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.
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 students can use to get feedback on their solutions to exercises.
If you want a rather concise introduction, Winter (2016) might be worth taking a look at.
Heim & Kratzer (1998) is a classic on the syntax-semantics interface, but I'm not a huge fan of it, because they use a kind of semi-formal notation without ever actually defining or even explaining such elementary concepts as lambda conversion, which I think is a bad thing to do in an introductory textbook.
Gamut (1991) is pretty good, the first volume provides an introduction to logic and the second volume is about intensional logic. It's perhaps a bit more technical than other introductions but doesn't fall short on detailed explanations. If you're specifically interested in intensional logic, type theory and Montague semantics and not so much a broader coverage of semantic topics, that one could be the first place to go.
Specifically for Montague grammar, Dowty, Wall & Peters (1981) could be said to be the standard reference. In order to make good use of it, it probably makes sense to have had some prior introduction to logic and formal semantics first.
To get an overview of the various topics semantics deals with, Kearns (2011) is a good place to start; if you're new to linguistic semantics it could be worth to start with the first chapter there before diving into the formal stuff, but for the latter other books are more suitable.
Coppock, Elizabeth & Champollion, Lucas (2020). Invitation to formal semantics. Manuscript, 20 August 2020 edition.
Dowty, David R., Wall, Robert & Peters, Stanley (1981). Introduction to Montague semantics. Springer Science & Business Media.
Gamut, LTF (1991). Logic, language, and meaning, Volume 1: Introduction to logic. University of Chicago Press.
Gamut, LTF (1991). Logic, language and meaning, Volume 2: Intensional logic and logical grammar. University of Chicago Press.
Heim, Irene & Kratzer, Angelika (1998). Semantics in generative grammar. Blackwell Oxford.
Kearns, Kate (2011). Semantics. Palgrave Macmillan, 2nd edition.
Winter, Yoad (2016). Elements of formal semantics: An introduction to the mathematical theory of meaning in natural language. Edinburgh University Press.
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.
