Routledge Dictionary of Language and Linguistics
In two-value formal logic the semantic evaluation of propositions with ‘true’ or ‘false.’ A proposition is ‘true,’ if the state of affairs designated by it is true, otherwise it is ‘false.’ The assertion It’s raining is true only if it is raining. Some forms of logic use a three-value system which specifies not only true and false propositions, but also ‘indefinite’ propositions (see Blau 1978) (
truth table for more information on the study of the truth values of complex propositions based on the truth values of their component propositions and their logical connectives). The concept of assigning
| | Negation | Adjunction | Conjunction | Implication | Equivalence | Contravalence | Tautology | Contradiction |
| p | q | ¬p | p  q | p Λ q | p→q | p↔q | p  q | e. g. p→ (q→p) | e.g. pΛ(qΛ¬q) |
| t | t | f | t | t | t | t | f | t | f |
| t | f | f | t | f | f | f | t | t | f |
| f | t | t | t | f | t | f | t | t | f |
| f | f | t | f | f | t | t | f | t | f |
extensional truth values in propositional logic is fundamental to the semantic description of natural languages ( Montague grammar).
References
Bäuerle, R. et al (eds) 1979. Semantics from different points of view. Berlin.
Black, M. 1948. The semantic definition of truth. Analysis 8.49–62.
Blau, U. 1978. Die dreiwertige Logik der Sprache. Berlin.
Davidson, D. 1967.
Truth and meaning. Synthese 17.304–33.
Evans, G. and J.McDowell (eds) 1976. Meaning and truth. Oxford.
Kripke, S. 1975. Outline of a theory of truth. JP 72.690–716.
Linsky, L. (ed.) 1952. Semantics and the philosophy of language. Chicago, IL.
Quine, W.V.O. 1970. Philosophy of logic. Englewood Cliffs, NJ. (2nd rev. edn 1973.)
Tarski, A. 1944. The semantic approach of truth and foundation of semantics. PPR 4.341–75.
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