FA as a TAG (Was: One cannot refer to inner nodes in Lojban PEG)

[Jacob Errington]

I'm making a separate thread out of this because I'm going on a tangent here.

On 7 April 2015 at 15:04, <co...@ccil.org> wrote:

Terms can have FA or tags equally well, but we don't want to merge
FA with BAI generally, to avoid things like "se fa" and ".i fa bo",
which are nonsense.

I agree that {se fa} has no clear interpretation upon first examination. However, {.i fa bo} can be interpreted like any other {.i TAG bo} construct.

.i broda .i TAG bo brode -> .i broda TAG lo su'u brode

Hence,

.i broda .i fa bo brode -> .i broda fa lo su'u brode

This provides us with another way to do essentially what {la'e di'e} does. For instance,

.i mi pu pensi la'e di'e .i lo mi bruna cu cmalu mutce -> .i mi pu pensi .ifebo lo mi bruna cu cmalu mutce

I was thinking about this: my brother is very short.

Taking this idea to the extreme, we can conceive of a somewhat silly higher-order predicate -- call it {brodrfV} for now -- whose x1 is an arbitrary sumti and whose x2 is a nullary predicate supplied with than fV having the value of the x1. We can define {brodrfV} with the following statement.

.i ko'a brodrfV lo du'u broda <=> broda fV ko'a

We can derive some obvious results from this statement.

.i lo brodrfV be lo du'u fV ko'a broda === ko'a

.i fV ko'a broda === .i fi'o brodrfV ko'a broda

This gives us a way to pick out sumti from du'u-abstractions, an otherwise arduous task for the fancylojban programmer/speaker.

Furthermore, this gives us a way to interpret {se fV}. Since {fV === fi'o brodrfV}, we have {se fV === fi'o se brodrfV}.

For instance

.i lo mi bruna cu cmalu mutce se fe lo du'u mi pu pensi -> mi pu pensi lo du'u lo mi bruna cu cmalu mutce

I've basically hijacked FA to recreate bridi relative clauses.

I'm sure there're plenty of holes in this idea since I cooked it up in just a few minutes. Feel free to come up with weird cases and we can examine them.

Do I want this to be a feature of standard Lojban? Not necessarily. Do I think it's a cool idea? Sure. I hope you do too :)

.i mi'e la tsani mu'o

[Jorge Llambías]

On Tue, Apr 7, 2015 at 6:52 PM, Jacob Errington <nict...@gmail.com> wrote:

I'm making a separate thread out of this because I'm going on a tangent here.

On 7 April 2015 at 15:04, <co...@ccil.org> wrote:

Terms can have FA or tags equally well, but we don't want to merge
FA with BAI generally, to avoid things like "se fa" and ".i fa bo",
which are nonsense.

I agree that {se fa} has no clear interpretation upon first examination. However, {.i fa bo} can be interpreted like any other {.i TAG bo} construct.

.i broda .i TAG bo brode -> .i broda TAG lo su'u brode

Hence,

.i broda .i fa bo brode -> .i broda fa lo su'u brode

This provides us with another way to do essentially what {la'e di'e} does. For instance,

.i mi pu pensi la'e di'e .i lo mi bruna cu cmalu mutce -> .i mi pu pensi .ifebo lo mi bruna cu cmalu mutce

I was thinking about this: my brother is very short.

There is a certain formal analogy, which may justify such use, but semantically the tag and the FA cases are different. 

Taking this idea to the extreme, we can conceive of a somewhat silly higher-order predicate -- call it {brodrfV} for now -- whose x1 is an arbitrary sumti and whose x2 is a nullary predicate supplied with than fV having the value of the x1. We can define {brodrfV} with the following statement.

.i ko'a brodrfV lo du'u broda <=> broda fV ko'a

I'm not sure that's a valid definition. If "ko'e du'u ko'a broda" is true, can I then say that "ko'a brodrfa ko'e" is also true? And what if I now re-express ko'e with an expression that doesn't use "ko'a" as the first argument, is it still true that "ko'a brodrfa ko'e"? The problem is that propositions ("nullary predicates") don't have arguments. Given a proposition p, it is not well defined what its brodrfa should be, its brodrfa seems to be a function of the expression we choose to express the proposition. ma brodrfa lo du'u no da klama? ma brodrfa lo du'u na ku ro da klama? 

We can derive some obvious results from this statement.

.i lo brodrfV be lo du'u fV ko'a broda === ko'a

.i fV ko'a broda === .i fi'o brodrfV ko'a broda

This gives us a way to pick out sumti from du'u-abstractions, an otherwise arduous task for the fancylojban programmer/speaker.

