Elimination of Redundant Links in Extended Connection Graphs

Abstract

The connection graph proof procedure [1, 2] allows us to remove a clause from the graph, if it is a tautology or a pure clause, i.e. if it is a clause which contains a literal which is not connected to any other literal in the graph.

This clause deletion rule can be transferred to links if we view a link as a potential clause: each link represents a potential factor, resolvent or paramodulant. Links which generate tautologies or pure clauses are called redundant links. Since non-redundant as well as redundant links are copied (i.e. inherited) in the process of a derivation, the elimination of redundant links as early as possible (i.e. immediately after their generation) prohibits their occasional exponential growth. We extend the connection graph proof procedure by several new types of links in order to formulate necessary and sufficient criteria that links are redundant. These criteria are used for an extension of the connection graph proof procedure by a reduction rule for redundant links which is currently being implemented and evaluated in the Markgraf Karl Refutation Procedure [4, 8]. These new links are also used to eliminate search on resolution-link inheritance [see 7]. The link-generation and inheritance rules for extended connection graphs are presented in [7].