Possible world semantics for first-order logic of proofs

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Abstract

In the tech report Artemov and Yavorskaya (Sidon) (2011) [4] an elegant formulation of the first-order logic of proofs was given, FOLP. This logic plays a fundamental role in providing an arithmetic semantics for first-order intuitionistic logic, as was shown. In particular, the tech report proved an arithmetic completeness theorem, and a realization theorem for FOLP. In this paper we provide a possible-world semantics for FOLP, based on the propositional semantics of Fitting (2005) [5]. We also give an Mkrtychev semantics. Motivation and intuition for FOLP can be found in Artemov and Yavorskaya (Sidon) (2011) [4], and are not fully discussed here.

This paper is dedicated to Sergei Artemov, an honored colleague and friend, who has made wonderful things for the rest of us to play with.

MSC

03B45
03B60
03F45
03F55

Keywords

Justification logic
Logic of proofs
Possible world semantics
First-order
Completeness

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