Graph Algorithms for Improving Type-Logical Proof Search

Abstract: Proof nets are a graph theoretical representation of proofs in various fragments of type-logical grammar. In spite of this basis in graph theory, there has been relatively little attention to the use of graph theoretic algorithms for type-logical proof search. In this paper we will look at several ways in which standard graph theoretic algorithms can be used to restrict the search space. In particular, we will provide an O(n4) algorithm for selecting an optimal axiom link at any stage in the proof search as well as a O(kn3) algorithm for selecting the k best proof candidates.