S. Artemov, "Unified Semantics for Modality and -terms via Proof Polynomials," to appear in Logic, Language and Computation'97, CSLI Publications, Stanford University, 1998.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Theorem 7.1 LPG Gamma 0 Gamma ) Delta iff LPG 0 Gamma ) Delta. J 7.12 Corollary. Cut elimination in LP. Every sequent derivable in LPG can be derived without the cut rule. Proof. Cut elimination for LP can be established by a direct system of reductions, and it has been done in [6] [7]. We may also get the cut elimination theorem for LP as a side product of the arithmetical completeness theorem for LP. Indeed, a straightforward analogue of Theorem 7.1 where LP 0 and LPG 0 are replaced by LP and LPG respectively holds. As in 7.1 it suffices to establish that if LPG 6 Gamma ) ....

....combinatory logic (cf. 73] 9.1 Definition. As usual (cf. 73] the intuitionistic version ILPG of LPG may be defined as the fragment of LPG consisting of sequents of the form Gamma ) Delta, there Delta contains at most one formula. The cut elimination theorem for ILPG was established in [6] [7]. 35 9.2 Definition. Under ground ( rule we mean the rule ( where the principal proof polynomial t contains no variables. An ILPG derivation D is pure if it uses no rules other than ( Delta) c) and ground ( It is clear that every pure derivation is normal since it has no ....

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S. Artemov, "Unified Semantics for Modality and -terms via Proof Polynomials," to appear in Logic, Language and Computation'97, CSLI Publications, Stanford University, 1998.

....on proofs that can be specified by means of modal logic Sergei N. Artemov Abstract Explicit modal logic was first sketched by Godel 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 ....

S. Artemov, "Unified Semantics for Modality and -terms via Proof Polynomials," to appear in Logic, Language and Computation'97, CSLI Publications, Stanford University, 1998 (?).

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