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First, I asked this on math.stackexchange, someone recommended to go here.

I am looking for information on the mathematical foundations of formal semantics in linguistic. After some time, I found this book (Mathematical methods in linguistics / by Barbara H. Partee, Alice ter Meulen and Robert E. Wall) which is no accessible for me. My problem is that I do not know exactly what I am looking for, as I am missing the right keywords when searching.

I am interested in:

  • Set theory/ first order logic as a basis for formal semantics or formal linguistic in general
  • Type theory as a basis for it
  • (Dis-)Advantages of one or the other

Thank you very much for any advice where to look, a short outline or references.

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    If you find Partee et al.'s book too difficult, you will probably find Gamut so, too. If you are just exploring the ways set theory, type theory and functional analysis are used in formal semantics, perhaps you could start with the short classic Allwood, Andersson & Dahl's Logic in Linguistics (CUP 1977), try Cann's Formal Semantics (CUP 1993) next, then look at Dowty, Wall & Peters Introduction to Montague Semantics (Kluwer 1981), then choose papers from Portner & Partee (eds.) Formal Semantics. The Essential Readings (Blackwell 2002), and read Gamut volume 2 only at the end, and selectively. – user6814 Mar 30 '15 at 19:10
  • Look into McCawley 1993, Everything That Linguists Have Always Wanted to Know About Logic Chicago (2nd ed). He covers pretty much everything; of course he's more interested in the phenomena that formal logic attempts to model than in the formal model itself. Many linguistic phenomena are not part of logic because they fall outside the limits of mathematics. – jlawler Apr 29 '15 at 22:51
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The book you mention (Partee et al.) is the best one. If it's not an option for you, I'd recommend this one: Gamut

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Here are two very elementary books that seem relevant:

Introduction to Symbolic Logic, by Hans Reichenbach. This is a classic with much about the application of predicate logic to the analysis of English, including the analysis of tense and aspect that has become more or less a standard.

Logics and Languages, by M. J. Cresswell. This requires no more than a smattering of naive set theory, and I think it is a lot of fun. Cresswell builds up a possible-worlds type of semantics for English. (A disadvantage is that it never became much known or referred to, for some reason.)

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This is the easiest book on the subject that I found. It should provide a very excellent foundation for acquiring a very good understanding of all of the underlying ideas. It has a whole chapter on type theory and it weaves set theory in here and there as needed.

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 linguistic framework. It presupposes no previous background in logic, but takes the student step-by-step from simple predicate/argument structures and their interpretation through to Montague's intentional logic. It covers all the major aspects, including set theory, propositional logic, type theory, lambda abstraction, traditional and generalised quantifiers, inference, tense and aspect, possible worlds semantics, and intensionality. Throughout the emphasis is on the use of logical tools for linguistic semantics, rather than on purely logical topics, and the introductory chapter situates formal semantics within the general framework of linguistic semantics. It assumes some basic knowledge of linguistics, but aims to be as non-technical as possible within a technical subject. Formal Semantics will be welcomed by students of linguistics, artificial intelligence and cognitive science alike.

https://www.cambridge.org/core/books/formal-semantics/D1BE99DD41C138A32971719EE0A57D6D

I can personally attest to the excellence of this book it explains all of the key concepts in a way that is much easier to understand than most other sources, such as Monatague's original papers.

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