I'm almost done reading Heim and Kratzer's Semantics in Generative Grammar and I'm looking for a good "second" book on formal semantics. Ideally, I would like it to emphasize the syntax-semantics interface like Heim and Kratzer do. Does anyone know of a book like that?
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 more logic can be found in Gamut (1991) (covering intensional logic and Montague Grammar) and Gregory (2015) (dealing some more with proof systems). A different kind of syntax-semantics that essentially derives a grammar from type theory (categorial grammar) is presented Carpenter (1998).
Of course, if you already have some knowledge of formal semantics, you could also consider taking a look at handbooks (collections of survey articles sketching the most fundamental problems and their proposed solutions, to get an overview of the core topics):
- Aloni, Maria & Dekker, Paul (eds.). 2016. The Cambridge Handbook of Formal Semantics. Cambridge University Press.
- Lappin, Shalom & Fox, Chris (eds.).1997- 2015. The Handbook of Contemporary Semantic Theory. Wiley Blackwell.
- Portner, Paul H. & Partee, Barbara H. (eds.) (2008). Formal semantics: The essential readings. Vol. 7. John Wiley & Sons.
- van Benthem, Johan & ter Meulen, Alice (eds.). 1997. Handbook of logic and language. Elesvier.
- von Heusinger, Klaus & Maienborn, Claudia & Portner, Paul (eds.). 2011-2012. Semantics: An International Handbook of Natural Language Meaning. De Gruyter Mouton.