in current use, and 47,156 obsolete
> words. To this may be added around 9,500 derivative words included as
> subentries. Over half of these words are nouns, about a quarter
> adjectives, and about a seventh verbs; the rest is made up of
> exclamations, conjunctions, prepositions, suffixes, etc. And these
> figures don't take account of entries with senses for different word
> classes (such as noun and adjective).
>
> This suggests that there are, at the very least, a quarter of a million
> distinct English words, excluding inflections, and words from technical
> and regional vocabulary not covered...
The last line is significant: there is an overwhelming amount of
technical vocabulary for every branch of science, engineering, finance,
law, business... and every department of every enterprise in any of
those fields has many local senses.
In fact, nearly every family has local words and word senses that
are rare or unknown outside the family. For example, 'heliotrope'
for "a cat that tries to stay warm in a moving shaft of sunshine."
For another example, see the dictionary of IBM Jargon,
http://www.comlay.net/ibmjarg.pdf
It grew informally for many years without official IBM approval.
See for example, the terms 'strategic' and 'counter-strategic'.
For 'strategic', I contributed the word sense "supported by managers
who had reached their level of incompetence." And for 'counter-
strategic', I contributed the sense "embarrassingly superior to
what is strategic." Although the dictionary itself was not official,
those definitions were officially purged, or at least weakened.
Note that the kinds of jargon can be highly cryptic. For example,
SVC13 means "to generate a large amount of waste." It's derived
from SuperVisor Call 13 for generating a memory dump in MVS.
These words are defined in terms of others. But any word can acquire
new "microsenses" at any occurrence. For examples, 'SVC13' or the
comic strip Calvin and Hobbs, which included
Any word in the English language can be verbed.
Verbing wierds language.
John
PC
>> The number of primitives may be finite, if for no other reason than
>> that the number of concepts that people learn over a lifetime is finite.
>
>> that the number of concepts that people learn over a lifetime is finite.
>
> [MW] I agree it is likely the number is finite, but I would argue that
> you can never be certain you have found all of them. To say that you
> would have to be able to show that there was no other perspective or
> nothing new that could possibly be discovered or invented.
When talking about infinity, think of the integers. No brain, computer,
> you can never be certain you have found all of them. To say that you
> would have to be able to show that there was no other perspective or
> nothing new that could possibly be discovered or invented.
or even the universe can store all of them. But when anyone sets an
upper limit, someone else finds an application that needs a larger one.
Do you remember when Bill Gates said that no personal computer would
ever need more than 640K bytes?
From
http://www.oxforddictionaries.com/words/how-many-words-are-there-in-the-english-language
> The Second Edition of the 20-volume Oxford English Dictionary contains
> full entries for 171,476 words in current use, and 47,156 obsolete
> words. To this may be added around 9,500 derivative words included as
> subentries. Over half of these words are nouns, about a quarter
> adjectives, and about a seventh verbs; the rest is made up of
> exclamations, conjunctions, prepositions, suffixes, etc. And these
> figures don't take account of entries with senses for different word
> classes (such as noun and adjective).
>
> This suggests that there are, at the very least, a quarter of a million
> distinct English words, excluding inflections, and words from technical
> and regional vocabulary not covered...
The last line is significant: there is an overwhelming amount of
technical vocabulary for every branch of science, engineering, finance,
law, business... and every department of every enterprise in any of
those fields has many local senses.
In fact, nearly every family has local words and word senses that
are rare or unknown outside the family. For example, 'heliotrope'
for "a cat that tries to stay warm in a moving shaft of sunshine."
For another example, see the dictionary of IBM Jargon,
http://www.comlay.net/ibmjarg.pdf
It grew informally for many years without official IBM approval.
See for example, the terms 'strategic' and 'counter-strategic'.
For 'strategic', I contributed the word sense "supported by managers
who had reached their level of incompetence." And for 'counter-
strategic', I contributed the sense "embarrassingly superior to
what is strategic." Although the dictionary itself was not official,
those definitions were officially purged, or at least weakened.
Note that the kinds of jargon can be highly cryptic. For example,
SVC13 means "to generate a large amount of waste." It's derived
from SuperVisor Call 13 for generating a memory dump in MVS.
These words are defined in terms of others. But any word can acquire
new "microsenses" at any occurrence. For examples, 'SVC13' or the
comic strip Calvin and Hobbs, which included
Any word in the English language can be verbed.
Verbing wierds language.
John
John Bottoms
Jan 19, 2016, 1:31:31 PM1/19/16
to ontolo...@googlegroups.com
On 1/19/2016 12:59 PM, John F Sowa
wrote:
Chomsky refers to "an infinite number of sentences". Because he is not a mathematician I'm not sure which sense of "infinite" he is using. Is his "sentence" merely a declarative statement, or could it be that he is indicating that the number of possible theses is infinite?
According to one website, "As of this year, the edition has defined 800,000 words and counting."
...and, "Estimated to be forty volumes by publication, the next OED [in 2034] would be twice the size of the 21,730-page second edition."
