Routledge Dictionary of Language and Linguistics
formal logic (also extensional/mathematical/ symbolic logic, logistics)
As the study of correct and logical thought, logic is fundamental to all theoretical and empirical sciences in that it provides a method for arriving at valid conclusions and at necessarily true sentences required to propose and test scientific theories. To represent the logical form of sentences formal logic uses a formalized artificial language with a distinctive inventory of symbols (see p. xvii) that can represent certain phenomena of natural language, but dispenses with all stylistic variants as well as ambiguity and vagueness. The main focus of formal logic is on (a) the study of logical connections of propositions and their truth values (
propositional logic), (b) the study of the internal structure of propositions ( predicate logic), (c) the theory of concluding and proving, and (d) the description of inferences ( presupposition).
References
Allwood, J., L.-G. Andersson, and Ö.Dahl. 1977. Logic in linguistics. Cambridge.
Cresswell, M.J. 1973. Logics and languages. London.
Feys, R. and F.Fitch. 1969. Dictionary of symbols of mathematical logic. Amsterdam.
Gabbay, D.M. and F.Guenthner (eds) 1983–9. Handbook of philosophical logic, 4 vols. Dordrecht.
Guttenplan, S. 1986. The languages of logic. Oxford.
Hodges, W. 1983. Elementary logic. In D.M.Gabbay and F.Guenthner (eds), Handbook of philosophical logic. Dordrecht. Vol.
2, 1–131.
Marciszewski, W. (ed.) 1981. Dictionary of logic as applied in the study of language: concepts, methods, theories. The Hague.
McCawley, J.D. 1981. Everything that linguists have always wanted to know about logic but were ashamed to ask. Oxford.
Moore, R.C. 1993. Logic and representation. Chicago, IL.
Quine, W.V.O. 1950. Methods of logic. New York.
Reichenbach, H. 1947. Elements of symbolic logic. New York (5th edn 1956.)
Van Fraassen, B. 1971. Formal semantics and logic. New York.
Wall, R. 1972. Introduction to mathematical linguistics. Englewood Cliffs, NJ.
Zierer, E. 1972. Formal logic and linguistics. The Hague.
Bibliographies
Partee, B., S.Sabsay, and J.Soper. 1971. Bibliography: logic and language. Bloomington. IN.
Petöfi, J.S. (ed.) 1978. Logic and the formal theory of natural language: selective bibliography. Hamburg.
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