Talk:reduced logical form

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Posted by rlpowell on Mon 08 of Nov., 2004 22:31 GMT posts: 14214

So, I see that you are obviously building a kernel language for Lojban, presumably one containing only the logical bits.

What I'm missing is why.

-Robin

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Posted by xorxes on Tue 09 of Nov., 2004 02:07 GMT posts: 1912

> So, I see that you are obviously building a kernel language for Lojban, > presumably one containing only the logical bits. > > What I'm missing is why.

Does there always have to be a why? :-)

I started doing it because of the eternal discussion about NA and its scope. I think using the reduced logical form we can more clearly see what the alternatives are.

But besides that, I think it is a useful thing to show that the logical language truly does match up with ordinary first order logic to a great extent, and it is also useful to know exactly where it does not.

I was pleasantly surprized by how easy it turned out to be doing the reduction, mostly. I have completely ignored indicators and free modifiers. So for example the algorithm won't produce a reduced form for {doi ro da poi me ko da cuxna pa karda}. I guess it should have to reduce to something like: {e'o ro da poi me do zo'u pa de poi karda zo'u cuxna fa da de}

Anyway, leaving indicators aside, I found two points where I could not do the reduction: mixed connective+tag, and VUhO relative-clauses.

I also still have to do sumti non-logical connectives, but I think those won't be a problem.

(And there are some issues I haven't considered yet, like {bu'a}, {no'a}, and the like, which may or may not need special treatment.)

mu'o mi'e xorxes


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rlpowellPosted by rlpowell on Tue 09 of Nov., 2004 20:59 GMT posts: 14214

> I started doing it because of the eternal discussion about NA and > its scope. I think using the reduced logical form we can more > clearly see what the alternatives are.

Coolness.

> But besides that, I think it is a useful thing to show that the > logical language truly does match up with ordinary first order > logic to a great extent, and it is also useful to know exactly > where it does not.

You mean second order, don't you?

> I was pleasantly surprized by how easy it turned out to be doing > the reduction, mostly. I have completely ignored indicators and > free modifiers.

As you should.

Good luck.

-Robin

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Posted by Anonymous on Wed 12 of Jan., 2005 01:30 GMT

Re: Reduced logical form So, I see that you are obviously building a kernel language for Lojban, presumably one containing only the logical bits.

What I'm missing is why.

-Robin

Posted by pycyn on Tue 09 of Nov., 2004 01:49 GMT posts: 2388

xorxes:

> sentence = selbri [fa sumti ...] /VAU/ > | NA KU ZOhU sentence > | tag /KU/ ZOhU sentence > | tag sumti ZUhU sentence > | quantifier DA > relative-clauses ZOhU sentence > | gek sentence gik sentence > > > selbri = Any untagged and unnegated selbri > (selbri-2 in the EBNF grammar) > > sumti = Any unquantified sumti (sumti-6 in > the EBNF grammar) > > tag = tag in the EBNF grammar > > gek = gek in the EBNF grammar > > gik = gik in the EBNF grammar > > (DA are da, de, di and any additional indexed > variables as needed) > > The above grammar is a sub-grammar of the > Lojban grammar. By that I mean that every > sentence it generates is a valid sentence of > the Lojban grammar. I contend that every Lojban > sentence has a corresponding reduced logical > form generated from this grammar.

Ah, the LoCCan use of words!. "Reduced" here applies, I suppose, the dropping the "logically irrelevant" bits; for the most part sentences are expanded to get these forms (prenexing requires anaphora, forethought connectives are regularly longer than afterthought and shifting to sentential requires repetitions). Terminology aside, however, this seems a useful thing to do for a logical language, moving toward (or away from, since this is likely a deeper structure grammar than the usual one — or so a logically corrupted linguist would say) the form suited for usual logical applications. The contention is the usual (ultimately unsupported — in natural languages) assumption of applied formalized logics.

>The idea is > simple: to get the reduced logical form > eliminate indicators and free modifiers, move > quantifiers and negations to the prenex, expand > all logical connectives to forethought sentence > connectives and finally move all the arguments > behind the selbri.

For the real deep logical sturcture, it would be good to get the modals etc. out to the front as well. This is somewhat problematic, since the modals (including tense/aspect and mood)is not grammatically, but only lexically, specifiable. And there may be cases where this brings to light ambiguities — in the speaker's intentions, though maybe not in the Lojban text (details of the relative placement of tense, mode, negation and quantification which cannot be dealt with in the narrow confines of the preselbri slot). The use of forethought connectives is tidy though not essential, as is the shift to VSO order. The devil is, of course, in > the details. I intend to work out an algorithm > for producing the reduced logical form for any > Lojban sentence. (In fact I think there are a > couple of tricky places where it may not be > doable, but at least this will show what they > are.)

