Modal Logic and Set Theory:
a Set-Theoretic Interpretation of Modal Logic

Giovanna D'Agostino, Angelo Montanari, and Alberto Policriti

Università di Udine
Dipartimento di Matematica e Informatica
Via delle Scienze 206
33100 Udine
Italy.
dagostino@dimi.uniud.it, http://www.dimi.uniud.it/~dagostin
montana@dimi.uniud.it, http://www.dimi.uniud.it/~montana
policriti@dimi.uniud.it http://www.dimi.uniud.it/~policrit

Abstract

In this paper, we describe a novel set-theoretic interpretation of modal logic and show how it allows us to build promising bridges between modal deduction and set-theoretic reasoning. More specifically, we describe a translation technique that maps modal formulae into set-theoretic terms, thus making it possible to successfully exploit derivability in first-order set theories to implement derivability in modal logic.

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