Formal semantics (natural language)

Formal semantics is the study of grammatical meaning in natural languages using formal tools from logic and theoretical computer science. It is an interdisciplinary field, sometimes regarded as a subfield of both linguistics and philosophy of language. It provides accounts of what linguistic expressions mean and how their meanings are composed from the meanings of their parts. The enterprise of formal semantics can be thought of as that of reverse engineering the semantic components of natural languages' grammars.


Aims and scope

Formal semantics studies the denotations of natural language expressions. High-level concerns include compositionality, nature of meaning, and reference. Key topic areas include scope, modality, anaphora, tense, and aspect. Semantics is distinct from pragmatics, which encompasses aspects of meaning which arise from interaction and communicative intent.

Formal semantics is an interdisciplinary field, often viewed as a subfield of both linguistics and philosophy, while also incorporating work from computer science, mathematical logic, and cognitive psychology. Depending on their particular background, formal semanticists may vary in how they view the nature of their enterprise. Particularly within philosophy, some formal semanticists adopt a Platonistic ontology and an externalist view of meaning.[1] Others, particularly within linguistics, tend to view it as part of the study of linguistic cognition. As a result, philosophers put more of an emphasis on conceptual issues while linguists are more likely to focus on the syntax-semantics interface and crosslinguistic variation.[2][3]


Formal semantics emerged as a major area of research in the early 1970s, with the pioneering work of the philosopher and logician Richard Montague. Montague proposed a formal system now known as Montague grammar which consisted of a novel syntactic formalism for English, a logical system called Intensional logic, and a set of homomorphic translation rules which linked the two. Montague grammar has been compared to a Rube Goldberg machine, but it was earth-shattering when first proposed, and many of its fundamental insights survive in the various semantic models which have superseded it.[4][5][6]

Montague Grammar was a major advance because it showed that natural languages could be treated as interpreted formal languages. Before Montague, many linguists had doubted that language could be understood in terms of logic, and logicians tended to view logic as a replacement for natural language rather than a tool for analyzing it.[6] Montague's work was published during the Linguistics Wars, and was not initially well-received. It used then-niche formal tools, departed from then-standard assumptions about syntax, and its goals were at odds with those of linguists. While linguists wanted a restrictive framework which could only predict phenomena that occur in the grammars of actual human languages, Montague sought a more flexible framework which could characterize the concept of meaning in general. At one conference, Montague told Barbara Partee that she was "the only linguist who it is not the case that I can’t talk to".[6]

In subsequent work, Partee developed a more linguistically plausible system which combined insights from both Montague Grammar and transformational grammar. Subsequent work by Irene Heim, Angelika Kratzer, Tanya Reinhart, Robert May and others showed that Montague's key ideas could be more deeply worked into the generative framework by positing a level of syntactic representation called logical form which undergoes semantic interpretation.[6] However, others such as Gerald Gazdar proposed models of the syntax-semantics interface which stayed closer to Montague's proposal, providing a system of interpretation in which denotations could be computed on the basis of surface structures. These approaches live on in frameworks such as categorial grammar.[7][6]

Varieties of formal semantics

Most current approaches to formal semantics fall within the paradigm of the so-called truth-conditional semantics, which attempts to explain the meaning of a sentence by providing the conditions under which it would be true.[1][8] However, several adherents to the truth-conditional program have also argued that there is more to meaning than truth-conditions.[9] Alternative approaches include more cognitive-oriented proposals such as Pietroski's treatment of meanings as instructions to build concepts, sentences being devoid of truth-conditions.[10] 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.[11]

Cognitive semantics emerged and developed as a reaction against formal semantics, but there have been recently several attempts at reconciling both positions.[12]

See also


  1. ^ a b Lewis, David (December 1970). "General Semantics". Synthese. 22 (1/2): 18–67. doi:10.1007/BF00413598.
  2. ^ Seth Yalcin (2014). "Semantics and metasemantics in the context of generative grammar". In Alexis Burgess; Brett Sherman (eds.). Metasemantics: new essays on the foundations of meaning. Oxford University Press. ISBN 9780199669592.
  3. ^ Borg, Emma (2004). Minimal semantics. Oxford University Press. ISBN 978-0199206926.
  4. ^ Barwise, Jon; Cooper, Robin (1981). "Generalized quantifiers and natural language". In Kulas, J; Fetzer, J.H.; Rankin, T.L. (eds.). Philosophy, Language, and Artificial Intelligence. Springer. doi:10.1007/978-94-009-2727-8_10.
  5. ^ For a very readable and succinct overview of how formal semantics found its way into linguistics, see The formal approach to meaning: Formal semantics and its recent developments by Barbara Abbott. In: Journal of Foreign Languages (Shanghai), 119:1 (January 1999), 2–20.
  6. ^ a b c d e Partee, Barbara (2011). "Formal semantics: Origins, issues, early impact". The Baltic International Yearbook of Cognition, Logic and Communication. 6.
  7. ^ Michael Moortgat (1988). Categorial investigations: logical and linguistic aspects of the Lambek calculus. Walter de Gruyter. ISBN 978-90-6765-387-9. Retrieved 5 April 2011.
  8. ^ Irene Heim; Angelika Kratzer (1998). Semantics in generative grammar. Wiley-Blackwell. ISBN 978-0-631-19713-3.
  9. ^ Stefano Predelli (2013). Meaning without truth. Oxford Scholarship. ISBN 9780199695638.
  10. ^ Paul Pietroski (2018). Conjoining meanings. Oxford University Press. ISBN 9780198812722.
  11. ^ Harry Bunt (2008). Computing Meaning. 3. Springer. p. 458. ISBN 978-1-4020-5957-5.
  12. ^ Hamm, Fritz; Kamp, Hans; Lambalgen, Michiel van (2006-09-01). "There is no opposition between Formal and Cognitive Semantics". Theoretical Linguistics. 32 (1): 1–40. CiteSeerX doi:10.1515/tl.2006.001. ISSN 1613-4060.

Further reading

  • Max Cresswell (2006). "Formal semantics". In Michael Devitt, Richard Hanley (ed.). 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.[self-published source]
  • Glyn V. Morrill (1994). Type logical grammar: categorial logic of signs. Springer. ISBN 978-0-7923-3095-0.
  • Reinhard Muskens. Type-logical Semantics[permanent dead link]. 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.)

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