In this paper we refer to the modal logic GL, of which GL-Lin, is an extension, that is the closure under Modus Ponens and Necessitation of propositional calculus and some special modal axioms. Our interest in GL-Lin is due to the completeness results with a particular subset of arithmetical formulas, and with a subset of formulas of GL. The link between modal logic and Peano Arithmetic consists in interpreting all modal formulas in a particular set of formulas of PA, called consistency assertions. Using computational techniques, we also prove that GL-Lin is decidable and enjoys the finite model property.

The modal logic of the consistency assertion of Peano Arithmetic

SOLITRO, Ugo;
1983

Abstract

In this paper we refer to the modal logic GL, of which GL-Lin, is an extension, that is the closure under Modus Ponens and Necessitation of propositional calculus and some special modal axioms. Our interest in GL-Lin is due to the completeness results with a particular subset of arithmetical formulas, and with a subset of formulas of GL. The link between modal logic and Peano Arithmetic consists in interpreting all modal formulas in a particular set of formulas of PA, called consistency assertions. Using computational techniques, we also prove that GL-Lin is decidable and enjoys the finite model property.
modal logic, Peano arithmetic, proof theory
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11562/932226
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