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Alex,
> my short ontology definition: formal theory
plus finite model :-)
Three problems with that definition:
1. There are infinitely many formal theories that have finite models, but nobody would consider them to be ontologies. For example, the integers modulo N for any N>2.
2. Integers are useful components of almost all ontologies, and they require an infinite model. The fact that there is no upper bound is a convenience, not a limitation.
3. And finally, many (most?) ontologies that need to interoperate with independently designed systems will have aspects that don't have a precise mapping to the other. WordNet definitions, for example, are vague. But WN is frequently used for mapping between ontologies.
John
Alex,
> my short ontology definition: formal theory plus finite model :-)Three problems with that definition:
1. There are infinitely many formal theories that have finite models, but nobody would consider them to be ontologies. For example, the integers modulo N for any N>2.
2. Integers are useful components of almost all ontologies, and they require an infinite model. The fact that there is no upper bound is a convenience, not a limitation.
3. And finally, many (most?) ontologies that need to interoperate with independently designed systems will have aspects that don't have a precise mapping to the other. WordNet definitions, for example, are vague. But WN is frequently used for mapping between ontologies.
John
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Alex:This is just our first rough cut at this topic.Your ontology definition should play a major role in the next version of this report.Your "ontology definition: formal theory plus finite model"Is very abstract and open. This definition provides a good basis for exploring different ontology types.
Questions your definition may help answer:What is the most minimal form of an ontology?
Can a specification for a collocation of "composable" ontology types be created?
What type of formal theories are acceptable?
What is the range of acceptable finite models?
What requirements are associated with a finite model?
The focus of the next version of this document is:What constitutes a "minimal ontology?"
How to compose two or more minimal ontology systems into a more complete individual ontology.
This is just the start.
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Alex,
If you use the word 'formal' in your definition, you're making a claim that your definition states the necessary and sufficient conditions for using the word 'ontology' correctly. My examples show that the following definition is neither necessary nor sufficient. Most things that people call ontologies do not conform to that definition:
> my short ontology definition: formal theory plus finite
model :-)
If you like, you could state that as a recommendation.
John
WordNet definitions, for example, are vague. But WN is frequently used for mapping between ontologies.
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Joe and Mary,
Thank you for nice initial system analysis of the contemporary situation with ontology definitions and beings.
Please look at my notes to your sentences.
"In other cases, complex concepts, knowledge structures, and relationships must be arranged in a manner that interfaces among humans, software agents and other ontology processes and software agents."
=The best internal representation is a formal theory. The structure of formal theory is simple: primary constants, predicates, and functions; axioms; definitions of secondary constants, predicates, and functions; theorems and it's proofing.
By the way, the Reasoner like DL-reasoner should be mentioned somehow as it is a way to get new knowledge from ontology, beginning from inconsistency;-)
"At the most fundamental level, an ontology is a catalog of the types of things that exist in any specified domain."
=Let me say it's a formal theory.
"The lack of understanding in the domain space can be associated with the ontology types or the relationships between the types in the catalog."
=But tell me the domain where we do not have scientists and therefore informal theory;-)
"A more formal ontology may include formal concept descriptions, classification templates, class attributes, class relationships, domain constraints, rules, and axioms."
=Let me put formal theory terms after | to your text to compare:
A more formal ontology|theory may include: formal concept descriptions|definitions, classification templates|?, class attributes|functions, class relationships|predicates, domain constraints|axioms, rules|derivation? and axioms.
"Each ART configuration has the capability to represent an independent model of the domain knowledge."
=This is one more way to create ontology - is there any example of ontology on ART?
"[Warfield, 1994] work in the area of the ‘science of generic design’ used binary matrices to encode domain knowledge. Charles Sanders Pierce's work in the area of the logic of relatives can be represented using binary matrices as shown by Jon Awbrey:
[ https://oeis.org/wiki/Peirce%27s_1870_Logic_Of_Relatives_%E2%80%A2_Part_1 ]."
=A matrix is a form to represent finite structure — binary relation.
If you use a relation of relations then welcome to HOL:-)
"An ontology is a very loosely defined term."
=This is where we turn to the ontological definition: today ontology is a random mixture of sentences from formal theory together with sentences of the finite model of this theory:-)
The nearest approximation to math ontology may be microtheories of Cyc. But this should be studied. The problem with finite structure is mostly logical as technically any finite structure may be embedded in the theory if we assign the constant to every finite structure element:-) In my plan to show how to embed graph, the finest finite structure, to OWL2 ontology:-)
Alex
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