If that translates to number of words, we are going to have around 1.6M words at that time. The dictionary wars seem to have echoes.
JS: Any word in the English language can be verbed.
Yes,
And any verb can be nouned. Is the Super Bowl a thing? I've heard it can be "held".
And prepositions can be verbed: "We to'd and fro'd carrying the stuff out." - John Osborne: The many Lives of he Angry Young Man, an others. It apparently used to be a common term.
-John Bottoms
Chomsky refers to "an infinite number of sentences". Because he is not a mathematician I'm not sure which sense of "infinite" he is using. Is his "sentence" merely a declarative statement, or could it be that he is indicating that the number of possible theses is infinite?
According to one website, "As of this year, the edition has defined 800,000 words and counting."
...and, "Estimated to be forty volumes by publication, the next OED [in 2034] would be twice the size of the 21,730-page second edition."
http://www.mhpbooks.com/third-edition-of-the-oed-to-be-completed-in-2034/
If that translates to number of words, we are going to have around 1.6M words at that time. The dictionary wars seem to have echoes.
JS: Any word in the English language can be verbed.
Yes,
And any verb can be nouned. Is the Super Bowl a thing? I've heard it can be "held".
And prepositions can be verbed: "We to'd and fro'd carrying the stuff out." - John Osborne: The many Lives of he Angry Young Man, an others. It apparently used to be a common term.
-John Bottoms
Patrick Cassidy
Jan 19, 2016, 2:14:49 PM1/19/16
to ontolo...@googlegroups.com
Matthew,
Thanks again for the additional info. One point in particular intrigues me:
[PC] >> But having a complete set of primitives isn't necessary for the approach to
[MW] > If only that were true. One of the problems of integration is that
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different
>perspective on what are essentially the same underlying things. This requires
>identifying an underlying view that supports each. This is what the picture of
>successive integrations in the paper illustrates.
>
It would be very instructive to see one or more specific examples of case(s) where addition of a new primitive to a foundation ontology (FO) or integration model (IM) causes problems for pre-existing interoperating applications; or cases where different applications " take a rather different perspective on what are essentially the same underlying things" . This goes to the heart of interoperability. Cases such as that would indicate the absence of essential primitives in the earlier FO/IM, and the question I would derive from that is, just how large an inventory of primitives was used in the earlier, incomplete case. Specifics would be very helpful.
The preexisting applications could always just continue to interoperate among themselves by using the earlier version of the FO or IM, but I'm not sure if the preexisting interoperability could be harmed by mere addition of new primitives, unless some primitives of the older model were changed in the process. It's unclear why that would ever be necessary, unless one started with a very small set of primitives. As for Interoperability among older and newer applications, the kind of problem you indicate suggests that the older applications actually generated erroneous inferences that were corrected by the revised set of primitives (I believe there is only one physical reality). Specific examples are important for such cases.
That possibility is, in any case, the motivation for trying to find as complete as possible a set of primitives from the earliest time. And that's why I am curious about what primitives others have found necessary or even just potentially useful. How many primitives are there in ISO 15926? How often are new primitives required for integrating a new application?
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
>-----Original Message-----
>From: ontolo...@googlegroups.com [mailto:ontolog-
>fo...@googlegroups.com] On Behalf Of Matthew West
>Sent: Tuesday, January 19, 2016 5:40 AM
>To: ontolo...@googlegroups.com
>Subject: RE: [ontolog-forum] More about the lattice of all possible theories
>
>interoperate without the new primitives,, as they did before the addition..
Thanks again for the additional info. One point in particular intrigues me:
[PC] >> But having a complete set of primitives isn't necessary for the approach to
> >be useful, since new primitives added for new applications will in general be
> >irrelevant to pre-existing linked applications, which can continue to
>>interoperate without the new primitives,, as they did before the addition..
> >irrelevant to pre-existing linked applications, which can continue to
[MW] > If only that were true. One of the problems of integration is that
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different
>perspective on what are essentially the same underlying things. This requires
>identifying an underlying view that supports each. This is what the picture of
>successive integrations in the paper illustrates.
>
The preexisting applications could always just continue to interoperate among themselves by using the earlier version of the FO or IM, but I'm not sure if the preexisting interoperability could be harmed by mere addition of new primitives, unless some primitives of the older model were changed in the process. It's unclear why that would ever be necessary, unless one started with a very small set of primitives. As for Interoperability among older and newer applications, the kind of problem you indicate suggests that the older applications actually generated erroneous inferences that were corrected by the revised set of primitives (I believe there is only one physical reality). Specific examples are important for such cases.
That possibility is, in any case, the motivation for trying to find as complete as possible a set of primitives from the earliest time. And that's why I am curious about what primitives others have found necessary or even just potentially useful. How many primitives are there in ISO 15926? How often are new primitives required for integrating a new application?