As noted, the history of doing this with natural languages shows that there seem to be intractable points, readily solved by human intervention but not algorithmable. They are not generally the logically interesting cases,though — since where they are differs from language to language -- sometimes they are crucial. Human intervention, alas, raises the possibility of special pleading -- doing the regimentation in a certain way to justify a certain (predetermined) result rather than for objective reasons, so it is to be used very sparingly.

The purpose of this exercise is to > clarify the argument for the scope of NA. In > the reduced logical form the relative scopes of > the different operators are fairly obvious.

The relative scope in each case is just everything after it in the same sentence (which is also rather better defined in this representation).

Is this all about the issue — which has been around since the beginning of Loglan — of where sentential negation goes? It is clear, of course, in prenex form — though in the shift to forethought connectives some problems could reappear if {nagi} is allows from {na.a} etc. (e.g. "only if" for conditionals). I suppose that, if we shifted everything to "reduced" form, some rules would be clearer but that does not solve the issue of where negation goes in colloquial usage — the issue that has come up over and over. The prenex position is logically desirable, but sociolinguistically someplace close to the verb (after it in VSO and VOS formats typically, and frequently also in --V)is the norm. It is not clear why this is the case, but it seems to be a powerful tendency, hard to get people to change from. I suppose that is whay it is retained in Loglan and then in Lojban, even with all the probolems it generates in other respects.

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Posted by xorxes on Tue 09 of Nov., 2004 01:49 GMT posts: 1912

pc: > Ah, the LoCCan use of words!. "Reduced" here > applies, I suppose, the dropping the "logically > irrelevant" bits;

Right, and also reducing the various ways of doing the same thing (as in afterthought vs. forethoght).

> for the most part sentences are > expanded to get these forms (prenexing requires > anaphora, forethought connectives are regularly > longer than afterthought and shifting to > sentential requires repetitions).

Yes, definitely. It's reduced in complexity, but usually expanded in size.

> Terminology > aside, however, this seems a useful thing to do > for a logical language, moving toward (or away > from, since this is likely a deeper structure > grammar than the usual one — or so a logically > corrupted linguist would say) the form suited for > usual logical applications. The contention is the > usual (ultimately unsupported — in natural > languages) assumption of applied formalized > logics.

In the case of Lojban the contention is much less contentious, given that it is almost purely a formal matter. I am not claiming that two sentences with the same reduced form will have the same meaning. All I say is that they have the same propositional content, but the meaning usually involves more than that. This is clear, as for example {ju'a do klama le zarci}, {xu do klama le zarci} and {e'u do klama le zarci} all have the same reduced form (i.e. propositional content) but obviously different meaning in a wider sense.

> For the real deep logical sturcture, it would be > good to get the modals etc. out to the front as > well.

If the modals are {ka'e} and company, they are already

there: that's what
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> This is somewhat problematic, since the > modals (including tense/aspect and mood)is not > grammatically, but only lexically, specifiable.

They are specified in the same way as negation: {na ku}, {pu ku}, {ka'e ku}, etc.

> And there may be cases where this brings to light > ambiguities — in the speaker's intentions, > though maybe not in the Lojban text (details of > the relative placement of tense, mode, negation > and quantification which cannot be dealt with in > the narrow confines of the preselbri slot).

I haven't fully considered this yet. Do you have any examples in mind?

> The > use of forethought connectives is tidy though not > essential, as is the shift to VSO order.

With forethought connecives we can get rid of all the bracketing stuff, much tidier. VSO order I just included to settle on a single form as the reduced form.


> The purpose of this exercise is to > > clarify the argument for the scope of NA. In > > the reduced logical form the relative scopes of > > the different operators are fairly obvious. > > The relative scope in each case is just > everything after it in the same sentence (which > is also rather better defined in this > representation).

Exactly.

> Is this all about the issue — which has been > around since the beginning of Loglan — of where > sentential negation goes? It is clear, of > course, in prenex form — though in the shift to > forethought connectives some problems could > reappear if {nagi} is allows from {na.a} etc. > (e.g. "only if" for conditionals).

{na.a} expands to {ganai ... gi ...}.

{nagi} is not grammatical.

