A-Ordered Tableaux

In resolution proof procedures refinements based on A-orderings of literals have a long tradition and are well investigated. In tableau proof proceduressuch refinements were only recently introduced by the authors of the present paper. In this paper we prove the following results: we give a completeness proof of A-ordered ground clause tableaux which is a lot easier to follow than the previous one. The technique used in the proof is extended to the non-clausal case as well as to the non-ground case and we introduce an ordered version of Hintikka sets that shares the model existence property of standard Hintikks sets. We show that A-ordered tableaux are a proof confluent refinement of tableaux and that Aordered tableaux together with the connection refinement yield an incomplete proof procedure. We introduce A-ordered first-order NNF tableaux, prove their completeness, and we briefly discuss implementation issues.