PatC
Patrick Cassidy
MICRA Inc.
cas...@micra.com
1-908-561-3416
>-----Original Message-----
>From: ontolo...@googlegroups.com [mailto:ontolog-
>fo...@googlegroups.com] On Behalf Of Matthew West
>Sent: Tuesday, January 19, 2016 5:40 AM
>To: ontolo...@googlegroups.com
>Subject: RE: [ontolog-forum] More about the lattice of all possible theories
>
>[MW>] If only that were true. One of the problems of integration is that
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different
>perspective on what are essentially the same underlying things. This requires
>identifying an underlying view that supports each. This is what the picture of
>successive integrations in the paper illustrates.
>
> As to specific primitives, I gather from reading that paper that ISO 15926-2
>should contain a good sample of primitives. Is there an easy way to
>distinguish the primitives from the derived concepts?
>[MW>] Nearly everything in ISO 15926 is a primitive. Only things that are
>specifically identified as an the intersection of other entity types or classes
>would be non-primitive.
>Regards
>
>Matthew West
>Information Junction
>Mobile: +44 750 3385279
>Skype: dr.matthew.west
>matthe...@informationjunction.co.uk
>http://www.informationjunction.co.uk/
>https://www.matthew-west.org.uk/
>This email originates from Information Junction Ltd. Registered in England
>and Wales No. 6632177.
>Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire,
>SG6 2SU.
>
>
>
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different
>perspective on what are essentially the same underlying things. This requires
>identifying an underlying view that supports each. This is what the picture of
>successive integrations in the paper illustrates.
>
> As to specific primitives, I gather from reading that paper that ISO 15926-2
>should contain a good sample of primitives. Is there an easy way to
>distinguish the primitives from the derived concepts?
>[MW>] Nearly everything in ISO 15926 is a primitive. Only things that are
>specifically identified as an the intersection of other entity types or classes
>would be non-primitive.
>Regards
>
>Matthew West
>Information Junction
>Mobile: +44 750 3385279
>Skype: dr.matthew.west
>matthe...@informationjunction.co.uk
>http://www.informationjunction.co.uk/
>https://www.matthew-west.org.uk/
>This email originates from Information Junction Ltd. Registered in England
>and Wales No. 6632177.
>Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire,
>SG6 2SU.
>
>
>
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Patrick Cassidy
Jan 19, 2016, 2:26:59 PM1/19/16
to ontolo...@googlegroups.com
Response to a couple of points by John Sowa:
[JS] >When we add primitives to an ontology, we are always adding a new theory -
On the second case, of infinite sets of things, like the positive integers, of course they can be represented using a very small number of primitives, such as 0,1, and the addition operator.
[JS] >When we add primitives to an ontology, we are always adding a new theory -
>- i.e., those definitions and axioms that specify the new primitives. That new
>theory may be added in various ways:
>
> 1. Conjunction (AND operator) at the top level. This adds more
> information about more kinds of things that may be used together.
> Therefore, it enables sentences that use the ontology to talk
> about more kinds of things and processes and all possible
> combinations and interactions of them.
>
> 2. Disjunction (OR operator) at the top level. This adds more
> information as in #1, but users must make a choice to use
> one or the other.
>
> 3. Conjunction or disjunction at a lower level (AKA microtheory).
> This adds more information, but only to the branch of the
> ontology at the level immediately above it.
>
In the sense I am considering, new primitives are simply added (AND) to the existing set of primitives. Wherever logically inconsistent theories are used, in this view they must be represented by specified microtheories, but those microtheories should all be representable by the same set of primitives. I would be interested to see examples of inconsistent microtheories that cannot be logically specified using the same set of primitives. The simplest case would be assertions 'A' and 'not A' where A has the same interpretation in both theories. But, if the different microtheories could not be represented by the same set of primitives, how could anyone understand what they are both intended to mean?
>theory may be added in various ways:
>
> 1. Conjunction (AND operator) at the top level. This adds more
> information about more kinds of things that may be used together.
> Therefore, it enables sentences that use the ontology to talk
> about more kinds of things and processes and all possible
> combinations and interactions of them.
>
> 2. Disjunction (OR operator) at the top level. This adds more
> information as in #1, but users must make a choice to use
> one or the other.
>
> 3. Conjunction or disjunction at a lower level (AKA microtheory).
> This adds more information, but only to the branch of the
> ontology at the level immediately above it.
>
On the second case, of infinite sets of things, like the positive integers, of course they can be represented using a very small number of primitives, such as 0,1, and the addition operator.
Matthew West
Jan 19, 2016, 2:33:12 PM1/19/16
to ontolo...@googlegroups.com
Dear John,
Dear Matthew and Pat C,
PC
>> The number of primitives may be finite, if for no other reason than
>> that the number of concepts that people learn over a lifetime is finite.
>
> [MW] I agree it is likely the number is finite, but I would argue that
> you can never be certain you have found all of them. To say that you
> would have to be able to show that there was no other perspective or
> nothing new that could possibly be discovered or invented.
When talking about infinity, think of the integers. No brain, computer, or even the universe can store all of them. But when anyone sets an upper limit, someone else finds an application that needs a larger one.
[MW>] My reason for saying the number will be finite is that there will:
a) not be an infinite number of people that every exist, and
b) no person will come up with an infinite number of distinct new concepts
So the worst case is likely to be in the hundreds of billions. But never mind, add another 20 zeros if you like, you are still talking about relatively small numbers compared to infinity.
