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Showing papers on "Modal operator published in 1981"


Journal ArticleDOI

58 citations


Journal ArticleDOI
TL;DR: A semantic account for modal logic is developed by considering only the values of sentences (and formulas) by subdividing truth into necessary truth and contingent truth (t) and falsity into contingent falsity and necessary falsity (impossibility: F).
Abstract: ?1. Four values. In this paper I will develop a semantic account for modal logic by considering only the values of sentences (and formulas). This account makes no use of possible worlds. To develop such an account, we must recognize four values. These are obtained by subdividing (plain) truth into necessary truth (T) and contingent truth (t); and by subdividing falsity into contingent falsity (f) and necessary falsity (impossibility: F). The semantic account results from reflecting on these concepts and on the meanings of the logical operators. To begin with, we shall consider the propositional language Lo. The language Lo has (1) infinitely many atomic sentences, (2) the two truth-functional connectives %, V, and the modal operator Cl. (Square brackets are used for punctuation.) The other logical expressions are defined as follows: Dl [A&B] =(def)-[ -A V -B], D2 [A v B] (def)[-A V B], D3 0 A =(def)FIp-A. I shall use matrices to give partial characterizations of the significance of logical expressions in Lo. For negation, this matrix is wholly adequate:

27 citations



Journal Article
TL;DR: In this article, the conditions générales d'utilisation (http://www.numdam.math.unipd.org/conditions) of the agreement with the Rendiconti del Seminario Matematico della Università di Padova are discussed.
Abstract: L’accès aux archives de la revue « Rendiconti del Seminario Matematico della Università di Padova » (http://rendiconti.math.unipd.it/) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/conditions). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.

3 citations