Abstract
This paper presents a prefixed tableaux calculus for Propositional Dynamic Logic with Converse based on a combination of different techniques such as prefixed tableaux for modal logics and model checkers for mu-calculus. We prove the correctness and completeness of the calculus and illustrate its features. We also discuss the transformation of the tableaux method (naively NEXPTIME) into an EXPTIME algorithm.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
P. Blackburn and E. Spaan. A modal perspective on computational complexity of attribute value grammar. J. of Logic, Language and Information, 2:129–169, 1993.
G. De Giacomo. Decidability of class-based knowledge representation formalisms. PhD thesis, Università di Roma “La Sapienza”, 1995.
G. De Giacomo and M. Lenzerini. Boosting the correspondence between description logics and propositional dynamic logics. In Proc. of AAAI-94, pages 205–212, 1994.
N. J. Fisher and R. E. Ladner. Propositional dynamic logic of regular programs. J. of Computer and System Sciences, 18:194–211, 1979.
M. Fitting. Proof Methods for Modal and Intuitionistic Logics. Reidel, 1983.
N. Friedman and J. Halpern. On the complexity of conditional logics. In Proc. of KR-94, 1994.
D. M. Gabbay. Labelled deductive systems. Tech. Rep. MPI-I-94-223, Max Plank Inst. für Informatik, Saarbrüken, Germany, 1994.
R. Goré. Tableaux method for modal and temporal logics. Tech. Rep. TR-ARP-15-5, Australian National University, 1995.
J. Halpern and Y. Moses. A guide to completeness and complexity for modal logics of knowledge and belief. Artificial Intelligence, 54:319–379, 1992.
D. Kozen and J. Tiuryn. Logics of programs. In Handbook of Theoretical Computer Science, pages 790–840. Elsevier, 1990.
F. Massacci. Strongly analytic tableaux for normal modal logics. In Proc. of CADE-94, LNAI 814, pages 723–737. Springer-Verlag, 1994.
V. R. Pratt. A practical decision method for propositional dynamic logic. In Proc. of STOC-78, pages 326–337, 1978.
V. R. Pratt. Models of program logics. In Proc. of FOCS-79, pages 115–122, 1979.
V. R. Pratt. A near-optimal method for reasoning about action. J. of Computer and System Sciences, 20:231–255, 1980.
K. Schild. A correspondence theory for terminological logics: Preliminary report. In Proc. of IJCAI-91, pages 466–471, 1991.
C. Stirling. Modal and temporal logic. In Handbook of Logic in Computer Science, pages 477–563. Clarendon Press, 1992.
C. Stirling and D. Walker. Local model checking in modal mu-calculus. Theoretical Computer Science, 89:161–177, 1991.
J. Van Benthem, J. Van Eijck, and V. Stebletsova. Modal logic, transition systems and processes. J. of Logic and Computation, 4(5):811–855, 1994.
M. Y. Vardi and P. Wolper. Automata-theoretic techniques for modal logics of programs. J. of Computer and System Sciences, 32:183–221, 1986.
W. A. Woods and J. G. Schmolze. The KL-ONE family. In Semantic Networks in Artificial Intelligence, pages 133–178. Pergamon Press, 1992.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1996 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
De Giacomo, G., Massacci, F. (1996). Tableaux and algorithms for Propositional Dynamic Logic with Converse. In: McRobbie, M.A., Slaney, J.K. (eds) Automated Deduction — Cade-13. CADE 1996. Lecture Notes in Computer Science, vol 1104. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61511-3_117
Download citation
DOI: https://doi.org/10.1007/3-540-61511-3_117
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-61511-8
Online ISBN: 978-3-540-68687-3
eBook Packages: Springer Book Archive