Journal Article10.1093/LOGCOM/6.6.819
A-Ordered Tableaux
Reiner Hähnle,Stefan Klingenbeck +1 more
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TL;DR: It is shown that regular A-ordered tableaux are a proof confluent refinement of tableaux and that A-orderings of literals together with well-known connection refinements yield an incomplete proof procedure.
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Abstract: 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.
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Citations
Depth-first proof search without backtracking for free-variable clausal tableaux
TL;DR: This work analyses the problem of constructing a deterministic proof procedure for free-variable clausal tableaux that performs depth-first proof search without backtracking and presents a solution based on a fairness strategy that uses weight orderings and a notion of tableau subsumption to avoid proof cycles.
16
Ordered Tableaux: Extensions and Applications
Reiner Hähnle,Christian Pape +1 more
- 13 May 1997
TL;DR: In this paper several conceptual extensions to the theory of order-restricted free variable clausal tableaux which was initiated in [9, 8] are presented: atom orderings are replaced by the more general concept of a selection function, the substitutivity condition required for lifting is for certain variants of the calculus replaced by a much weaker assumption.
•Dissertation
Tableau-Based Reasoning for Decidable Fragments of First-Order Logic
Hilverd Geert Reker
- 17 Mar 2012
TL;DR: This thesis reviews existing work on incorporating unification into first-order and modal tableau procedures, shows how the closure fairness problem arises, and discusses existing solutions to it, and outlines a calculus which addresses theclosure fairness problem.
7
Discoveries and experiments in the automation of mathematical reasoning
Benjamin Price Shults,Larry M. Hines,Robert S. Boyer +2 more
- 01 Jan 1997
TL;DR: In this article, the authors propose a method to solve the problem of "uniformity" and "uncertainty" in the context of data mining, and propose a solution.
5
Rule Refinement for Semantic Tableau Calculi
Dmitry Tishkovsky,Renate A. Schmidt +1 more
- 25 Sep 2017
TL;DR: An easy to apply, general principle of atomic rule refinement is introduced, which depends on a purely syntactic condition that can be easily verified, which allows for routine development of hypertableau-like calculi for logics with disjunction and negation.
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First-Order Logic and Automated Theorem Proving
Melvin Fitting,David Gries +1 more
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TL;DR: This monograph on classical logic presents fundamental concepts and results in a rigorous mathematical style and is intended for those interested in computer science and mathematics at the beginning graduate level.
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Rewrite-based Equational Theorem Proving with Selection and Simplification
Leo Bachmair,Harald Ganzinger +1 more
TL;DR: This paper forms an abstract notion of redundancy and shows that the deletion of redundant clauses during the theorem proving process preserves refutation completeness, and presents various refutationally complete calculi for first-order clauses with equality that allow for arbitrary selection of negative atoms in clauses.
SETHEO: a high-performance theorem prover
TL;DR: A sound and complete theorem prover for first-order logic is presented, which is based on the connection method, and incorporates a powerful preprocessing module for a reduction of the input formula.
251
Dissolution: making paths vanish
Neil V. Murray,Erik Rosenthal +1 more
TL;DR: A rule of inference that operates on formulas in negation normal form and that employs a representation called semantic graphs is introduced, which has several advantages in comparison with many other reference technologies.
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