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In "linguistics, formal semantics seeks to understand "linguistic meaning by constructing precise mathematical models of the principles that speakers use to define relations between expressions in a "natural language and the world that supports meaningful discourse. The mathematical tools used are the confluence of "formal logic and "formal language theory, especially "typed lambda calculi.
Linguists rarely employed formal semantics until "Richard Montague showed how English (or any natural language) could be treated like a formal language. His contribution to linguistic semantics, which is now known as "Montague grammar, was the basis for further developments, like the "categorial grammar of "Bar-Hillel and colleagues, and the more recent "type-logical semantics (or grammar) based on "Lambek calculus.
Another line of inquiry, using "linear logic, is "Glue semantics, which is based on the idea of "interpretation as deduction", closely related to the "parsing as deduction" paradigm of categorial grammar.
"Cognitive semantics emerged and developed as a reaction against formal semantics, but there have been recently several attempts at reconciling both positions.
- Max Cresswell (2006). "Formal semantics". In Michael Devitt, Richard Hanley. The Blackwell guide to the philosophy of language. Wiley-Blackwell. "ISBN "978-0-631-23142-4. A very accessible overview of the main ideas in the field.
- John I. Saeed (2008). Semantics. Introducing linguistics (3rd ed.). Wiley-Blackwell. "ISBN "978-1-4051-5639-4. Chapter 10, Formal semantics, contains the best chapter-level coverage of the main technical directions
- Johan van Benthem; Alice Ter Meulen (2010). Handbook of Logic and Language (2nd ed.). Elsevier. "ISBN "978-0-444-53726-3. The most comprehensive reference in the area.
- Emmon W. Bach (1989). Informal lectures on formal semantics. SUNY Press. "ISBN "978-0-88706-772-3. One of the first textbooks. Accessible to undergraduates.
- Ronnie Cann (1993). Formal semantics: an introduction. Cambridge University Press. "ISBN "978-0-521-37610-5.
- Irene Heim; Angelika Kratzer (1998). Semantics in generative grammar. Wiley-Blackwell. "ISBN "978-0-631-19713-3.
- Gennaro Chierchia; "Sally McConnell-Ginet (2000). Meaning and grammar: an introduction to semantics (2nd ed.). "MIT Press. "ISBN "978-0-262-53164-1.
- Sean A. Fulop (2004). On the Logic and Learning of Language. Trafford Publishing. "ISBN "978-1-4120-2381-8.
- Glyn V. Morrill (1994). Type logical grammar: categorial logic of signs. Springer. "ISBN "978-0-7923-3095-0.
- Reinhard Muskens Type-logical Semantics to appear in the Routledge Encyclopedia of Philosophy Online.
- Bob Carpenter (1998). Type-logical semantics. MIT Press. "ISBN "978-0-262-53149-8.
- Johan van Benthem (1995). Language in action: categories, lambdas, and dynamic logic. MIT Press. "ISBN "978-0-262-72024-3.
- Barbara H. Partee: Reflections of a formal semanticist as of Feb 2005. Ample historical information. (an extended version of the introductory essay in Barbara H. Partee: Compositionality in Formal Semantics: Selected Papers of Barbara Partee. Blackwell Publishers, Oxford, 2004.)