{na ga ... gi ...} is equivalent to {genai ... ginai ....} which is also {ge naku zo'u .... gi naku zo'u ...}.

> I suppose > that, if we shifted everything to "reduced" form, > some rules would be clearer but that does not > solve the issue of where negation goes in > colloquial usage — the issue that has come up > over and over.

Yes. But seeing what the shift rules are in full (or as much in full as we can manage) will hopefully make it easier to decide which rule we should to adopt.

mu'o mi'e xorxes


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Posted by pycyn on Tue 09 of Nov., 2004 01:51 GMT posts: 2388

wrote:

> pc: > > Terminology > > aside, however, this seems a useful thing to > do > > for a logical language, moving toward (or > away > > from, since this is likely a deeper structure > > grammar than the usual one — or so a > logically > > corrupted linguist would say) the form suited > for > > usual logical applications. The contention is > the > > usual (ultimately unsupported — in natural > > languages) assumption of applied formalized > > logics. > > In the case of Lojban the contention is much > less > contentious, given that it is almost purely a > formal matter. > I am not claiming that two sentences with the > same reduced > form will have the same meaning. All I say is > that they > have the same propositional content, but the > meaning > usually involves more than that. This is clear, > as > for example {ju'a do klama le zarci}, {xu do > klama le zarci} > and {e'u do klama le zarci} all have the same > reduced form > (i.e. propositional content) but obviously > different meaning > in a wider sense. > These last examples are just the modes that ought also be included in what gets carried over into the logical form.

> > For the real deep logical sturcture, it would > be > > good to get the modals etc. out to the front > as > > well. > > If the modals are {ka'e} and company, they are > already

> there: that's what
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> provides. > see above: questioning, comanding, hypothesizing and do on all play significant logical roles.

> > This is somewhat problematic, since the > > modals (including tense/aspect and mood)is > not > > grammatically, but only lexically, > specifiable. > > They are specified in the same way as negation: > {na ku}, {pu ku}, {ka'e ku}, etc. > I meant that there is not agrammatical way to specify which things are modals, etc. They are spread over half a dozen form classes, each of which contains any number of things that are not modal. But we can list what ought to be included item by item (it would take a while and some thought but it is a finite task).

> > And there may be cases where this brings to > light > > ambiguities — in the speaker's intentions, > > though maybe not in the Lojban text (details > of > > the relative placement of tense, mode, > negation > > and quantification which cannot be dealt with > in > > the narrow confines of the preselbri slot). > > I haven't fully considered this yet. Do you > have any > examples in mind? > The usual cases in natural languages are mixed prefixes: modal and quantifier, for example: "there is some that did" and "there was something that did" or tense and modal "it used to be possible that" v. "it is possible that it used to be." These are significant differences for which the tight preselbri usually allows at most one expression — not clearly one or the other. Sorting those out may test the algorithms.

> > > Is this all about the issue — which has been > > around since the beginning of Loglan — of > where > > sentential negation goes? It is clear, of > > course, in prenex form — though in the shift > to > > forethought connectives some problems could > > reappear if {nagi} is allows from {na.a} etc. > > (e.g. "only if" for conditionals). > > {na.a} expands to {ganai ... gi ...}.

A good rule for the purpose, but a hard one to teach for some reason. > > {nagi} is not grammatical.

That was a more dubious call, since even in Polish the distinction is often colloquially useful (but also often just confusing). > > {na ga ... gi ...} is equivalent to {genai ... > ginai ....} > which is also {ge naku zo'u .... gi naku zo'u > ...}. > > > I suppose > > that, if we shifted everything to "reduced" > form, > > some rules would be clearer but that does not > > solve the issue of where negation goes in > > colloquial usage — the issue that has come > up > > over and over. > > Yes. But seeing what the shift rules are in > full > (or as much in full as we can manage) will > hopefully > make it easier to decide which rule we should > to adopt. > I didn't know the rules were up for grabs. What -- aside from people being too lazy or ignorant to use them — was the matter with the set we had? And the two obvious problems don't seem to be reasons to change the rules. > > '''''''''''''''''''''''''''''''''''''''''''__ > Do you Yahoo!? > Check out the new Yahoo! Front Page. > www.yahoo.com > > > > >

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Posted by xorxes on Tue 09 of Nov., 2004 01:51 GMT posts: 1912

pc: > > as > > for example {ju'a do klama le zarci}, {xu do > > klama le zarci} > > and {e'u do klama le zarci} all have the same > > reduced form > > (i.e. propositional content) but obviously > > different meaning > > in a wider sense. > > > These last examples are just the modes that ought > also be included in what gets carried over into > the logical form.

