# FOL representation of pronoun “it” - quantifier case.

If I have expression like "I like apple", can translate it to FOL as

$$\exists x, \forall y, I(x), apple(y), like(x, y)$$

Now assume that I have a sentence "I like it". Will it have the same translation to FOL?

$$\exists x, \forall y, I(x), it(y), like(x, y)$$

or do I need different quantifier for "it"?

• Representing the deixis of pronouns is quite a can of worms to open ... Usually, "it" should refer to a (constant or concretely defined) object somewhere nearby – Hagen von Eitzen Jul 26 '19 at 21:25
• You cannot just put commas and quantified variables everywhere and claim it's a FOL sentence. Where are the conjunctions, the implications, the brackets? – Vsotvep Jul 26 '19 at 21:32
• @Vsotvep, I thought commas is usually used for conjunctions? – user1700890 Jul 26 '19 at 21:39
• Usually you use the symbol $\land$ or $\&$ / $\&\&$, or even $\times$. These being opposed to disjunction $\lor$, $|$ / $||$ and $+$. This is the first time I see a comma being used. – Vsotvep Jul 26 '19 at 21:42
• "I like it" must be $\text {Like} (\text I,x)$ – Mauro ALLEGRANZA Jul 27 '19 at 7:47

## 1 Answer

This is as much meant as an indirect answer to this question, as it is to answer some other of your questions (this one and this one), since they all seem to follow the same pattern of asking how to translate something into FOL.

FOL is in itself a really nice and solid logic to work with. It is especially powerful for doing mathematics. However, to capture the intricacies of natural language, pure FOL is often woefully unsuited.

There are many linguistical logics out there, each having their own purposes, bringing their own solutions to linguistical problems and having problems of their own in expressing them. To name a few prominent logical systems in linguistics, you could take a look at Montague grammar, intensional logic, modal logic or fuzzy logic.

So instead of asking "how to translate this and that sentence of natural language into first-order logic?", perhaps the right question ought to be "is first-order logic suitable to adequately express this and that?"

The answer to this last question in the context of translating "it" is: no, FOL is not adequate to express how we use the word "it" in natural language.

If you are really interested in linguistical semantics, I recommend reading "Logic, Language and Meaning" from L.T.F. Gamut (which is a collective pseudonym)

• "no, FOL is not adequate to express how we use the word "it" in natural language." - I'm sorely tempted to write a two-line answer which says "Replace 'it' with its antecedent first, and then try to translate your sentence into FoL." But that would sort of miss the point of your answer. – Kevin Jul 26 '19 at 22:05
• It would be a solution of some sorts, in that it is a way to translate the meaning of the sentence within a context. However, it is not a translation of the semantical meaning of "it". – Vsotvep Jul 26 '19 at 22:08
• @Kevin, It think this is what discourse representation theory is doing (replacing with antecedent). – user1700890 Jul 27 '19 at 12:20
• I went through Gamut vol 1. – user1700890 Jul 27 '19 at 12:21
• Then I would recommend vol 2. That's where the real fun starts, with the introduction of modalities, intesionality, categorial grammars and lambda calculus :) – Vsotvep Jul 27 '19 at 13:21