On the modal logic K plus theories
K + T is the prepositional modal logic K with the elements of the finite set T as additional axioms.
We develop a sequent calculus that is suited for proof search in K + T and discuss methods to improve the efficiency. An implementation of the resulting decision procedure is part of the Logics Workbench LWB.
Then we show that — in contrast to K, KT, S4 — there are theories T and formulas A where a counter-model must have a superpolynomial diameter in the size of T plus A.
In the last part we construct an embedding of S4 in K + T.
Unable to display preview. Download preview PDF.
- 1.Laurent Catach. Tableaux: A general theorem prover for modal logics. Journal of Automated Reasoning, 7:489–510, 1991.Google Scholar
- 2.Melvin Fitting. Proof Methods for Modal and Intuitionistic Logics. Reidel, Dordrecht, 1983.Google Scholar
- 3.Melvin Fitting. First-order modal tableaux. Journal of Automated Reasoning, 4:191–213, 1988.Google Scholar
- 4.Rajeev Goré. Tableau methods for modal and temporal logics. Technical report, TR-15-95, Automated Reasoning Project, Australian National University, Canberra, Australia, 1995. To appear in Handbook of Tableau Methods, Kluwer, 199?Google Scholar
- 5.Rajeev Goré, Wolfgang Heinle, and Alain Heuerding. Relations between propositional normal modal logics: an overview. Submitted.Google Scholar
- 6.Joseph Y. Halpern and Yoram Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379, 1992.Google Scholar
- 7.Alain Heuerding, Gerhard Jäger, Stefan Schwendimann, and Michael Seyfried. Propositional logics on the computer. In Theorem Proving with Analytic Tableaux and Related Methods, LNCS 918, 1995.Google Scholar
- 8.Richard E. Ladner. The computational complexity of provability in systems of modal propositional logic. SIAM Journal on Computing, 6(3):467–480, 1977.Google Scholar
- 9.Ilkka Niemelä and Heikki Tuominen. Helsinki logic machine: A system for logical expertise. Technical report, Digital Systems Laboratory, Department of Computer Science, Helsinki University of Technology, 1987.Google Scholar
- 10.F. Oppacher and E. Suen. Harp: A tableau-based theorem prover. Journal of Automated Reasoning, 4:69–100, 1988.Google Scholar
- 11.Dan Sahlin, Torkel Franzén, and Seif Haridi. An intuitionistic predicate logic theorem prover. Journal of Logic and Computation, 2(5):619–656, 1992.Google Scholar
- 12.Kurt Schütte. Vollständige Systeme modaler und intuitionistischer Logik. Springer, 1968.Google Scholar
- 13.Alasdair Urquhart. Complexity of proofs in classical propositional logic. In Yiannis N. Moschovakis, editor, Logic from Computer Science, pages 597–608. Springer, 1992.Google Scholar
- 14.Lincoln Wallen. Automated Proof Search in Non-Classical Logics. M.I.T. Press, Cambridge, Massachusetts, 1990.Google Scholar