It should be an arduous task because du'u-abstractions don't really have sumti. It's the predicates used to construct du'u-abstractions that have sumti, and the same du'u-abstraction could be constructed with different predicates which could have different arguments. 

Furthermore, this gives us a way to interpret {se fV}. Since {fV === fi'o brodrfV}, we have {se fV === fi'o se brodrfV}.

For instance

.i lo mi bruna cu cmalu mutce se fe lo du'u mi pu pensi -> mi pu pensi lo du'u lo mi bruna cu cmalu mutce

I've basically hijacked FA to recreate bridi relative clauses.

I'm sure there're plenty of holes in this idea since I cooked it up in just a few minutes. Feel free to come up with weird cases and we can examine them.

It may be workable, but I wouldn't explain it in terms of brodrfV. It would have to be explained in terms of the words being used, not just in terms of their meanings.

Do I want this to be a feature of standard Lojban? Not necessarily. Do I think it's a cool idea? Sure. I hope you do too :)

 

ie zabna sidbo

mu'o mi'e xorxes

[guskant]

la xorxes has already replied while I am preparing my response, but this may make the problem clearer.

I may agree the point of your idea, but have some objections.

Le mercredi 8 avril 2015 06:52:23 UTC+9, Jacob Errington a écrit :

I'm making a separate thread out of this because I'm going on a tangent here.

On 7 April 2015 at 15:04, <co...@ccil.org> wrote:

Terms can have FA or tags equally well, but we don't want to merge
FA with BAI generally, to avoid things like "se fa" and ".i fa bo",
which are nonsense.

I agree that {se fa} has no clear interpretation upon first examination. However, {.i fa bo} can be interpreted like any other {.i TAG bo} construct.

.i broda .i TAG bo brode -> .i broda TAG lo su'u brode

Hence,

.i broda .i fa bo brode -> .i broda fa lo su'u brode

This provides us with another way to do essentially what {la'e di'e} does. For instance,

.i mi pu pensi la'e di'e .i lo mi bruna cu cmalu mutce -> .i mi pu pensi .ifebo lo mi bruna cu cmalu mutce

I was thinking about this: my brother is very short.

Taking this idea to the extreme, we can conceive of a somewhat silly higher-order predicate -- call it {brodrfV} for now -- whose x1 is an arbitrary sumti and whose x2 is a nullary predicate supplied with than fV having the value of the x1. We can define {brodrfV} with the following statement.

.i ko'a brodrfV lo du'u broda <=> broda fV ko'a

Your idea seems not a kind of higher-order logic, but simply extraction of an argument from a bridi. Higher-order logic deals with both predicates and arguments in its universe of discourse, while your idea does not seem requiring a universe of discourse in the clause composing x2 of {brodrfV}.

Therefore, {du'u} should be replaced with {ka}, because a bridi in {du'u}-clause has a truth value based on its own universe of discourse, which is generally distinguished from the universe of discourse of the outer bridi. On the other hand, a bridi in {ka}-clause is an open sentence with a free variable {ce'u}. A bridi in {si'o}-clause is also an open sentence with all variables are free, but not suitable for the current topic in which only one argument is extracted by {brodrfV}.

The definition should be then :

.i ko'a brodrfV lo ka fV ce'u broda <=> broda fV ko'a

 

We can derive some obvious results from this statement.

.i lo brodrfV be lo du'u fV ko'a broda === ko'a

.i fV ko'a broda === .i fi'o brodrfV ko'a broda

Based on the same idea, the first line should be :

.i lo brodrfV be lo ka fV ce'u broda = ko'a

which denotes a substitution of a constant satisfying x1 of {brodrfV} by {ko'a}, not a result derived from the definition of {brodrfV}.

mu'o

[Jorge Llambías]

On Tue, Apr 7, 2015 at 10:02 PM, guskant <gusni...@gmail.com> wrote:

Le mercredi 8 avril 2015 06:52:23 UTC+9, Jacob Errington a écrit :

.i ko'a brodrfV lo du'u broda <=> broda fV ko'a

The definition should be then :

.i ko'a brodrfV lo ka fV ce'u broda <=> broda fV ko'a

I don't know. Is it different from "ckaji"? 

.i ca'e ko'e du lo ka ce'u citka lo cakla kei lo ka lo cakla cu se citka ce'u

.i ca'e ko'a citka lo cakla

.i xu ko'a brodrfa ko'e .i xu ko'a brodrfe ko'e .i xu ko'a brodrfi ko'e

The problem is that FA doesn't deal with propositions or with properties. A proposition is independent of the text used to express it. A property also is independent of the text used to express it. Different texts can be used to express the same proposition, or the same property. 

