Abstract
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, the latest obtained (in)consistency results can be kept. We have implemented a caching mechanism based on bit matrices in *sat. Experimenting with the TANCS 2000 benchmarks for modal logic K, we show that bit matrices (i) allow for considerable speedups, and (ii) lead to better performances both in space and time than the natural alternative, i.e., hash tables.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Hollunder, B., Nutt, W., Schmidt-Schauß, M.: Subsumption Algorithms for Concept Description Languages. In: Proc. 8th European Conference on Artificial Intelligence, pp. 348–353 (1990)
Baader, F., Franconi, E., Hollunder, B., Nebel, B., Profitlich, H.J.: An Empirical Analysis of Optimization Techniques for Terminological Representation Systems or: Making KRIS get a move on. Applied Artificial Intelligence. Special Issue on Knowledge Base Management 4, 109–132 (1994)
Giunchiglia, F., Sebastiani, R.: Building decision procedures for modal logics from propositional decision procedures - the case study of modal K. In: McRobbie, M.A., Slaney, J.K. (eds.) CADE 1996. LNCS (LNAI), vol. 1104. Springer, Heidelberg (1996)
Giunchiglia, E., Giunchiglia, F., Sebastiani, R., Tacchella, A.: More evaluation of decision procedures for modal logics. In: Sixth International Conference on Principles of Knowledge Representation and Reasoning, KR 1998 (1998)
Heuerding, A., Jager, G., Schwendimann, S., Seyfried, M.: The Logics Workbench LWB: A Snapshot. Euromath Bulletin 2(1), 177–186 (1996)
Horrocks, I.: Using an expressive description logic: FaCT or fiction? In: Sixth International Conference on Principles of Knowledge Representation and Reasoning (KR 1998), pp. 636–647 (1998)
Tacchella, A.: *sat system description. In: Lambrix, P., Borgida, A., Lenzerini, M., Möller, R., Patel-Schneider, P. (eds.) Collected Papers from the International Description Logics Workshop (DL 1999). CEUR (July 999)
Giunchiglia, E., Giunchiglia, F., Tacchella, A.: SAT-Based Decision Procedures for Classical Modal Logics. Journal of Automated Reasoning (2000) (to appear)
Voronkov, A.: KK: a theorem prover for K. In: Ganzinger, H. (ed.) CADE 1999. LNCS (LNAI), vol. 1632, pp. 383–387. Springer, Heidelberg (1999)
Patel-Schneider, P.F.: DLP system description. In: Franconi, E., De Giacomo, G., MacGregor, R.M., Nutt, W., Welty, C.A., Sebastiani, F. (eds.) Collected Papers from the International Description Logics Workshop (DL 1998), CEUR, pp. 87–89 (May 1998)
Haarslev, V., Moeller, R.: HAM-ALC. In: Franconi, E., De Giacomo, G., MacGregor, R.M., Nutt, W., Welty, C.A., Sebastiani, F. (eds.) Collected Papers from the International Description Logics Workshop (DL 1998). CEUR (May 1998)
Boyapati, V., Goré, R.: KtSeqC: System description. In: Murray, N.V. (ed.) TABLEAUX 1999. LNCS (LNAI), vol. 1617, pp. 29–31. Springer, Heidelberg (1999)
Hustadt, U., Schmidt, R.A., Weidenbach, C.: MSPASS: Subsumption testing with SPASS. In: Lambrix, P., Borgida, A., Lenzerini, M., Möller, R., Patel- Schneider, P. (eds.) Collected Papers from the International Description Logics Workshop (DL 1999). CEUR, pp. 136–137 (July 1999)
Massacci, F.: Results of the TANCS comparison (1999), Accessed March 9 (2000), http://www.dis.uniroma1.it/~tancs/results.shtml
Horrocks, I., Patel-Schneider, P.F.: Advances in propositional modal satisfiability (1999) (manuscript)
Chellas, B.F.: Modal Logic - an Introduction. Cambridge University Press, Cambridge (1980)
Davis, M., Longemann, G., Loveland, D.: A machine program for theorem proving. Journal of the ACM 5(7) (1962)
Plaisted, D.A., Greenbaum, S.: A Structure-preserving Clause Form Translation. Journal of Symbolic Computation 2, 293–304 (1986)
Halpern, J.Y., Moses, Y.: A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence 54, 319–379 (1992)
Ladner, R.: The computational complexity of provability in systems of modal propositional logic. SIAM J. Comp. 6(3), 467–480 (1977)
Massacci, F.: Design and results of the Tableaux 1999 Non-classical (Modal) Systems comparison. In: Murray, N.V. (ed.) TABLEAUX 1999. LNCS (LNAI), vol. 1617, pp. 14–18. Springer, Heidelberg (1999)
Hoffman, J., Koehler, J.: A new method to index and query sets. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence (IJCAI 1999), pp. 462–467 (1999)
Tacchella, A.: Evaluating *sat on TANCS2000 benchmarks. In: Dyckhoff, R. (ed.) TABLEAUX 2000. LNCS (LNAI), vol. 1847. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Giunchiglia, E., Tacchella, A. (2000). A Subset-Matching Size-Bounded Cache for Satisfiability in Modal Logics. In: Dyckhoff, R. (eds) Automated Reasoning with Analytic Tableaux and Related Methods. TABLEAUX 2000. Lecture Notes in Computer Science(), vol 1847. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10722086_20
Download citation
DOI: https://doi.org/10.1007/10722086_20
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67697-3
Online ISBN: 978-3-540-45008-5
eBook Packages: Springer Book Archive