On the other hand, compared to the number of concepts we have access to today, probably in the tens of millions, that might as well be infinity.
Regards
Matthew West
Information Junction
Mobile: +44 750 3385279
Skype: dr.matthew.west
matthe...@informationjunction.co.uk
http://www.informationjunction.co.uk/
https://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire, SG6 2SU.
Dear Matthew and Pat C,
PC
>> The number of primitives may be finite, if for no other reason than
>> that the number of concepts that people learn over a lifetime is finite.
>
> [MW] I agree it is likely the number is finite, but I would argue that
> you can never be certain you have found all of them. To say that you
> would have to be able to show that there was no other perspective or
> nothing new that could possibly be discovered or invented.
When talking about infinity, think of the integers. No brain, computer, or even the universe can store all of them. But when anyone sets an upper limit, someone else finds an application that needs a larger one.
a) not be an infinite number of people that every exist, and
b) no person will come up with an infinite number of distinct new concepts
So the worst case is likely to be in the hundreds of billions. But never mind, add another 20 zeros if you like, you are still talking about relatively small numbers compared to infinity.
On the other hand, compared to the number of concepts we have access to today, probably in the tens of millions, that might as well be infinity.
Regards
Matthew West
Information Junction
Mobile: +44 750 3385279
Skype: dr.matthew.west
matthe...@informationjunction.co.uk
http://www.informationjunction.co.uk/
https://www.matthew-west.org.uk/
This email originates from Information Junction Ltd. Registered in England and Wales No. 6632177.
Registered office: 8 Ennismore Close, Letchworth Garden City, Hertfordshire, SG6 2SU.
Matthew West
Jan 19, 2016, 2:59:01 PM1/19/16
to ontolo...@googlegroups.com
Dear Pat C,
Matthew,
It's unclear why that would ever be necessary, unless one started with a very small set of primitives.
[MW>] We never start with more primitives than we think we need for the current purpose, and we can never know that we have all the primitives for any purpose.
As for Interoperability among older and newer applications, the kind of problem you indicate suggests that the older applications actually generated erroneous inferences that were corrected by the revised set of primitives (I believe there is only one physical reality). Specific examples are important for such cases.
[MW>] Well sometimes that might have been the case, but no, I'm assuming all systems are fit for purpose, whatever that was, just not necessarily fit for some other purpose.
That possibility is, in any case, the motivation for trying to find as complete as possible a set of primitives from the earliest time. And that's why I am curious about what primitives others have found necessary or even just potentially useful. How many primitives are there in ISO 15926? How often are new primitives required for integrating a new application?
[MW>] I don't know the number of primitives currently, probably approaching 100,000. It would be unusual for integrating a new application (of a new type) not to involve addition of new concepts. Someone was just talking to me the other day about adding something about financial instruments. I would expect hundreds to thousands of new concepts for that.
To view this discussion on the web visit https://groups.google.com/d/msgid/ontolog-forum/04b901d152ed%24a6e83e60%24f4b8bb20%24%40micra.com.
Matthew,
Thanks again for the additional info. One point in particular intrigues me:
[PC] >> But having a complete set of primitives isn't necessary for the approach to
> >be useful, since new primitives added for new applications will in
> >general be irrelevant to pre-existing linked applications, which can
> >continue to
>>interoperate without the new primitives,, as they did before the addition..
[MW] > If only that were true. One of the problems of integration is that
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different >perspective on what are essentially the same underlying things. This requires >identifying an underlying view that supports each. This is what the picture of >successive integrations in the paper illustrates.
>
It would be very instructive to see one or more specific examples of case(s) where addition of a new primitive to a foundation ontology (FO) or integration model (IM) causes problems for pre-existing interoperating applications; or cases where different applications " take a rather different perspective on what are essentially the same underlying things" . This goes to the heart of interoperability. Cases such as that would indicate the absence of essential primitives in the earlier FO/IM, and the question I would derive from that is, just how large an inventory of primitives was used in the earlier, incomplete case. Specifics would be very helpful.
[MW>] I retired from Shell many years ago now, so I do not have access to specifics.
[PC] >> But having a complete set of primitives isn't necessary for the approach to
> >be useful, since new primitives added for new applications will in
> >general be irrelevant to pre-existing linked applications, which can
> >continue to
>>interoperate without the new primitives,, as they did before the addition..
[MW] > If only that were true. One of the problems of integration is that
>many domains overlap to a large extent with other neighbouring domains.
>However, far from having the same concepts, they take a rather different >perspective on what are essentially the same underlying things. This requires >identifying an underlying view that supports each. This is what the picture of >successive integrations in the paper illustrates.
>
It would be very instructive to see one or more specific examples of case(s) where addition of a new primitive to a foundation ontology (FO) or integration model (IM) causes problems for pre-existing interoperating applications; or cases where different applications " take a rather different perspective on what are essentially the same underlying things" . This goes to the heart of interoperability. Cases such as that would indicate the absence of essential primitives in the earlier FO/IM, and the question I would derive from that is, just how large an inventory of primitives was used in the earlier, incomplete case. Specifics would be very helpful.
