Efficient Rule-Matching for Hyper-Tableaux

14 pages•Published: November 25, 2013

Abstract

Over the past decades, a number of calculi for automated
reasoning have been proposed that share some core features:
1. proofs are built in a tableau/sequent style as trees where
nodes are labeled with literals, and 2. these proofs are expanded
by interpreting the problem clause set as a set of rules, and
requiring all negative literals in clauses to present on a branch
for expansion. This applies to hyper-tableaux, MGTP, coherent
logic, and others. Existing implementations typically spend much
of their time in the process of matching branch literals with the
negative literals of the input clauses. We present an
alternative to this matching process by applying a modified
version of the RETE algorithm. The RETE algorithm was developed
in the 1970s for production systems in artificial
intelligence. We exploit the similarities between the mentioned
calculi and production systems in order to make the RETE
algorithm solve the matching problem. We also investigate the
effect of working on several independent branches present in
tableau proof search but not in production systems.

Keyphrases: automated theorem proving, coherent logic, first-order logic, Rete

In: Konstantin Korovin, Stephan Schulz and Eugenia Ternovska (editors). IWIL 2012. The 9th International Workshop on the Implementation of Logics, vol 22, pages 4--17

Links:	https://easychair.org/publications/paper/SC7c
	https://doi.org/10.29007/r5m4