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  Logic with Equality: Partisan Corroboration and Shifted Pairing

Gurevich, Y., & Veanes, M. (1999). Logic with Equality: Partisan Corroboration and Shifted Pairing. Information and Computation, 152(2), 205-235.

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 Creators:
Gurevich, Yuri, Author
Veanes, Margus1, Author           
Affiliations:
1Programming Logics, MPI for Informatics, Max Planck Society, ou_40045              

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 Abstract: Herbrand's theorem plays a fundamental role in automated theorem proving methods based on tableaux. The crucial step in procedures based on such methods can be described as the \emph{corroboration} problem or the \emph{Herbrand skeleton} problem, where, given a positive integer $m$, called \emph{multiplicity}, and a quantifier free formula, one seeks a valid disjunction of $m$ instantiations of that formula. In the presence of \emph{equality}, which is the case in this paper, this problem was recently shown to be undecidable. The main contributions of this paper are two theorems. The first, the \emph{Partisan Corroboration Theorem}, relates corroboration problems with different multiplicities. The second, the \emph{Shifted Pairing Theorem}, is a finite tree automata formalization of a technique for proving undecidability results through direct encodings of valid Turing machine computations. These theorems are used in the paper to explain and sharpen several recent undecidability results related to the \emph{corroboration} problem, the \emph{simultaneous rigid E-unification} problem and the \emph{prenex fragment of intuitionistic logic with equality}.

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Language(s): eng - English
 Dates: 2010-03-121999
 Publication Status: Issued
 Pages: -
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 Table of Contents: -
 Rev. Type: Peer
 Identifiers: eDoc: 519740
Other: Local-ID: C1256104005ECAFC-BF6765C77376770AC125675B0065156D-GurevichVeanes99
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Title: Information and Computation
Source Genre: Journal
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Pages: - Volume / Issue: 152 (2) Sequence Number: - Start / End Page: 205 - 235 Identifier: -