We can't have predicates that relate a proposition or a property to its "fa-argument", its "fe-argument", and so on, because propositions/properties don't have such things. It is only some of the texts used to express the propositions/properties that can may consist of a predicate with fa-/fe-/fi-arguments, but not the du'u/ka themselves.

We could have "ko'a brodrfa lu lo nixli cu citka lo cakla li'u" meaning that "ko'a du lo nixli", (via "ko'a du la'e lo'u lo nixli le'u") but I don't think it really makes sense with du'u or ka.

[guskant]

Le jeudi 9 avril 2015 09:15:04 UTC+9, xorxes a écrit :

On Tue, Apr 7, 2015 at 10:02 PM, guskant <gusni...@gmail.com> wrote:

Le mercredi 8 avril 2015 06:52:23 UTC+9, Jacob Errington a écrit :

.i ko'a brodrfV lo du'u broda <=> broda fV ko'a

The definition should be then :

.i ko'a brodrfV lo ka fV ce'u broda <=> broda fV ko'a

I don't know. Is it different from "ckaji"? 

bridi of {brodrfV} series form a subset of bridi of {ckaji}.

The difference is only that {brodrfV} does not permit plural {ce'u}, and that the place of the only {ce'u} is explicit by the last part of the word.

 

.i ca'e ko'e du lo ka ce'u citka lo cakla kei lo ka lo cakla cu se citka ce'u

.i ca'e ko'a citka lo cakla

.i xu ko'a brodrfa ko'e .i xu ko'a brodrfe ko'e .i xu ko'a brodrfi ko'e

The last line should be formed with {citkrfV} and {selcitkrfV}, or more precisely, {fe zei lo zei cakla zei citkrfV} and {fa zei lo zei cakla zei selcitkrfV}.

.i xu ko'a citkrfa ko'e .i go'i

.i xu ko'a citkrfe ko'e .i na go'i

.i xu ko'a citkrfi ko'e .i na go'i

.i xu ko'a selcitkrfa ko'e .i na go'i

.i xu ko'a selcitkrfe ko'e .i go'i

.i xu ko'a selcitkrfi ko'e .i na go'i

 

The problem is that FA doesn't deal with propositions or with properties. A proposition is independent of the text used to express it. A property also is independent of the text used to express it. Different texts can be used to express the same proposition, or the same property. 

We can't have predicates that relate a proposition or a property to its "fa-argument", its "fe-argument", and so on, because propositions/properties don't have such things. It is only some of the texts used to express the propositions/properties that can may consist of a predicate with fa-/fe-/fi-arguments, but not the du'u/ka themselves.

We could have "ko'a brodrfa lu lo nixli cu citka lo cakla li'u" meaning that "ko'a du lo nixli", (via "ko'a du la'e lo'u lo nixli le'u") but I don't think it really makes sense with du'u or ka.

I agree, but my understanding of la_tsani's idea is only creating a mapping from a range of F(x_1, x_2, ...) to a range of G(x_i) by fixing the values x_j to constants c_j (i!=j). 

This mapping does not impose any excessive role to FA. 

x_1 of {brodrfV} is not related to propositions. 

I would suggest {ka} instead of {du'u} in order to enjoy the open sentence (therefore, it does not signify a proposition) in the clause. {brod-} part of {brodrfV} means a predicate that have all the arguments other than x_i being substituted by constants.

In this sense, {ka} and {ckaji} of Lojban should have broader meaning than "property" of English.

[Jorge Llambías]

On Thu, Apr 9, 2015 at 12:42 AM, guskant <gusni...@gmail.com> wrote:

Le jeudi 9 avril 2015 09:15:04 UTC+9, xorxes a écrit :

 

.i ca'e ko'e du lo ka ce'u citka lo cakla kei lo ka lo cakla cu se citka ce'u

.i ca'e ko'a citka lo cakla

.i xu ko'a brodrfa ko'e .i xu ko'a brodrfe ko'e .i xu ko'a brodrfi ko'e

The last line should be formed with {citkrfV} and {selcitkrfV}, or more precisely, {fe zei lo zei cakla zei citkrfV} and {fa zei lo zei cakla zei selcitkrfV}.

ua! I didn't realize "brod" in "brodrfV" was a variable! I thought we were talking about just five predicates, "brodrfa", "brodrfe", ... "brodrfu". No wonder I was confused.

