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 procedures such 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 A-ordered 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

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 procedures such 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 A-ordered 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

Programmverifikationssystem Tatzelwurm. Weiterentwicklung während des KORSO-Projekts

Der Bericht enthält eine kurze Darstellung der Entwicklungsarbeiten, die im Rahmen des KORSO-Projekts erfolgt sind. Eine Versionsverwaltung erlaubt den Einsatz des Verifikationssystems während der Programmentwicklungsphase. Zum Beweis der in allen Phasen der Softwareentwicklung anfallenden Verifikations- bedingungen wurde der Beweiser erheblich weiterentwickelt. Der Benutzer hat die Möglichkeit, eigene Beweisregeln zu definieren. Eine Sprache zur Formulierung von Beweisplnen erleichtert die während der Entwicklung von korrekter Software oftmals notwendige Wiederholung von Beweisen. Mit Hilfsmitteln zur Erzeugung von Gegenbeispielen bei unbeweisbaren Formeln erhält der Anwender nützliche Hinweise zur Lokalisierung von Fehlern

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 first-order ground tableau procedure complete for A-ordering restrictions. Introduction In recent years one could observe a kind of renaissance of tableau-related methods in automated theorem proving after the field has been dominated by resolution approaches for many years 2 . Tableaux are easy to adjust to nonclassical logics, and they have already a number of advantages for classical first-order logic that..

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 procedures such 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 one published previously. 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 Hintikka sets. We show that regular A-ordered tableaux are a proof confluent refinement of tableaux and that A-ordered tableaux together with well-known connection refinements yield an incomplete proof procedure. We introduce regular A-ordered firstorder NNF tableaux, prove their completeness, and we briefly discuss implementation issues. 1 Introduction In resolution proof ..