That will have to wait for stage 2, then. For the moment I'm concentrating on the basic stuff: negation, quantifiers and connectives. Tenses come almost for free since they behave more or less like negation (in Lojban grammar).

> I meant that there is not agrammatical way to > specify which things are modals, etc. They are > spread over half a dozen form classes, each of > which contains any number of things that are not > modal. But we can list what ought to be included > item by item (it would take a while and some > thought but it is a finite task).

Ok, I'll play if you want to start it, but that's not what I'm doing here as yet.

> The usual cases in natural languages are mixed > prefixes: modal and quantifier, for example: > "there is some that did" and "there was something > that did" or tense and modal "it used to be > possible that" v. "it is possible that it used to > be."

Those are both doable in the proposed reduced form:

{su'o da zo'u pu ku zo'u ....} vs {pu ku zo'u su'o da zo'u ...}

and {pu ku zo'u ka'e ku zo'u ...} vs {ka'e ku zo'u pu ku zo'u ...}

> > {na.a} expands to {ganai ... gi ...}. > > A good rule for the purpose, but a hard one to > teach for some reason.

Because it looks as if {na} was negating {a} rather than the first connectand, I suppose.

> > {nagi} is not grammatical. > > That was a more dubious call, since even in > Polish the distinction is often colloquially > useful (but also often just confusing).

{ge ... naku gi ...} is quite acceptable though.

> > Yes. But seeing what the shift rules are in > > full > > (or as much in full as we can manage) will > > hopefully > > make it easier to decide which rule we should > > to adopt. > > > I didn't know the rules were up for grabs. What > — aside from people being too lazy or ignorant > to use them — was the matter with the set we > had?

Incompleteness, mainly.

We don't know for sure, for example, whether {na broda gi'e brode} is {(na broda) gi'e (brode)}, as the parser says, or {na (broda gi'e brode)}.

> And the two obvious problems don't seem to > be reasons to change the rules.

If there are no good reasons, and we can figure out what the rules actually are, they probably won't be changed.

mu'o mi'e xorxes


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Posted by pycyn on Tue 09 of Nov., 2004 01:53 GMT posts: 2388

wrote:

>pc:

> > The usual cases in natural languages are > mixed > > prefixes: modal and quantifier, for example: > > "there is some that did" and "there was > something > > that did" or tense and modal "it used to be > > possible that" v. "it is possible that it > used to > > be." > > Those are both doable in the proposed reduced > form: > > {su'o da zo'u pu ku zo'u ....} vs > {pu ku zo'u su'o da zo'u ...} > > and {pu ku zo'u ka'e ku zo'u ...} > vs {ka'e ku zo'u pu ku zo'u ...}

Sorry I was unclear. Of course these can be done in prenex since they caan be done in standard logic, which is what prenex is, more or less. What the problem is is to figure out — let alone algorithmatize — which of these the normal forms mean. The obvious automatic rules will laeways give a decision, but, based on the work in natural languages, the decision is only randomly the one intended. Throw in some negations too to make it fun.

> > > > {na.a} expands to {ganai ... gi ...}. > > > > A good rule for the purpose, but a hard one > to > > teach for some reason. > > Because it looks as if {na} was negating {a} > rather > than the first connectand, I suppose. > It's hard even for those who think that that would have to be {naku}

> > > {nagi} is not grammatical. > > > > That was a more dubious call, since even in > > Polish the distinction is often colloquially > > useful (but also often just confusing). > > {ge ... naku gi ...} is quite acceptable > though.

Nice; it creates the same problem, indeed more so since its negation seems to point only to the right (on what seems to be the general reading of the {naku} form) but actually goes only left.

> > > > Yes. But seeing what the shift rules are in > > > full > > > (or as much in full as we can manage) will > > > hopefully > > > make it easier to decide which rule we > should > > > to adopt. > > > > > I didn't know the rules were up for grabs. > What > > — aside from people being too lazy or > ignorant > > to use them — was the matter with the set we > > had? > > Incompleteness, mainly. > Incompleteness in the sense that there are situations where there is no rule to get to a more transparent format? Are there such? Incompleteness in the sense that there are forms in the transparent format which we cannot get from the normal format definitely occurs (can't give examples because then it is possible to argue that that is what the rule gives, in which case it is the other form that is wanted, but if I give that as an example, then....).

