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I'm looking for a cheap, thorough but reasonably accessible introduction to formal semantics. There appear to be lots of options on the market. I assume there are plenty of experts in formal semantics / computational linguistics /AI / applied logicians who can give me their suggestions while noting the emphases of different textbooks.
(I didn't see a question like this posted, so I figured this would be worth asking and useful to the wider linguistics community.)
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 interested in the interface between syntax and semantics and working a generative grammar background for syntax. Intentionally a bit light on the logical background, but formal enough to read a great percentage of current work in formal semantics if you mastered this. (It does not cover intensions though)
Gamut 1991: (as mentioned in the comments) a great 2 volume book which leans more towards the logical side of semantics not so much on the syntax. Brings you all the way to Montague grammar and also contains chapters on more “recent” dynamic theories.
Carpenter 1997: Great and detailed intro to semantics using a categorial grammar background. If you want to go into the more computational / AI / math direction, this is a great one.
Zimmermann & Sternefeld 2013: Can be viewed as an updated version of Heim & Kratzer with a bit less syntax, but more other stuff like presuppositions, common ground etc. I used this recently in one of my classes and it was pretty good.
Carpenter, Bob (1997): Type-Logical Semantics. Cambridge, MA: MIT Press. Gamut, L.T.F. (1991a): Logic, Language, and Meaning. Vol. 1: Introduction to Logic. Chicago: University of Chicago Press.
Gamut, L.T.F. (1991b): Logic, Language, and Meaning. Vol. 2: Intensional Logic and Logical Grammar. Chicago: University of Chicago Press.
Heim, Irene & Angelika Kratzer (1998): Semantics in Generative Grammar. Oxford: Blackwell.
Zimmermann, omas Ede & Wolfgang Sternefeld (2013): Introduction to Semantics. An Essential Guide to the Composition of Meaning. Berlin and New York: de Gruyter.
Copy-pasting from various comments I wrote here and there:
As a general introduction, I would recommend you the Introduction to Semantics by T. E. Zimmermann & W. Sternefeld (2013).
They have a very set-theoretical approach, but for formal semantics I guess this is a helpful introduction.
They introduce the basic issues of semantics (lexical, structural and scope ambiguity, compositonality, truth values), explain how to compositionally derive the meaning of complex expressions with some focus on genealized quantifiers and a short excurs to logical types, an introduction to intensionality (not very extensive, but it's good in explaining why we need it and what possible words should be), a chapter on presuppositions (which is usually regarded a concern of pragmatics and therefore more of a bonus to the book, but they try to explain why most in the discussion of presupposition can actually be accounted for purely semantically) and in the end a wrap-up involving predicate logic, lambda expressions and problems of variable bindining, however that chapter is rather dense and probably not most well suited as a gentle introduction to such formal representations. The rest is, I'd say, well readable.
I would NOT recommend Semantics in generative grammar by Heim & Kratzer (1998).
I think it's often used as a textbook in semantics classes and has its focus mostly on the interface between syntax and semantics which is an interesting approach, but IMO there are just too many things that are formally questionable.
I understand not every textbook has to be a Gamut (see below), but if you then still start introducing formal stuff, you should do it properly. You can not just randomly place lambda symbols in a syntax tree and act like you have a formal system now without even properly defining what you are doing.
Also, the book unfortunately doesn't cover intensions, which I think is important to at least have heard of in semantics.
Having said that, if you are interested in Montague semantics, there is no way around reading the original article on The Proper Treatment of Quantification in Ordinary English (PTQ) and maybe also Universal Grammar.
I know that the syntax rules with all these special symbols look complicated at first sight, but the essence of the paper (best exemplified by the well-known unicorn sentences) is an actually quite simple, yet important insight for the study of intensional semantics.
There is also Logic, Language and Meaning by L.T.F. Gamut (1991), two volumes (the first one a general logic introduction, the second one focussing on intensions).
I think it's very good for formal logic used in linguistics and it covers quite a lot and in good detail; I like it especially because it is one of the few textbooks that actually provide properly formulated and not just wishy-washy definitions that make you understand what is mathematically actually behind it. I frequently use it to take reliable definitions of basic concepts from.
However, people tend to find it harder to read for beginners, so if you're not already familiar with logic from mathematics or something else, it might be better to start with one of the other books mentioned.
Finally, if you want it a bit more gentle and from a more philosophical point of view, I know about Logic by Winfrid Hodges (1977/2001). It explains the basic ideas of logic, truth-functional semantics and calculi like natural deduction in a probably "softer" way than, e.g., Gamut, but it is not primarily motivated by linguistics.
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.