The preexisting applications could always just continue to interoperate among themselves by using the earlier version of the FO or IM, but I'm not sure if the preexisting interoperability could be harmed by mere addition of new primitives, unless some primitives of the older model were changed in the process.
[MW>] Indeed, I did not mean to suggest otherwise. However, concepts in those domains necessary for that purpose are not necessarily sufficient for another overlapping domain in the area of overlap. It is usually a matter of the level of detail a classification scheme is required at, or perhaps an additional cross-cutting classification scheme of the same things for a different purpose, where the intersections need to be identified to cut the original data to be fit for the new purpose.
It's unclear why that would ever be necessary, unless one started with a very small set of primitives.
As for Interoperability among older and newer applications, the kind of problem you indicate suggests that the older applications actually generated erroneous inferences that were corrected by the revised set of primitives (I believe there is only one physical reality). Specific examples are important for such cases.
That possibility is, in any case, the motivation for trying to find as complete as possible a set of primitives from the earliest time. And that's why I am curious about what primitives others have found necessary or even just potentially useful. How many primitives are there in ISO 15926? How often are new primitives required for integrating a new application?
John F Sowa
Jan 20, 2016, 2:30:36 AM1/20/16
to ontolo...@googlegroups.com
Dear Matthew, Pat C, and Bruce,
Matthew
about the lattice of all possible theories:
1. Assume Common Logic as the version of logic used to specify the
theories. CL allows any Unicode character string as a permissible
name.
2. Any name N in a theory T may be considered non-primitive in T
iff every occurrence of N may be replaced by some expression X
of T in which the name N does not occur.
3. But the name N, which may be a primitive in some theories of the
lattice, may be non-primitive (i.e., replaceable) in other theories.
4. If there is no upper bound for the length of names, the lattice
would have infinitely many primitives and non-primitives. With
some reasonable upper bound (say 256 characters), there would be
more than enough names for most practical purposes.
Bruce
> My own instinct tends to the group of meanings associated with the
> Wikipedia section on primitives in computer science... "A primitive is
> the smallest 'unit of processing' available to a programmer of a given
> machine, or can be an atomic element of an expression in a language."
Pat
> a “primitive” is an ontology element (type, relation) whose intended
> meaning cannot be logically specified as a combination of other
> elements in the ontology... What one may use as a “primitive” in
> a given ontology may vary from what is used in other ontologies.
Those definitions are compatible with the lattice of theories and
the definition of primitive and non-primitive in #2 and #3 above.
John
Matthew
> compared to the number of concepts we have access to today,
> [the number of primitives is] probably in the tens of millions,
> that might as well be infinity.
Pat
> In the sense I am considering, new primitives are simply added (AND)
> to the existing set of primitives. Wherever logically inconsistent
> theories are used, in this view they must be represented by specified
> microtheories, but those microtheories should all be representable
> by the same set of primitives.
Both of those comments are compatible with what I have been saying
> to the existing set of primitives. Wherever logically inconsistent
> theories are used, in this view they must be represented by specified
> microtheories, but those microtheories should all be representable
> by the same set of primitives.
about the lattice of all possible theories:
1. Assume Common Logic as the version of logic used to specify the
theories. CL allows any Unicode character string as a permissible
name.
2. Any name N in a theory T may be considered non-primitive in T
iff every occurrence of N may be replaced by some expression X
of T in which the name N does not occur.
3. But the name N, which may be a primitive in some theories of the
lattice, may be non-primitive (i.e., replaceable) in other theories.
4. If there is no upper bound for the length of names, the lattice
would have infinitely many primitives and non-primitives. With
some reasonable upper bound (say 256 characters), there would be
more than enough names for most practical purposes.
Bruce
> My own instinct tends to the group of meanings associated with the
> Wikipedia section on primitives in computer science... "A primitive is
> the smallest 'unit of processing' available to a programmer of a given
> machine, or can be an atomic element of an expression in a language."
Pat
> a “primitive” is an ontology element (type, relation) whose intended
> meaning cannot be logically specified as a combination of other
> elements in the ontology... What one may use as a “primitive” in
> a given ontology may vary from what is used in other ontologies.
Those definitions are compatible with the lattice of theories and
the definition of primitive and non-primitive in #2 and #3 above.
John
Christopher Menzel
Jan 20, 2016, 12:57:33 PM1/20/16
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On 17 Jan 2016, at 1:47 PM, Patrick Cassidy <p...@micra.com> wrote:
It appears that John is describing the mathematical set-theoretic sense of "general" here.
It seems from John's definition that the most "general" theory would be something like:
"something exists"
That's exactly right. "Something exists" — usually formalized as ∃x∀y y=x — is a logical truth of first-order logic (with identity) and, indeed, first-order logic, which has no (non-logical) axioms, is the most general (first-order) theory; it holds in all domains (ignoring issues in quantum mechanics etc that suggest the need for non-classical logics). As soon as you add a non-logical axiom, the theory is no longer applicable to domains where that axiom might not be true.
