14 votes
Accepted

Besides logics, what mathematical tools are used in the study of linguistics?

Nice question, I think this is good to ask for linguistic theory in general, because people who are not so familiar with linguistic research often find this hard to imagine. First of all, logic in ...
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8 votes

Textbooks in Formal Semantics / Montague semantics

I really depends on what you are after. Here is a list of my favorite text books, together with some short annotations. Heim & Kratzer 1998: one of the best intro to semantics if you are ...
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  • 326
8 votes
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What explanatory advantages does so-called "type theory" have?

I can't see the sense in reducing everything in a language to either an "e" or a "t". Maybe this is a good place to start. Type theory (more accurately: so-called simple type ...
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6 votes

Textbooks in Formal Semantics / Montague semantics

I warmly recommend Coppock & Champollion (2020). It's free, very accessibly written and essentially a formally precise version of Heim & Kratzer's style. It also comes with a computer program ...
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6 votes

the difference between upward and downward entailment

Upward entailment means that if a relation holds for some set X, then the relation will hold for a superset of X. Downward entailment means that if a relation holds for some X, then the relation will ...
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6 votes
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Truth conditional semantics and wffs

As the name already suggests, truth conditional semantics is only interested in the truth of a statement, not so much in whether or not that statement makes sense pragmatically. Form a truth-...
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6 votes

How active formal semantics as a research field today?

There are fewer academic jobs now compared to the 70's and 80's (in general), and the wave of "baby boom" retirements is just starting. Formal semantics is a "later" field and scholars in that field ...
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6 votes
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Intuitionistic type theory in linguistics

It's really nice to know that there are some other guys who are interested in type-theoretical semantics. I will give you some advice and references that might be interesting. First, there is a ...
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  • 99
5 votes
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How is category theory applied in linguistics?

Here's a short and perhaps inadequate answer: the correspondence is briefly but clearly sketched in the wikipedia article "pregroup grammar". The simplest pop-sci reference I know of is an article ...
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  • 176
5 votes

logic symbol for 'unlike, differing from'

(Why is there still no MathJax support for this SE?! Googling and copy-pasting unicode symbols every time you want to talk about semantics is really annoying.) What you want to say is basically ¬φ(a)...
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5 votes

Formalizing Natural Languages

This is a ridiculously complicated area, and the need to eventually narrow down your interest is a high priority. I would start with classical generative syntax as practiced by Noam Chomsky, and I ...
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4 votes

'sibling-in-law' constructions: Why the polysemy/vagueness?

The expression of family relations does not occur in a social vacuum: it is tied up with the cultural norms surrounding those relations. If you live in a society where the dominant norm is the nuclear ...
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4 votes

Computational/Formal Approaches to Paragraph-Level Semantics

I'm surprised you don't mention DRT (Discourse Representation Theory). DRT is a semantic framework that developed, amongst others, from the need to account for anaphoric references (pronouns) across ...
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4 votes
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What's a good second formal semantics book?

Coppock & Champollion (2021) adopts a formally more rigid version of the Heim & Kratzer style and covers a number of advanced topics. Intermediate-level formal semantics with less syntax and ...
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3 votes

Truth conditional semantics and wffs

Theorems are wffs, but not all wffs are theorems. Theorems are demonstrable, but other wffs are not. The central notion in logic is implication, not truth. It is possible to answer questions about ...
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3 votes

Can an indefinite article trigger a presupposition?

While the definite article is assumed to exhibit both an existence and a uniqueness presupposition, combining to an "exactly one" presupposition: I saw the bear yesterday → There is a bear → ...
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3 votes

Computational/Formal Approaches to Paragraph-Level Semantics

When we implemented our software for 'paragraph analysis' it ended up looking like a 'union of propositions' with two minor changes. 1. paragraphs were often preceded by headings which we used to set ...
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3 votes

What explanatory advantages does so-called "type theory" have?

Type theory avoids the paradoxes in set theory that were discovered early in the last century, e.g. Russell's paradox. It is not the only way to avoid the paradoxes. It is often used in the formal ...
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3 votes

'some students,' 'many students' etc. in logical formula

To express "some students" in the sense of "more than one", you could say that there exist at least two distinct individuals both of which are students and met by John (and yes, ...
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3 votes
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Series of textbooks to learn semantics from beginners' to advanced level

Gamut is certainly a good entry point, but is already quite dated and not that mathematical. After Gamut I'd recommend Partee et al. 'Mathematical Methods in Linguistics', which gives you some ...
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2 votes

Why does not 'the x dislikes the y and the y is a fox' = 'the x dislikes the fox'?

I'm not sure I entirely got the point (I find it weird to say that the variable can be eliminated in natural language, because 1. you don't explicitly use variables in natural language anyway and 2. "...
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2 votes

Formal Semantics - Set theory/Proofing (Not sure how to go around it)

Judging from your comments above, I'm guessing that your task is to show how the principle of compositionality applies to the interpretation of your example "a former president with red hair". If so, ...
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2 votes

Can an indefinite article trigger a presupposition?

I think perhaps with an qualifying adjective. "Are you a good mother?" Presupposes that the referent of "you" is, in fact, a mother.
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  • 89
2 votes

Truth-conditions of predicate-logic formulas for donkey sentences

a) Correct. Some fine-tuning to your answer: The donkey that Jake owns in own(j,x), is not the same donkey that was beaten in beat(j,x). It is not necessarily the same. Depending on which ...
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2 votes

Formal semantics (Montague, type-theoretical) of adverbial clauses

I don't see the problem. If you know how to handle restrictive relative clauses, then you must know how to handle adverbial clauses. The example "you can sit where you like" means "you can sit in ...
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2 votes
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"in relation to which" - what type of subordinated clause and is this conjunction somehow distinct?

It is a relative clause. A plot of land is acting as the lexical head of the RC, and in relation to was 'moved' to before the relative pronoun (not conjunction) which through the process of pied ...
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2 votes

directed graph representation of LF

Yes. See Arc pair grammar....
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2 votes

Textbooks in Formal Semantics / Montague semantics

Formal Semantics: An Introduction (Cambridge Textbooks in Linguistics) by Ronnie Cann This book provides a clear and accessible introduction to formal, and especially Montague, semantics within a ...
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  • 121
2 votes
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Motivation behind the definition for existential quantifiers such as *some* in compositional semantics

The reason is as follows: For ALL we need "for all objects, if they are P, then they are also Q". If we would use logical AND, it would mean "for all objects, they are P and they are Q" which is ...
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  • 251
2 votes

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

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 ...
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