.i xu ko'a citkrfa ko'e .i go'i

.i xu ko'a citkrfe ko'e .i na go'i

.i xu ko'a citkrfi ko'e .i na go'i

.i xu ko'a selcitkrfa ko'e .i na go'i

.i xu ko'a selcitkrfe ko'e .i go'i

.i xu ko'a selcitkrfi ko'e .i na go'i

So "citkrfa" means something like "x1 is the eater in x2", "citkrfe" means "x1 is what gets eaten in x2", and so on. Then I think "du'u" does make sense:

citkrfa: x1 is that which proposition x2 claims eats.

citkrfe: x1 is that which proposition x2 claims is eaten.

Events could also make sense:

citkrfa: x1 is what eats when x2 happens.

citkrfe: x1 is what is eaten when x2 happens.

Or a property:

citkrfa: x1 eats when it has property x2

citkrfe: x1 is eaten when it has property x2

[guskant]

Le vendredi 10 avril 2015 08:56:56 UTC+9, xorxes a écrit :

So "citkrfa" means something like "x1 is the eater in x2", "citkrfe" means "x1 is what gets eaten in x2", and so on. Then I think "du'u" does make sense:

citkrfa: x1 is that which proposition x2 claims eats.

citkrfe: x1 is that which proposition x2 claims is eaten.

Events could also make sense:

citkrfa: x1 is what eats when x2 happens.

citkrfe: x1 is what is eaten when x2 happens.

Or a property:

citkrfa: x1 eats when it has property x2

citkrfe: x1 is eaten when it has property x2

I want to avoid using {du'u} for the following reason.

a formulation like

> citkrfa: x1 is that which proposition x2 claims eats. ......F1

makes sense, but is not suitable for the interpretation of

fa ko'a citka ko'e === fi'o citkrfa ko'a citka ko'e ......S1

which is derived from what la_tsani stated. 

F1 brings an ambiguity of interpretation that is shared with {fi'o citka be ko'e ko'a} or any BAI/{fi'o fe'u}-structure. 

Formulation with {nu} or any other cmavo of NU that does not take {ce'u} as an argument will produce the same ambiguity. 

sa'unai Accoding to F1, a statement

ko'a citkrfa lo du'u ko'a citka ko'e ......S2

fixes the proposition {ko'a citka ko'e}: 

referents of {ko'a} and {ko'e} are fixed respectively. 

Then, a statement {fi'o citkrfa ko'a citka ko'e} does not necessarily signify the same proposition as {ko'a citka ko'e} in S2. 

The former signifies a proposition that ko'a who eats ko'e is involved in a proposition that zo'e eats ko'e. 

An interpretation of ko'a!=zo'e makes sense when a tapeworm eats things eaten by the host, for example.

This ambiguity of interpretation comes from fixing the proposition in x2 of

{citkrfa}.

In order to make S1 always true, x2 of {citkrfa} should not be a proposition but an open sentence, which leaves one place be free for use in any other statement, and fixes referents of the other arguments to the same as the proposition intended. 

Then, when {fi'o citkrfa ko'a} appears in a statement, we can have a consistent interpretation that {ko'a} occupies the free place of the open sentence, and this occupation brings a proposition intended.

The reasonable English translation of definition of {brodrfV} that satisfies

x1 brodrfV lo ka fV ce'u broda <=> broda fV x1 

would be:

x1 brings a proposition by satisfying a formula stated in {ka}-clause.

mu'o

 

[Jorge Llambías]

On Fri, Apr 10, 2015 at 1:25 AM, guskant <gusni...@gmail.com> wrote:

fa ko'a citka ko'e === fi'o citkrfa ko'a citka ko'e ......S1

ko'a citkrfa lo du'u ko'a citka ko'e ......S2

Then, a statement {fi'o citkrfa ko'a citka ko'e} does not necessarily signify the same proposition as {ko'a citka ko'e} in S2. 

The former signifies a proposition that ko'a who eats ko'e is involved in a proposition that zo'e eats ko'e. 

An interpretation of ko'a!=zo'e makes sense when a tapeworm eats things eaten by the host, for example.

OK, but how is the ka-version different, given that:

fi'o citkrfa ko'a citka ko'e = fi'o citkrfa ko'a fa zo'e citka ko'e

 

This ambiguity of interpretation comes from fixing the proposition in x2 of

{citkrfa}.

In order to make S1 always true, x2 of {citkrfa} should not be a proposition but an open sentence, which leaves one place be free for use in any other statement, and fixes referents of the other arguments to the same as the proposition intended. 

