Abstract
The method of labelled tableaux for proof search in modal logics is extended and modified to give a labelled sequent system for the tense logic K t. Soundness and completeness proofs are sketched, and results of an initial lean Prolog implementation in the programming style of lean T A P are presented. The sequent system is modular in that small modifications capture any combination of the reflexive, transitive, euclidean, symmetric and serial extensions of K t.
Supported by an Australian Research Council Queen Elizabeth II Fellowship.
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B Beckert and R Goré. Free variable tableaux for propositional modal logics. In Proc. TABLEAUX-97, LNCS 1227, pages 91–106. Springer, 1997.
N Bonnette and R Goré. A labelled sequent system for tense logic K t. Technical Report TR-ARP-1-1998, ARP, 1998. http://arp.anu.edu.au:80/ftp/techreports/1998/TR-ARP-1-1998.ps.gz.
B Beckert and J Posegga. leanT A P: Lean tableau-based deduction. Journal of Automated Reasoning, 15(3):339–358, 1995.
M Fitting. Proof Methods for Modal and Intuitionistic Logics, volume 169 of Synthese Library. D. Reidel, Dordrecht, Holland, 1983.
M Fitting. Leantap revisited. J. of Logic and Computation 8:33–47, 1998.
D Gabbay. Labelled Deductive Systems. Oxford University Press, 1996.
R Goré. Tableau methods for modal and temporal logics. Technical Report TR-ARP-15-1995, ANU, 1995.
G Governatori. Labelled tableaux for multi-modal logics. In Proc. TABLEAUX-95, LNCS 918, pages 79–94. Springer, 1995.
G E Hughes and M J Cresswell. A Companion to Modal Logic. Methuen, London, 1984.
G E Hughes and M J Cresswell. A New Introduction To Modal Logic. Routledge, 1996.
A Heuerding and S Schwendimann. On the modal logic K plus theories. In Proc. CSL95, volume LNCS 1092, pages, 308–319. Springer, 1996.
U. Hustadt and R. A. Schmidt. Simplification and backjumping in modal tableau. In Proc. TABLEAUX-98, LNAI 1397, pages 189–201. Springer, 1998.
A Heuerding, M Seyfried, and H Zimmermann. Efficient loop-check for backward proof search in some non-classical logics. In Proc. TABLEAUX-96, LNAI 1071, pages 210–225. Springer, 1996.
S. Kanger. Provability in Logic. Stockholm Studies in Philosophy, University of Stockholm, Almqvist and Wiksell, Sweden, 1957.
F Massacci. Strongly analytic tableaux for normal modal logics. In A Bundy, editor, Proc. CADE-12, LNAI 814, pages 723–737. Springer, 1994.
F Massacci. Simplification: a general constraint propagation technique for propositional and modal tableaux. In Proc. TABLEAUX-98, LNAI 1397, pages 217–231. Springer, 1998.
H Nakamura, M Fujita, S Kono, and H Tanaka. Temporal logic based fast verification system using cover expressions. In C H Séquin, editor, Proceedings VLSI’87, pages 101–111, 1987.
J Pitt and J Cunningham. Distributed modal theorem proving with KE. In Proc. TABLEAUX-96, LNAI 1071, pages 160–176. Springer, 1996.
N Rescher and A Urquhart. Temporal Logic. Springer-Verlag, 1971.
C Stirling. Modal and temporal logics for processes. Lecture Notes in Computer Science, 1043:149–237, 1996.
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Bonnette, N., Goré, R. (1998). A labelled sequent system for tense logic Kt . In: Antoniou, G., Slaney, J. (eds) Advanced Topics in Artificial Intelligence. AI 1998. Lecture Notes in Computer Science, vol 1502. Springer, Berlin, Heidelberg . https://doi.org/10.1007/BFb0095042
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DOI: https://doi.org/10.1007/BFb0095042
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