## Unified Semantics for Modality and lambda-terms via Proof Polynomials

Citations: | 3 - 1 self |

### BibTeX

@MISC{Artemov_unifiedsemantics,

author = {Sergei N. Artemov},

title = {Unified Semantics for Modality and lambda-terms via Proof Polynomials},

year = {}

}

### OpenURL

### Abstract

It is shown that the modal logic S4, simple -calculus and modal -calculus admit a realization in a very simple propositional logical system LP , which has an exact provability semantics. In LP both modality and -terms become objects of the same nature, namely, proof polynomials. The provability interpretation of modal -terms presented here may be regarded as a system-independent generalization of the Curry-Howard isomorphism of proofs and -terms. 1 Introduction The Logic of Proofs (LP , see Section 2) is a system in the propositional language with an extra basic proposition t : F for "t is a proof of F ". LP is supplied with a formal provability semantics, completeness theorems and decidability algorithms ([3], [4], [5]). In this paper it is shown that LP naturally encompasses -calculi corresponding to intuitionistic and modal logics, and combinatory logic. In addition, LP is strictly more expressive because it admits arbitrary combinations of ":" and propositional connectives. The id...