> We don't know for sure, for example, whether > {na broda gi'e brode} is {(na broda) gi'e > (brode)}, > as the parser says, or {na (broda gi'e brode)}. > If the parser says one way rather than the other, then that presumably is what it is. What more do you want in the way of a rule? (Although I have to admit that parser boxes are often right only for this peculiar grammar and not for any obvious general linguidstic description — one of the consequences of trying to write a grammar for a real languages which is LALR1 — another being a mass of empty grammatical constructions and the need for countless little words that don't really do anything. In this case, however, the parser is in accord with the general pattern of the language and we would expect a left parenthesis after {na} to get the other form.)

> > And the two obvious problems don't seem to > > be reasons to change the rules. > > If there are no good reasons, and we can figure > out > what the rules actually are, they probably > won't be > changed. > It seems by the last example that when you have a case of what the rules actually are you still have questions. What more is wanted for figureing out what the rules actually are. (I thought this was about questions for which the parse is no help since they are about cross format equivalences, not interformat structures.)

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Posted by xorxes on Tue 09 of Nov., 2004 01:54 GMT posts: 1912

pc: > > --- Jorge Llambías > > We don't know for sure, for example, whether > > {na broda gi'e brode} is {(na broda) gi'e > > (brode)}, > > as the parser says, or {na (broda gi'e brode)}. > > > If the parser says one way rather than the other, > then that presumably is what it is. What more do > you want in the way of a rule?

I'm happy to go with the parser here. You argued for the other interpretation at some point. Notice that means that for example in {su'o da na broda gi'e brode}, {na} can't have scope over {su'o}. So the general rule that pre-selbri {na} goes to the beginning of the prenex appears to be in conflict with the parse in this case.

> In this case, however, the parser > is in accord with the general pattern of the > language and we would expect a left parenthesis > after {na} to get the other form.)

No left parenthesis possible there, but {naku} will do it.

> It seems by the last example that when you have a > case of what the rules actually are you still > have questions. What more is wanted for > figureing out what the rules actually are.

I only mentioned that case because it is one where you opposed the parse in the past, but if you now don't oppose it, we are in agreement.

>(I > thought this was about questions for which the > parse is no help since they are about cross > format equivalences, not interformat structures.)

Yes, it's mostly about those.

mu'o mi'e xorxes


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Posted by pycyn on Tue 09 of Nov., 2004 01:55 GMT posts: 2388

wrote:

> > pc: > > > > --- Jorge Llambías > > > > We don't know for sure, for example, > whether > > > {na broda gi'e brode} is {(na broda) gi'e > > > (brode)}, > > > as the parser says, or {na (broda gi'e > brode)}. > > > > > If the parser says one way rather than the > other, > > then that presumably is what it is. What > more do > > you want in the way of a rule? > > I'm happy to go with the parser here. You > argued for > the other interpretation at some point.

Hmmm! I wonder what the question was at that time. Maybe I'll have to reconsider in abroader context.

> Notice > that > means that for example in {su'o da na broda > gi'e brode}, > {na} can't have scope over {su'o}. So the > general rule > that pre-selbri {na} goes to the beginning of > the > prenex appears to be in conflict with the parse > in this case.

Ah so! Yes, that does make a difference. The whole cannot be unpacked as {su'o da na broda ije su'o da brode} since the two {su'o da} do not collapse. The "source" must then be {su'o da na broda ije da brode}, hence {su'o da zo'u da na broda ije da brode}, where the scope of {su'o} is clearly over that of {na}. I wonder what was the problem under discussion that led me to the other view. Oops!

> > > In this case, however, the parser > > is in accord with the general pattern of the > > language and we would expect a left > parenthesis > > after {na} to get the other form.) > > No left parenthesis possible there, but {naku} > will > do it.

Surely there is some device that will give {na (broda gi'e brode)}, whether or not it is called a parenthesis. Working out the "source" for this is going to be a bit messy, though; apparently it is {naku zo'u su'o da zo'u ge da broda gi da brode} but there are questions, I suspect, about this. > > > It seems by the last example that when you > have a > > case of what the rules actually are you still > > have questions. What more is wanted for > > figureing out what the rules actually are. > > I only mentioned that case because it is one > where > you opposed the parse in the past, but if you > now don't > oppose it, we are in agreement. > > >(I > > thought this was about questions for which > the > > parse is no help since they are about cross > > format equivalences, not interformat > structures.) > > Yes, it's mostly about those.