First-order logic and automated theorem proving
First-order logic and automated theorem proving
JELIA '96 Proceedings of the European Workshop on Logics in Artificial Intelligence
Non-elementary Speedups between Different Versions of Tableaux
TABLEAUX '95 Proceedings of the 4th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
Automated Deduction and Formal Methods
CAV '96 Proceedings of the 8th International Conference on Computer Aided Verification
On evaluating decision procedures for modal logic
IJCAI'97 Proceedings of the 15th international joint conference on Artifical intelligence - Volume 1
Anytime approximate model reasoning
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
Using Resolution for Testing Modal Satisfiability and Building Models
Journal of Automated Reasoning
Reduction Theorems for Boolean Formulas Using Delta-Trees
JELIA '00 Proceedings of the European Workshop on Logics in Artificial Intelligence
TABLEAUX '99 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Towards an Efficient Tableau Method for Boolean Circuit Satisfiability Checking
CL '00 Proceedings of the First International Conference on Computational Logic
CL '00 Proceedings of the First International Conference on Computational Logic
Unrestricted vs restricted cut in a tableau method for Boolean circuits
Annals of Mathematics and Artificial Intelligence
Improvements to the Tableau Prover PITP
TABLEAUX '07 Proceedings of the 16th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Optimization techniques for propositional intuitionistic logic and their implementation
Theoretical Computer Science
Fast decision procedure for propositional Dummett logic based on a multiple premise tableau calculus
Information Sciences: an International Journal
FCUBE: an efficient prover for intuitionistic propositional logic
LPAR'10 Proceedings of the 17th international conference on Logic for programming, artificial intelligence, and reasoning
Unit propagation in a tableau framework
TABLEAUX'05 Proceedings of the 14th international conference on Automated Reasoning with Analytic Tableaux and Related Methods
Normal forms for knowledge compilation
ISMIS'05 Proceedings of the 15th international conference on Foundations of Intelligent Systems
Simplification Rules for Intuitionistic Propositional Tableaux
ACM Transactions on Computational Logic (TOCL)
Refutation in dummett logic using a sign to express the truth at the next possible world
IJCAI'11 Proceedings of the Twenty-Second international joint conference on Artificial Intelligence - Volume Volume Two
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Tableau and sequent calculi are the basis for most popular interactive theorem provers for formal verification. Yet, when it comes to automatic proof search, tableaux are often slower than Davis-Putnam, SAT procedures or other techniques. This is partly due to the absence of a bivalence principle (viz. the cut-rule) but there is another source of inefficiency: the lack of constraint propagation mechanisms.This paper proposes an innovation in this direction: the rule of simplification, which plays for tableaux the role of subsumption for resolution and of unit for the Davis-Putnam procedure.The simplicity and generality of simplification make possible its extension in a uniform way from propositional logic to a wide range of modal logics. This technique gives an unifying view of a number of tableaux-like calculi such as DPLL, KE, HARP, hyper-tableaux, BCP, KSAT.We show its practical impact with experimental results for random 3- SAT and the industrial IFIP benchmarks for hardware verification.