Semantic Tableaux with Ordering Restrictions

The aim of this paper is to make restriction strategies based on orderings of the Herbrand universe available for semantic tableau-like calculi as well. A marriage of tableaux and ordering restriction strategies seems to be most promising in applications where generation of counter examples is required. In this paper, starting out from semantic trees, we develop a formal tool called refutation graphs, which (i) serves as a basis for completeness proofs of both resolution and tableaux, and (ii) is compatible with so-called A-ordering restrictions. The main result is a rst-order ground tableau procedure complete for A-ordering restrictions .