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Abstract: Explicit modal logic was first sketched by Gödel in [16] as the logic with the atoms "t is a proof of F". The complete axiomatization of the Logic of Proofs LP was found in [4] (see also [6],[7],[18]). In this paper we establish a sort of a functional completeness property of proof polynomials which constitute the system of proof terms in LP. Proof polynomials are built from variables and constants by three operations on proofs: "\Delta" (application), "!" (proof checker), and "+" (choice).... (Update)
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BibTeX entry: (Update)
@misc{ artemov-operations,
author = "Sergei Artemov",
title = "Operations on Proofs That Can Be Specified By Means of Modal Logic",
url = "citeseer.ist.psu.edu/199386.html" }
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6 Some Remarks on the Notion of Proof (context) - Myhill - 1960
5 Proof realizations of typed -calculi (context) - Artemov - 1997
5 Kolmogorov logic of problems and a provability interpretatio.. (context) - Artemov - 1990
4 Arithmetical necessity, provability and intuitionistic logic (context) - Goldblatt - 1978
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4 Intensional Set Theory (context) - Myhill - 1985
4 The logic of provability (context) - Kuznetsov, Yu - 1976
4 Intensional Mathematics and Constructive Mathematics (context) - Shapiro - 1985
3 Classical extensions of intuitionistic mathematics (context) - Kleene - 1965
3 Explicit provability: the intended semantics for intuitionis.. - Artemov - 1998
2 Realizability (context) - Troelstra - 1998
2 Constructivism in Marthematics (context) - Troelstra, van Dalen - 1988
2 Unified Semantics for Modality and -terms via Proof Polynomi.. (context) - Artemov - 1998
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