Abstract
Game logic is a modal logic the modalities of which model the interaction of two players, Angel and Demon. It is known that game logic is not adequately interpreted through relation based Kripke models. The basic mechanism behind neighborhood models, which are used instead, is given through effectivity functions. We give a brief introduction to effectivity functions based on sets, indicate some of their coalgebraic properties, and move on to a definition of stochastic effectivity functions over general measurable spaces. An interpretation of game logics in terms of these effectivity functions is sketched, and their relationship to probabilistic Kripke models and to the interpretation of the PDL fragment is indicated.
Access provided by Autonomous University of Puebla. Download to read the full chapter text
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Doberkat, E.-E.: A stochastic interpretation of propositional dynamic logic: Expressivity. J. Symb. Logic 77(2), 687–716 (2012)
Doberkat, E.-E.: Algebraic properties of stochastic effectivity functions. J. Logic and Algebraic Progr. 83, 339–358 (2014)
Doberkat, E.-E.: Special Topics in Mathematics for Computer Science: Sets, Categories, Topologies, Measures. Springer (in print, 2015)
Doberkat, E.-E., Sànchez Terraf, P.: Stochastic nondeterminism and effectivity functions. J. Logic and Computation (in print, 2015) (arxiv: 1405.7141)
Kozen, D.: A probabilistic PDL. J. Comp. Syst. Sci. 30(2), 162–178 (1985)
Parikh, R.: The logic of games and its applications. In: Karpinski, M., van Leeuwen, J. (eds.) Topics in the Theory of Computation, vol. 24, pp. 111–140. Elsevier (1985)
Pauly, M., Parikh, R.: Game logic — an overview. Studia Logica 75, 165–182 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2015 Springer International Publishing Switzerland
About this paper
Cite this paper
Doberkat, EE. (2015). Towards a Probabilistic Interpretation of Game Logic. In: Kahl, W., Winter, M., Oliveira, J. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2015. Lecture Notes in Computer Science(), vol 9348. Springer, Cham. https://doi.org/10.1007/978-3-319-24704-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-319-24704-5_3
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-24703-8
Online ISBN: 978-3-319-24704-5
eBook Packages: Computer ScienceComputer Science (R0)