I think that practical knowledge engineers consider "general" to mean "generally useful" in which case an ontology with more primitives would be one that is more generally useful, i.e. "general". It covers more cases, and, with proper editing, can be made as small and efficient as is required for any specific application.
I really doubt this is a widespread meaning of "general" within knowledge engineering but be that as it may, it just isn't correct, unless you are only talking about the addition of unaxiomatized (hence, meaningless) primitives to the lexicon of an ontology. Because as soon as you axiomatize a term or predicate, unless the axiom is logically trivial, your ontology, as a straightforward logical matter, covers fewer cases, not more. If I'm axiomatizing a domain where there are no flightless birds I might well add "All birds fly" as an axiom for the predicate "Birds". But my ontology is now useless in Antarctica.
-chris
Gregg Reynolds
Jan 20, 2016, 5:22:40 PM1/20/16
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On Jan 20, 2016 11:57 AM, "Christopher Menzel" <chris....@gmail.com> wrote:
>
> On 17 Jan 2016, at 1:47 PM, Patrick Cassidy <p...@micra.com> wrote:
>>
>> It appears that John is describing the mathematical set-theoretic sense of "general" here.
>> It seems from John's definition that the most "general" theory would be something like:
>>
>> "something exists"
>
>
> That's exactly right. "Something exists" — usually formalized as ∃x∀y y=x
Doesn't that mean "exactly one thing exists"? Not quite the same as "something exists", I think.
Gregg
Christopher Menzel
Jan 22, 2016, 4:41:24 PM1/22/16
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On 20 Jan 2016, at 4:22 PM, Gregg Reynolds <d...@mobileink.com> wrote:
On Jan 20, 2016 11:57 AM, "Christopher Menzel" <chris....@gmail.com> wrote:> On 17 Jan 2016, at 1:47 PM, Patrick Cassidy <p...@micra.com> wrote:
>>
>> It appears that John is describing the mathematical set-theoretic sense of "general" here.
>> It seems from John's definition that the most "general" theory would be something like:
>>
>> "something exists"
>
>
> That's exactly right. "Something exists" — usually formalized as ∃x∀y y=xDoesn't that mean "exactly one thing exists"?
DOH! Of course it does. :-/ What I meant to write was "∃x∃y y=x". This is of course equivalent to simply "∃x x=x" but I prefer it to the latter because one usually expresses "x exists" as "∃y y=x" — i.e., x is identical to something — and so something exists is then naturally expressed as the existential generalization of that.
Sorry, I hope no one was confused by the error .
-chris
Gregg Reynolds
Jan 23, 2016, 2:34:40 PM1/23/16
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Hmm. I'm not sure that really buys us anything. Your last formula won't do since it leaves x unbound. The first two formulae are problematic for various reasons, but the main thing is that FOL quantificational propositions are only intelligible on the presupposition that there is a domain or universe of quantification - emphasis on "there is". So the logical formalism itself depends on extra-logical, ontological presuppositions. In other words, it doesn't matter what P is in \Exists x.P - you can't treat it as a meaningful proposition without making an implicit antecedent commitment to the existence of at least one universe of quantification. Even if it's false, something must exist, otherwise it could not be false (or true).
But even that does not capture "something exists", as far as I can see. Maybe the universe of quantification is the only thing that exists. I can't see how to get to "something exists" without introducing modalities - e.g. one thing exists, but possibly others things exist too. And even if it were expressible in FOL, it would not count as a logical truth, since it's expression would depend on extra-logical concepts.
Not trolling, btw, I just find the subtleties of logic loads of fun, and virtually endless.
Gregg
Christopher Menzel
Jan 23, 2016, 9:20:03 PM1/23/16
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On 23 Jan 2016, at 1:34 PM, Gregg Reynolds <d...@mobileink.com> wrote:
On Jan 22, 2016 3:41 PM, "Christopher Menzel" <chris....@gmail.com> wrote:
>
> On 20 Jan 2016, at 4:22 PM, Gregg Reynolds <d...@mobileink.com> wrote:
>>
>> On Jan 20, 2016 11:57 AM, "Christopher Menzel" <chris....@gmail.com> wrote:
>>
>> > On 17 Jan 2016, at 1:47 PM, Patrick Cassidy <p...@micra.com> wrote:
>> >>
>> >> It appears that John is describing the mathematical set-theoretic sense of "general" here.
>> >> It seems from John's definition that the most "general" theory would be something like:
>> >>
>> >> "something exists"
>> >
>> >
>> > That's exactly right. "Something exists" — usually formalized as ∃x∀y y=x
>>
>> Doesn't that mean "exactly one thing exists"?
>
> DOH! Of course it does. :-/ What I meant to write was "∃x∃y y=x". This is of course equivalent to simply "∃x x=x" but I prefer it to the latter because one usually expresses "x exists" as "∃y y=x" — i.e., x is identical to something — and so something exists is then naturally expressed as the existential generalization of that.
