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Abstract: The intended meaning of intuitionistic logic is given by the Brouwer-Heyting-Kolmogorov (BHK) semantics which informally defines intuitionistic truth as provability and specifies the intuitionistic connectives via operations on proofs. The natural problem of formalizing the BHK semantics and establishing the completeness of propositional intuitionistic logic Int with respect to this semantics remained open until recently. This question turned out to be a part of the more general problem of the ... (Update)
Context of citations to this paper: More
...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...
...( s t) B ( c) c : A 5 where A is an axiom A0 A4 from section 2, and c is a proof constant. 3.1 Proposition. [2], 3] LPGi ) F i LPi V F . The proof proceeds by a straightforward induction both ways. The cut elimination theorem for LPGi was...
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BibTeX entry: (Update)
S. Artemov, "Explicit provability: the intended semantics for intuitionistic and modal logic" Tech. Rep. CFIS 98-10, Cornell University, September 1998. http://citeseer.ist.psu.edu/article/artemov98explicit.html More
@misc{ artemov98explicit,
author = "S. Artemov",
title = "Explicit provability: the intended semantics for intuitionistic and modal
logic",
text = "S. Artemov, Explicit provability: the intended semantics for intuitionistic
and modal logic Tech. Rep. CFIS 98-10, Cornell University, September 1998.",
year = "1998",
url = "citeseer.ist.psu.edu/article/artemov98explicit.html" }
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Documents on the same site (http://www.math.cornell.edu/~artemov/publ.html): More
Deep Isomorphism of Modal Derivations and λ-Terms - Artemov (1999) (Correct)
Logic of Proofs: a Unified Semantics for Modality and lambda-Terms - Artemov (1998) (Correct)
Proof Realizations of Typed lambda-Calculi - Artemov (1997) (Correct)
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