# What is the best/state-of-the-art logic for representing English language?

I know people have used lambda terms which "compile into" first-order logic, but based on what I have seen that is not particularly great for representing complex sentences with causal or temporal relations, or dealing with certain quantifiers. There are so many flavors of logic (modal, epistemic, temporal, higher-order) - has anybody opined about the logic which can represent the maximal subset of English language? I've read about Episodic Logic, which seems promising, but I haven't seen it used by researchers outside of Computer Science.

• There is no "best". Each researcher has their own preferences. And there are quite a few logic-based formalisms like TLG, CCG, ACG, CVG, and so on. Perhaps you should reword your question to be more specific?
– prash
Commented Aug 6, 2017 at 16:35

The wording of your question seems to imply an equivalence between first order predicate logic and higher order logics. They are not equivalent. First order predicate logic was shown to be consistent and complete by Kurt Gödel, but "Stronger logics, such as second-order logic, are not complete." (Consistency.)

Whether first order predicate logic is sufficient to describe the logic of natural languages is an open question.

• 1. The completeness of higher-order logic depends on the semantics used. Under general semantics (Henkin's semantics) higher-order logic is equivalent to first-order logic and therefore complete. 2. FOL is sufficient to describe the logic of natural languages (proved by Hobbs). Commented Aug 7, 2017 at 0:58
• Oh. So you mean that it is possible to take the view that there is no such thing as a higher order logic as distinct from first order logic, and so, in that view, higher order logic cannot be necessary for anything at all, including natural language. Hmmm. Commented Aug 7, 2017 at 1:50
• Unlike FOL, second-order logic doesn't have one semantics. As is well-known, under general semantics (discovered by Henkin) SOL is complete. Under standard semantics (where predicate variables range over whole power sets), SOL is indeed incomplete (for the power sets are uncountable). It's important to be precise and tell the whole truth. Commented Aug 7, 2017 at 2:01

I'd recommend looking at Jerry Hobbs' way of parsing and representing English, it's one of the most elaborate ones when it comes to logic and commonsense representation:

Jerry Hobbs: "Discourse and Inference"

• And McCawley's matched pair of Syntax and Logic books gives you a stereo viewpoint that's compatible with most of Hobbs. Commented Aug 6, 2017 at 14:00
• @jlawler Hobbs' biggest contribution is in showing that one doesn't need modal or fuzzy or other fancy logics which McCawley's book is about for FOL is sufficient for NLU and commonsense reasoning. Commented Aug 6, 2017 at 14:08
• Like I said, stereo. Commented Aug 6, 2017 at 14:20