>
Hmm. I'm not sure that really buys us anything.
It's not supposed to "buy us anything" it's simply a standard way of expressing that something exists in first-order logic.
Your last formula won't do since it leaves x unbound.
It won't do as what? It is, as I said, an absolutely standard way of expressing that a given individual x exists. It does exceedingly well at that task — variables can take values, right? But if you are unhappy with unbound variables (despite the the fact that they are used ubiquitously in logic, philosophy, and knowledge engineering) then let me rephrase my claim: For any name α, "∃y y=α" expresses that the denotation of α exists. For example, let "b" denote Obama. Then "∃y y=b" expresses that Obama exists. M'k? No free variables.
The first two formulae are problematic for various reasons,
Sorry, they're not. They are utterly unproblematic.
but the main thing is that FOL quantificational propositions are only intelligible on the presupposition that there is a domain or universe of quantification - emphasis on "there is".
I'm not sure what it is you are trying to say here. Near as I can tell, you are saying that the sentences of a first-order language need to be interpreted to have any meaning. That is certainly true, but mundane — part of what makes first-order logic first-order logic is that it has a semantics, or model theory, that defines the notion of an interpretation for first-order languages. And indeed, in the semantics of first-order logic, every interpretation of a first-order language specifies a nonempty set to serve as the range of the quantifiers. And relative to that semantics, once again, "∃x∃y y=x" will express (under every interpretation) that something (in the domain of the interpretation) exists, i.e., that something is identical to something.
Now, there are of course other semantic theories — notably, so-called substitutional semantics — for first-order languages under which "∃x∃y y=x" might not have that interpretation. Perhaps that point is lurking in your comment above. That point is entirely true, but entirely irrelevant to my post.
So the logical formalism itself depends on extra-logical, ontological presuppositions.
The "logical formalism" in question — by which I take it you mean the formulas of a first-order language — depends on no such thing. The sentences of a first-order language are simply the output of a well-defined syntax. Of course, for the sentences in a first-order language to express, or mean, one thing or another may well depend on ontological presuppositions. If I want "∃xEx" to express that there are electrons, then in order for it to be true (in my "intended" interpretation), there do indeed have to be electrons. If I want "∃x∃y y=x" to express that something exists, then in order for it to be true (in a given interpretation) something has to exist (and, again, something will, in any interpretation). If this is your point, it is entirely correct and well-understood. But again, it simply has no bearing on my post.
In other words, it doesn't matter what P is in \Exists x.P - you can't treat it as a meaningful proposition without making an implicit antecedent commitment to the existence of at least one universe of quantification.
You seem to be losing sight of the issue. My claim in my post was that "∃x∃y x=y" expresses that something exists in first-order logic. (Granted, I didn't specify that I was assuming first-order logic explicitly but that has been a presupposition of pretty much all discussion in this forum.) "∃x∃y x=y" is a "meaningful proposition" in first-order logic because, once again, part of the semantics of first-order logic is that the domain specified for the quantifiers in any interpretation is nonempty. This guarantees that "∃x∃y x=y" expresses that something exists under any interpretation. If you wish to object to the standard semantics of first-order logic, have at it. Perhaps there is substance to your objections. But your objections are another topic entirely and are completely irrelevant to the simple and utterly uncontroversial claim in my post.
But even that does not capture "something exists", as far as I can see. Maybe the universe of quantification is the only thing that exists.
I can make absolutely no sense of that claim. You, for example, I'm guessing, are not a universe of quantification (since you are not a set).
I can't see how to get to "something exists" without introducing modalities - e.g. one thing exists, but possibly others things exist too.
The first conjunct of your claim "one thing exists" — the non-modal part — entails "something exists" so I don't where you're going here at all; the modality adds nothing to that claim.
And even if it were expressible in FOL, it would not count as a logical truth, since it's expression would depend on extra-logical concepts.
The proposition "one thing exists but possibly other things exist, too" is of course not expressible in FOL because it involves a modal operator. However, in first-order modal logic the modal operators are logical, not extra-logical.
Not trolling, btw, I just find the subtleties of logic loads of fun, ...
Then I hope you've enjoyed the above. I went on quite a lot longer than I'd intended and won't be commenting further in this thread. That is not an attempt to have the last word, just letting you know I've said all I have to say on this matter.
Regards,
-chris
Michael Brunnbauer
Jan 24, 2016, 5:35:36 AM1/24/16
to ontolo...@googlegroups.com
Hello Gregg,
there should be lots of descriptions of first-order logic that answer all
your questions and are accessible to the layman. The one I can recommend
wholeheartedly is this (translated from German):
http://www.springer.com/de/book/9783540058199
Unfortunately, it is expensive despite its age. Maybe someone can point out
a cheap or free alternative?
