Abstract
Temporal epistemic logics are known, from results of Halpern and Vardi, to have a wide range of complexities of the satisfiability problem: from PSPACE, through non-elementary, to highly undecidable. These complexities depend on the choice of some key parameters specifying, inter alia, possible interactions between time and knowledge, such as synchrony and agents’ abilities for learning and recall. In this work we develop practically implementable tableau-based decision procedures for deciding satisfiability in single-agent synchronous temporal-epistemic logics with interactions between time and knowledge. We discuss some complications that occur, even in the single-agent case, when interactions between time and knowledge are assumed and show how the method of incremental tableaux can be adapted to work in EXPSPACE, respectively 2EXPTIME, for these logics, thereby also matching the upper bounds obtained for them by Halpern and Vardi.
This is a preview of subscription content, log in via an institution to check access.
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
Ajspur, M., Goranko, V.: Tableaux-based decision method for single-agent linear time synchronous temporal epistemic logics with interacting time and knowledge. Technical report (2012), http://www2.imm.dtu.dk/~vfgo/papers/AjspurGoranko-ICLA2013-TechReport.pdf
Dixon, C., Nalon, C., Fisher, M.: Tableaux for logics of time and knowledge with interactions relating to synchrony. Journal of Applied Non-Classical Logics 14(4), 397–445 (2004)
Goranko, V., Shkatov, D.: Tableau-based decision procedure for full coalitional multiagent temporal-epistemic logic of linear time. In: Decker, Sichman, Sierra, Castelfranchi (eds.) Proc. of AAMAS 2009 (2009)
Halpern, J.Y., Vardi, M.Y.: The complexity of reasoning about knowledge and time I: Lower bounds. Journal of Computer and System Sciences 38(1), 195–237 (1989)
Halpern, J.Y., Vardi, M.Y.: Reasoning about knowledge and time: Synchronous systems, IBM Research Report (1989)
Kontchakov, R., Lutz, C., Wolter, F., Zakharyaschev, M.: Temporalizing tableaux. Studia Logica 76(1), 91–134 (2004)
Nalon, C., Dixon, C., Fisher, M.: Resolution for synchrony and no learning. In: Schmidt, R., et al. (eds.) Advances in Modal Logic 5, pp. 231–248 (2004)
Pratt, V.R.: A practical decision method for propositional dynamic logic. In: Proc. of the 10th Annual ACM Symp. on the Theory of Computing, San Diego, California, pp. 326–337 (1979)
Wolper, P.: The tableau method for temporal logic: an overview. Logique et Analyse 28(110-111), 119–136 (1985)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ajspur, M., Goranko, V. (2013). Tableaux-Based Decision Method for Single-Agent Linear Time Synchronous Temporal Epistemic Logics with Interacting Time and Knowledge. In: Lodaya, K. (eds) Logic and Its Applications. ICLA 2013. Lecture Notes in Computer Science, vol 7750. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-36039-8_8
Download citation
DOI: https://doi.org/10.1007/978-3-642-36039-8_8
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-36038-1
Online ISBN: 978-3-642-36039-8
eBook Packages: Computer ScienceComputer Science (R0)