A Structure-preserving Clause Form Translation
Journal of Symbolic Computation
On the complexity of epistemic reasoning
Proceedings of the Fourth Annual Symposium on Logic in computer science
Minimizing the number of clauses by renaming
CADE-10 Proceedings of the tenth international conference on Automated deduction
Attributive concept descriptions with complements
Artificial Intelligence
A guide to completeness and complexity for modal logics of knowledge and belief
Artificial Intelligence
Boosting combinatorial search through randomization
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
A machine program for theorem-proving
Communications of the ACM
SAT-Based Decision Procedures for Classical Modal Logics
Journal of Automated Reasoning
A New Method to Index and Query Sets
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
A Subset-Matching Size-Bounded Cache for Satisfiability in Modal Logics
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
Design and Results of TANCS-2000 Non-classical (Modal) Systems Comparison
TABLEAUX '00 Proceedings of the International Conference on Automated Reasoning with Analytic Tableaux and Related Methods
CADE-13 Proceedings of the 13th International Conference on Automated Deduction: Automated Deduction
System Description: *SAT: A Platform for the Development of Modal Decision Procedures
CADE-17 Proceedings of the 17th International Conference on Automated Deduction
Spartacus: A Tableau Prover for Hybrid Logic
Electronic Notes in Theoretical Computer Science (ENTCS)
InKreSAT: modal reasoning via incremental reduction to SAT
CADE'13 Proceedings of the 24th international conference on Automated Deduction
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The implementation of efficient decision procedures for modal logics is a major research problem in automated deduction. Caching the result of intermediate consistency checks has experimentally proved to be a very important technique for attaining efficiency. Current state-of-the-art systems implement caching mechanisms based on hash tables. In this paper we present a data type – that we call “bit matrix” – for caching the (in)consistency of sets of formulas. Bit matrices have three distinguishing features: (i) they can be queried for subsets and supersets, (ii) they can be bounded in size, and (iii) if bounded, they can easily implement different policies to resolve which results have to be kept. We have implemented caching mechanisms based on bit matrices and hash tables in *SAT. In *SAT, the bit matrix cache is bounded, and keeps the latest obtained (in)consistency results. We experiment with the benchmarks proposed for the modal logic K at the “TABLEAUX Non Classical Systems Comparison (TANCS) 2000”. On the basis of the results, we conclude that *SAT performances are improved by (i) caching the results of intermediate consistency checks, (ii) using bit matrices instead of hash tables, and (iii) storing a small number of results in the bit matrices.