You could also try the Wikipedia article:
https://en.wikipedia.org/wiki/First-order_logic
The problem of empty domains is explicitly mentioned there:
https://en.wikipedia.org/wiki/First-order_logic#Empty_domains
Regards,
Michael Brunnbauer
On Sat, Jan 23, 2016 at 01:34:38PM -0600, Gregg Reynolds wrote:
> On Jan 22, 2016 3:41 PM, "Christopher Menzel" <chris....@gmail.com>
> wrote:
> >
> > On 20 Jan 2016, at 4:22 PM, Gregg Reynolds <d...@mobileink.com> wrote:
> >>
> >> On Jan 20, 2016 11:57 AM, "Christopher Menzel" <chris....@gmail.com>
> wrote:
> >>
> >> > On 17 Jan 2016, at 1:47 PM, Patrick Cassidy <p...@micra.com> wrote:
> >> >>
> >> >> It appears that John is describing the mathematical set-theoretic
> sense of "general" here.
> >> >> It seems from John's definition that the most "general" theory would
> be something like:
> >> >>
> >> >> "something exists"
> >> >
> >> >
> y=x
> >>
> >> Doesn't that mean "exactly one thing exists"?
> >
> > DOH! Of course it does. :-/ What I meant to write was "???x???y y=x". This is
> >>
> >> Doesn't that mean "exactly one thing exists"?
> >
> of course equivalent to simply "???x x=x" but I prefer it to the latter
> because one usually expresses "x exists" as "???y y=x" ??? i.e., x is identical
> to something ??? and so something exists is then naturally expressed as the
> existential generalization of that.
> >
>
> Hmm. I'm not sure that really buys us anything. Your last formula won't
> do since it leaves x unbound. The first two formulae are problematic for
> various reasons, but the main thing is that FOL quantificational
> propositions are only intelligible on the presupposition that there is a
> domain or universe of quantification - emphasis on "there is". So the
> logical formalism itself depends on extra-logical, ontological
> presuppositions. In other words, it doesn't matter what P is in \Exists
> x.P - you can't treat it as a meaningful proposition without making an
> implicit antecedent commitment to the existence of at least one universe of
> quantification. Even if it's false, something must exist, otherwise it
> could not be false (or true).
>
> But even that does not capture "something exists", as far as I can see.
> Maybe the universe of quantification is the only thing that exists. I
> can't see how to get to "something exists" without introducing modalities -
> e.g. one thing exists, but possibly others things exist too. And even if
> it were expressible in FOL, it would not count as a logical truth, since
> it's expression would depend on extra-logical concepts.
>
> Not trolling, btw, I just find the subtleties of logic loads of fun, and
> virtually endless.
>
> Gregg
>
> >
>
> Hmm. I'm not sure that really buys us anything. Your last formula won't
> do since it leaves x unbound. The first two formulae are problematic for
> various reasons, but the main thing is that FOL quantificational
> propositions are only intelligible on the presupposition that there is a
> domain or universe of quantification - emphasis on "there is". So the
> logical formalism itself depends on extra-logical, ontological
> presuppositions. In other words, it doesn't matter what P is in \Exists
> x.P - you can't treat it as a meaningful proposition without making an
> implicit antecedent commitment to the existence of at least one universe of
> quantification. Even if it's false, something must exist, otherwise it
> could not be false (or true).
>
> But even that does not capture "something exists", as far as I can see.
> Maybe the universe of quantification is the only thing that exists. I
> can't see how to get to "something exists" without introducing modalities -
> e.g. one thing exists, but possibly others things exist too. And even if
> it were expressible in FOL, it would not count as a logical truth, since
> it's expression would depend on extra-logical concepts.
>
> Not trolling, btw, I just find the subtleties of logic loads of fun, and
> virtually endless.
>
> Gregg
>
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Till Mossakowski
Jan 24, 2016, 6:16:24 AM1/24/16
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John F Sowa
Jan 24, 2016, 9:08:11 AM1/24/16
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Thanks for the reference.
That pointer also leads to a collection of various free and
open text books on logic, ranging from introductory to advanced:
https://github.com/OpenLogicProject/OpenLogic/wiki/Other-Logic-Textbooks
Re licensing:
> "Free" means: can be downloaded for free. "Open" means: available
> under an open license, i.e., modification and distribution is
> permitted. "Open source" means the source files from which PDFs
> can be produced are available.
For a short (about 30 pages) summary of terminology and definitions
on math and logic, I posted Appendix A from my 1984 book, which I
revised for my 2000 book, and continue to revise from time to time:
http://www.jfsowa.com/logic/math.htm
Over the past 16 years, it's had about 209,000 downloads.
John
That pointer also leads to a collection of various free and
open text books on logic, ranging from introductory to advanced:
https://github.com/OpenLogicProject/OpenLogic/wiki/Other-Logic-Textbooks
Re licensing:
> "Free" means: can be downloaded for free. "Open" means: available
> under an open license, i.e., modification and distribution is
> permitted. "Open source" means the source files from which PDFs
> can be produced are available.
For a short (about 30 pages) summary of terminology and definitions
on math and logic, I posted Appendix A from my 1984 book, which I
revised for my 2000 book, and continue to revise from time to time:
http://www.jfsowa.com/logic/math.htm
Over the past 16 years, it's had about 209,000 downloads.
John
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