I don't see how you insure that zo'e must take the value ko'a with the ka-version. Why can't one be the tapeworm and the other the host with the ka-version of citkrfa, given that both satisfy the same property?

 

Then, when {fi'o citkrfa ko'a} appears in a statement, we can have a consistent interpretation that {ko'a} occupies the free place of the open sentence, and this occupation brings a proposition intended.

I think I must be missing something. It seems that "citkrfa" can't be an ordinary predicate that could be found in the dictionary, but one that changes its meaning depending on which sentence it is used in. Maybe "fa" could be something like "fi'o te bridi be lo ka ce'u nei", where "te bridi be lo ka ce'u nei" is a predicate that relates an argument x1 to the proposition about x1 that results from filling "lo ka ce'u nei" with x1. I don't think we escape the tapeworm situation with this either though. OTOH, "fa ko'a fa zo'e citka ko'e" also allows for the tapeworm situation, doesn't it?

 

The reasonable English translation of definition of {brodrfV} that satisfies

x1 brodrfV lo ka fV ce'u broda <=> broda fV x1 

would be:

x1 brings a proposition by satisfying a formula stated in {ka}-clause.

But that's de definition of "ckaji". Surely the definition of "citkrfa" has to say something about eating. 

[guskant]

Le samedi 11 avril 2015 23:07:16 UTC+9, xorxes a écrit :

On Fri, Apr 10, 2015 at 1:25 AM, guskant <gusni...@gmail.com> wrote:

fa ko'a citka ko'e === fi'o citkrfa ko'a citka ko'e ......S1

ko'a citkrfa lo du'u ko'a citka ko'e ......S2

Then, a statement {fi'o citkrfa ko'a citka ko'e} does not necessarily signify the same proposition as {ko'a citka ko'e} in S2. 

The former signifies a proposition that ko'a who eats ko'e is involved in a proposition that zo'e eats ko'e. 

An interpretation of ko'a!=zo'e makes sense when a tapeworm eats things eaten by the host, for example.

OK, but how is the ka-version different, given that:

fi'o citkrfa ko'a citka ko'e = fi'o citkrfa ko'a fa zo'e citka ko'e

 

This ambiguity of interpretation comes from fixing the proposition in x2 of

{citkrfa}.

In order to make S1 always true, x2 of {citkrfa} should not be a proposition but an open sentence, which leaves one place be free for use in any other statement, and fixes referents of the other arguments to the same as the proposition intended. 

I don't see how you insure that zo'e must take the value ko'a with the ka-version. Why can't one be the tapeworm and the other the host with the ka-version of citkrfa, given that both satisfy the same property?

 

It's because {ko'a} does not appear to replace {ce'u} besides the proposition in which {fi'o citkrfa ko'a} appears.

fi'o citkrfa be lo du'u ko'a citka ko'e kei ko'a zo'e citka ko'e ......S3

fi'o citkrfa be lo ka ce'u citka ko'e kei ko'a zo'e citka ko'e ......S4

S3 has two propositions {ko'a citka ko'e} and {zo'e citka ko'e}, then ko'a!=zo'e is possible.

S4 has only one proposition {zo'e citka ko'e}. In order to make {ko'a} satisfying {ce'u citka ko'e} be involved the proposition {zo'e citka ko'e} without any additional proposition, there is no choice other than ko'a=zo'e.

 

Then, when {fi'o citkrfa ko'a} appears in a statement, we can have a consistent interpretation that {ko'a} occupies the free place of the open sentence, and this occupation brings a proposition intended.

I think I must be missing something. It seems that "citkrfa" can't be an ordinary predicate that could be found in the dictionary, but one that changes its meaning depending on which sentence it is used in. Maybe "fa" could be something like "fi'o te bridi be lo ka ce'u nei", where "te bridi be lo ka ce'u nei" is a predicate that relates an argument x1 to the proposition about x1 that results from filling "lo ka ce'u nei" with x1. I don't think we escape the tapeworm situation with this either though. OTOH, "fa ko'a fa zo'e citka ko'e" also allows for the tapeworm situation, doesn't it?

 

Sure, and in S4, there is no proposition {ko'a citka ko'e}, while there is one in S3.

 

The reasonable English translation of definition of {brodrfV} that satisfies

x1 brodrfV lo ka fV ce'u broda <=> broda fV x1 

would be:

x1 brings a proposition by satisfying a formula stated in {ka}-clause.

But that's de definition of "ckaji". Surely the definition of "citkrfa" has to say something about eating. 

.ie

but I don't know how to express it in English in a form applicable to all cases of {brodrfV}.

mu'o