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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 ...
Natalie Clarius's user avatar
9 votes
Accepted

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 ...
Natalie Clarius's user avatar
7 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 ...
Natalie Clarius's user avatar
7 votes
Accepted

Do predicates always map to truth values in formal semantics?

in formal semantics, predicates are always functions that map from individuals (i.e. arguments) to truth values Not quite; it is specifically individual predicates which take individual arguments and ...
Natalie Clarius's user avatar
6 votes
Accepted

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-...
Natalie Clarius's user avatar
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 ...
Natalie Clarius's user avatar
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 ...
user6726's user avatar
  • 83.2k
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 ...
Fred's user avatar
  • 99
6 votes

What are the semantics of questions and requests/commands?

In an approach quite close to the one you seem to assume for declaratives, questions can be seen as denoting lambda-abstractions. The set of true answers is the set of arguments with which such an ...
Keelan's user avatar
  • 4,221
5 votes
Accepted

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 ...
Linas's user avatar
  • 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)...
Natalie Clarius's user avatar
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 ...
user6726's user avatar
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5 votes
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What is the difference between function and predicate?

There is two kinds of "functions" that could be meant in your context: Thinking of the content expressed by a predicate as a function which takes individuals as an input and gives a truth ...
Natalie Clarius's user avatar
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 ...
Nick Nicholas's user avatar
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 ...
Natalie Clarius's user avatar
4 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 ...
Greg Lee's user avatar
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4 votes
Accepted

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 ...
Natalie Clarius's user avatar
4 votes

An Overview of Mathematical-Logical Approaches in Formalizing Natural Languages

Seconding the Kornai stuff mentioned above; it's all great. Probably the seminal text here from the point of view of relatively modern linguistics would be Partee's 1993 book, which while somewhat old ...
Fred's user avatar
  • 511
4 votes

On colorless green ideas

Chomsky observed (Syntactic structures p. 15) that "Colorless green ideas sleep furiously" and "Furiously sleep ideas green colorless" are both "equally nonsensical", but ...
user6726's user avatar
  • 83.2k
4 votes

On colorless green ideas

First, it should be clear that in natural languages nothing has a rigid definition. To make sense of a sentence is thus to select "definitions" so that the sentence has the intended meaning. ...
Dodezv's user avatar
  • 421
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 ...
Greg Lee's user avatar
  • 12.5k
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 → ...
Natalie Clarius's user avatar
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, ...
Natalie Clarius's user avatar
3 votes
Accepted

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 ...
sequitur's user avatar
  • 176
3 votes

What aspect of meaning is not captured by the translation from natural language to PropL?

Somebody who neither drinks nor drives would say I don't drink or drive. I don't drink and drive pragmatically means I don't drive when I am or might be under the influence of alcohol. The only ...
Colin Fine's user avatar
  • 7,464
3 votes
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Should λ-terms all be easily translated back into natural language syntax?

(a) is the denotation for gray proposed in (11) on p. 66. Its type is (et)et so that when applied to cat with type et we get gray cat with type et as well. In (b) we have a predicate f of which Ann is ...
Keelan's user avatar
  • 4,221
3 votes

An Overview of Mathematical-Logical Approaches in Formalizing Natural Languages

There’s probably a good encyclopedia article or handbook on mathematical linguistics, Andras Kornai wrote some books on this. You might like this blog post. https://blog.juliosong.com/linguistics/...
Julius Hamilton's user avatar
3 votes

An Overview of Mathematical-Logical Approaches in Formalizing Natural Languages

I’m a grad student in mathematics doing research in Formal Semantics. Work in the Montague Semantics pulls upon a lot more than just Lambda Calculus. There’s a lot of work with non-standard logic (...
m. lekk's user avatar
  • 267
3 votes

An Overview of Mathematical-Logical Approaches in Formalizing Natural Languages

Before pointing to some literature I want to clarify the interaction between Montague semantics and categorial grammar: Montague semantics is intimately related to categorial grammar. Indeed, one the ...
sequitur's user avatar
  • 176

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