Formal semantics has roots in the disciplines of logic, philosophy and mathematics with pioneering work by Frege and Russell in the early 20th Century and work in the first half of the 20th Century by Tarski and Carnap in particular; it emerged as a sub-discipline in linguistics in the 1970s from seminal work in the field of logic by Richard Montague.

Tarski's model theory (going back to the 1930s) involved the representation of meaning of formal logic using mathematical concepts in terms of set theory; it embodied both aspects of meaning that philosophers and logicians during that period had worked out — "Sinn" ("sense") and "Bedeutung" ("reference") in Frege's terms, "intension" and "extension" in Carnap's terms. Tarski's model theoretic approach to formal logic opened up an opportunity for work on the semantics of natural languages. Drawing on Tarski's work on designed formal systems, Montague (e.g. 1970) set out to treat “English as a formal language”. This filled a void in linguistics since linguists had not yet developed an account of meaning along formal lines and inspired logicians and linguists to respond. A number of linguists, including Dowty, Bach, Partee, and Keenan, thereafter worked to develop formal semantics as an approach within linguistics. This work within linguistics has also included relating formal semantics to different theories of syntax, including categorial grammar and lexical functional grammar. Here an important aspect in the pairing of syntax and semantics has been the principle of compositionality. Extending the domain of formal semantics from propositions to phenomena within discourse, Kamp (e.g. 1981) has developed discourse representation theory (see also Kamp and Reyle, 1993), which covers discourse phenomena including context sensitive expressions such as pronouns and presuppositions; further developments include “dynamic semantics”.

For linguists before Montague, the semantic explication of ambiguity, anomaly and synonymy formed the major task where the key questions were related to the “readings” of a sentence — how many readings a sentence has and which sentences share readings? As the individuation of readings is possible, there were always significant disagreements about data. The introduction of truth-condition as the basic semantic property of a sentence by Montague contributed to the expansion of semantics research (or research on semantics). The principle of entailment (closely associated with presupposition) has been a central semantic concern in logic and likewise remains central to formal linguistics. Issues such as whether expressions refer to objects or to concepts and whether semantics is a branch of mathematics or psychology (as Chomskyans treat it later on) are still questions in formal linguistics. Natural language metaphysics is another important area within formal semantics connecting it to linguistics typology.

Formal semantics, thus, starting its journey in the works of Montague, has become an influential tradition in semantics. In recent years fruitful applications of many aspects of formal semantics have been made in computational semantics and natural language processing, and “many innovations (such as methods for working with underspecified representations rather than with large sets of meanings of ambiguous expressions) have in turn come from the computational semantics community” (Partee, 2001).

References

Kamp, Hans. 1981. “A theory of truth and semantic interpretation.” In J. Groenendijk, T. Janssen and M. Stokhof (eds.). Formal methods in the study of language. Amsterdam: Mathematical Center tracts, 277--322.

Kamp, Hans. & Reyle, Uwe. 1993. From Discourse to Logic. Introduction to Model theoretic Semantics of Natural Language, Formal Logic and Discourse Representation Theory, Dordrecht ,Kluwer Academic Publishers.

Montague, Richard. 1970. “Universal Grammar,” Theoria, 36, 373-98.

Partee, Barbara Hall. 2001. “Montague grammar.” In Smelser, Neil J. and Baltes, Paul B. (eds). International encyclopedia of the social and behavioural sciences. Oxford: Pergamon/Elsevier Science.

Recommended test-books

Allan, Keith. 2001. Natural language semantics. Oxford: Blackwell Publishers.

Bach, Emmon. 1989. Informal lectures on formal semantics. Albany, NY: State University of New York Press.

Cann,  Ronnie. 1993. Formal semantics: an Introduction. Cambridge University Press.

Dowty, D., R. Wall & S. Peters. 1981. Introduction to Montague semantics. Dordrecht: Reidel. 

Lappin, Shalom (ed.). 1996. The handbook of contemporary semantic theory. Oxford: Blackwell.

Summary Written By

Abhishek Kumar

Department of Linguistics

Macquarie University