First-order logic and automated theorem proving
First-order logic and automated theorem proving
An efficient strategy for non-Horn deductive databases
Selected papers of the workshop on Deductive database theory
Journal of Automated Reasoning
Consolution as a framework for comparing calculi
Journal of Symbolic Computation
Ordered Semantic Hyper-Linking
Journal of Automated Reasoning
Positive Unit Hyperresolution Tableaux and Their Application to Minimal Model Generation
Journal of Automated Reasoning
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
A Tableau Calculus for Minimal Model Reasoning
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
The Disconnection Method - A Confluent Integration of Unification in the Analytic Framework
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Tableaux for Diagnosis Applications
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Ordered Tableaux: Extensions and Applications
TABLEAUX '97 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Hyper Tableau - The Next Generation
TABLEAUX '98 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
SATCHMO: A Theorem Prover Implemented in Prolog
Proceedings of the 9th International Conference on Automated Deduction
Semantically Guided First-Order Theorem Proving using Hyper-Linking
CADE-12 Proceedings of the 12th International Conference on Automated Deduction
Non-Horn Magic Sets to Incorporate Top-down Inference into Bottom-up Theorem Proving
CADE-14 Proceedings of the 14th International Conference on Automated Deduction
Using Matings for Pruning Connection Tableaux
CADE-15 Proceedings of the 15th International Conference on Automated Deduction: Automated Deduction
FDPLL - A First Order Davis-Putnam-Longeman-Loveland Procedure
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
DCTP - A Disconnection Calculus Theorem Prover - System Abstract
IJCAR '01 Proceedings of the First International Joint Conference on Automated Reasoning
SATCHMOREBID: SATCHMO(RE) with BIDirectional relevancy
New Generation Computing
The model evolution calculus as a first-order DPLL method
Artificial Intelligence
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
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A family of tableau methods, called iordered semantic hyper (iOSH) itableau methods for first-order theories with function symbols, is presented. These methods permit semantic information to guide the search for a proof. They also may make use of orderings on literals, clauses, and interpretations to guide the search. In a typical tableau, the branches represent conjunctions of literals, and the tableau represents the disjunction of the branches. An OSH tableau is as usual except that each branch iB has an interpretation iI0[iB] associated with it, where iI0 is an interpretation supplied at the beginning and iI0[iB] is the interpretation most like iI0 that satisfies iB. Only clauses that iI0[iB] falsifies may be used to expand the branch iB, thus restricting the kinds of tableau that can be constructed. This restriction guarantees the igoal sensitivity of these methods if iI0 is properly chosen. Certain choices of iI0 may produce a purely bottom-up tableau construction, while others may result in goal-oriented evaluation for a given query. The choices of which branch is selected for expansion and which clause is used to expand this branch are examined and their effects on the OSH tableau methods considered. A branch reordering method is also studied, as well as a branch pruning technique called icomplement modification, that adds additional literals to branches in a soundness-preserving manner. All members of the family of OSH tableaux are shown to be sound, complete, and proof convergent for refutations. Proof convergence means that any allowable sequence of operations will eventually find a proof, if one exists. OSH tableaux are powerful enough to be treated as a generalization of several classes of tableau discussed in the literature, including forward chaining and backward chaining procedures. Therefore, they can be used for efficient query processing.