ML-1995-02: Modal Deduction in Second-Order Logic and Set Theory

ML-1995-02: van Benthem, Johan and D'Agostino, Giovanna and Montanari, Angelo and Policriti, Alberto (1995) Modal Deduction in Second-Order Logic and Set Theory. [Report]

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We investigate modal deduction through translation into standard logic and set theory. Derivability in the minimal modal logic is captured precisely by translation into a weak, computationally attractive set theory \Omega. This approach is shown equivalent to working with standard first­order translations of modal formulas in a theory of general frames. Next, deduction in a more powerful second­order logic of general frames is shown equivalent with set­theoretic derivability in an `admissible variant' of \Omega. Our methods are mainly model­theoretic and set­theoretic, and they admit extension to richer languages than that of basic modal logic.

Item Type: Report
Report Nr: ML-1995-02
Series Name: Mathematical Logic and Foundations (ML)
Year: 1995
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40

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