On Graph Refutation for Relational Inclusions

Abstract

We introduce a graphical refutation calculus for relational inclusions: it reduces establishing a relational inclusion to establishing that a graph constructed from it has empty extension. This sound and complete calculus is conceptually simpler and easier to use than the usual ones

A Graph Calculus for Predicate Logic

“…Graph calculi rely on two-dimensional representations providing better visualization [2]. 1 In the realm of binary relations, a simple calculus (with linear derivations) [2,3] was extended for handling complement: direct calculi [5,7] and refutation calculi [13]. Our new calculus is a further extension, inheriting much of the earlier terminology (such as 'graph', 'slice' and 'arc'), together with some ideas from Peirce's diagrams for relations [11,4].…”