English
 
User Manual Privacy Policy Disclaimer Contact us
  Advanced SearchBrowse

Item

ITEM ACTIONSEXPORT

Released

Journal Article

Logic with Equality: Partisan Corroboration and Shifted Pairing

MPS-Authors
/persons/resource/persons45662

Veanes,  Margus
Programming Logics, MPI for Informatics, Max Planck Society;

Locator
There are no locators available
Fulltext (public)
There are no public fulltexts available
Supplementary Material (public)
There is no public supplementary material available
Citation

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


Cite as: http://hdl.handle.net/11858/00-001M-0000-000F-365A-9
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}.