A History Based Logic for Dynamic Preference Updates
Tóm tắt
History based models suggest a process-based approach to epistemic and temporal reasoning. In this work, we introduce preferences to history based models. Motivated by game theoretical observations, we discuss how preferences can dynamically be updated in history based models. Following, we consider arrow update logic and event calculus, and give history based models for these logics. This allows us to relate dynamic logics of history based models to a broader framework.
Tài liệu tham khảo
Anderson, G., McCusker, G., & Pym, D. (2016). A logic for the compliance budget. In Q. Zhu, T. Alpcan, E. Panaousis, M. Tambe, & W. Casey (Eds.), Proceedings, GameSec 2016—Decision and game theory for security (pp. 370–381).
Baltag, A., Moss, L., & Solecki, S. (1998). The logic of public announcements and common knowledge and private suspicions. In I. Gilboa (Ed.), Proceedings of the 7th conference on theoretical aspects of rationality and knowledge, TARK 98 (pp. 43–56).
Başkent, C. (2011). A logic for strategy updates. In H. van Ditmarsch & J. Lang (Eds.), Proceedings of the third international workshop on logic, rationality and interaction (LORI-3), volume LNCS 6953 (pp. 382–383).
Blackburn, P., de Rijke, M., & de Venema, Y. (2001). Modal logic. Cambridge Tracts in Theoretical Computer Science. Cambridge: Cambridge University Press.
Brandenburger, A. (2014). The language of game theory. Singapore: World Scientific Publishing.
Fagin, R., Geanakoplos, J., Halpern, J. Y., & Vardi, M. Y. (1999). The hierarchical approach to modeling knowledge and common knowledge. International Journal of Game Theory, 28, 331–365.
Fagin, R., Halpern, J. Y., Moses, Y., & Vardi, M. Y. (1995). Reasoning about knowledge. Cambridge: MIT Press.
Fagin, R., Halpern, J. Y., & Vardi, M. Y. (1991). A model-theoretic analysis of knowledge. Journal of the Association for Computing Machinery, 38(2), 382–428.
Gabbay, D. M., Kurucz, A., Wolter, F., & Zakharyaschev, M. (2003). Many dimensional modal logics: Theory and applications. Amsterdam: Elsevier.
Gerbrandy, J. (1999). Bisimulations on planet Kripke. PhD thesis, Institute of Logic, Language and Computation; Universiteit van Amsterdam.
Halpern, J. Y. (2008). Computer science and game theory: A brief survey. In S. N. Durlauf & L. E. Blume (Eds.), Palgrave dictionary of economics. London: Palgrave MacMillan.
Halpern, J. Y. & Pass, R. (2017). A knowledge-based analysis of the blockchain protocol. In J. Lang (Ed.), Proceedings of the sixteenth conference on theoretical aspects of rationality and knowledge. TARK 2018, EPTCS 251 (pp. 324–335).
Halpern, J. Y., & Vardi, M. Y. (1989). The complexity of reasoning about knowledge and time. I. Lower bounds. Journal of Computer and System Sciences, 38(1), 195–237.
Halpern, J. Y., Vardi, M. Y., & van der Meyden, R. (2004). Complete axiomatization for reasoning about knowledge and time. SIAM Journal of Computing, 33(2), 674–703.
Hanson, S. O. (2001). Preference logic. In D. Gabbay & F. Guenthner (Eds.), Handbook of philosophical logic (Vol. 4, pp. 319–393). Dordrecht: Kluwer.
Harsanyi, J. C. (1967). Games with incomplete information played by ‘Bayesian’ players: I. The basic model. Management Science, 14(3), 159–182.
Hodges, W. (2013) Logic and games. In Zalta, E. N. (Ed.), The Stanford encyclopedia of philosophy. Retrieved 2009, from http://plato.stanford.edu/archives/spr2009/entries/logic-games.
Kooi, B., & Renne, B. (2011). Arrow update logic. The Review of Symbolic Logic, 4(4), 536–559.
Kurtonina, N., & de Rijke, M. (1997). Bisimulations for temporal logic. Journal of Logic, Language and Information, 6, 403–425.
Leyton-Brown, K., & Shoham, Y. (2008). Essentials of game theory. San Rafael: Morgan & Claypool.
Lorini, E., & Moisan, F. (2011). An epistemic logic of extensive games. Electronic Notes in Theoretical Computer Science, 278, 245–260.
Moss, L. S. (2015). Dynamic epistemic logic. In H. van Ditmarsch, J. Y. Halpern, W. van der Hoek, & B. Kooi (Eds.), Handbook of epistemic logic (pp. 261–312). London: College Publications.
Osborne, M. J., & Rubinstein, A. (1994). A course in game theory. Cambridge: MIT Press.
Osherson, D., & Weinstein, S. (2012). Preference based on reasons. The Review of Symbolic Logic, 5(1), 122–147.
Pacuit, E. (2007). Some comments on history based structures. Journal of Applied Logic, 5(4), 613–624.
Pacuit, E., Parikh, R., & Cogan, E. (2006). The logic of knowledge based obligation. Synthese, 149(2), 311–341.
Parikh, R., & Ramanujam, R. (2003). A knowledge based semantics of messages. Journal of Logic, Language and Information, 12(4), 453–467.
Ramanujam, R., & Simon, S. (2008). Dynamic logic on games with structured strategies. In G. Brewka, & J. Lang (Eds.), Proceedings of the 11th international conference on principles of knowledge representation and reasoning. KR-08 (pp. 49–58).
Renne, B., Sack, J., & Yap, A. (2016). Logics of temporal-epistemic actions. Synthese, 193(3), 813–849.
Sack, J. (2008). Temporal languages for epistemic programs. Journal of Logic, Language and Information, 17(2), 183–216.
van Benthem, J. (2005). An essay on sabotage and obstruction. In D. Hutter (Ed.), Mechanizing mathematical reasoning (pp. 268–276). Berlin: Springer.
van Benthem, J. (2014). Logic in games. Cambridge: MIT Press.
van Benthem, J., Gerbrandy, J., & Pacuit, E. (2007). Merging frameworks for interaction: Del and etl. In D. Samet (Ed.), Proceedings of tark 2007.
van Benthem, J., Girard, P., & Roy, O. (2009). Everything else being equal: A modal logic for ceteris paribus preferences. Journal of Philosophical Logic, 38(1), 83–125.
van Benthem, J., & Liu, F. (2007). Dynamic logic of preference upgrade. Journal of Applied Non-Classical Logics, 17(2), 157–182.
van der Meyden, R. (1994). Axioms for knowledge and time in distributed systems with perfect recall. In Proceedings of IEEE symposium on logic in computer science (pp. 448–457).
van der Meyden, R., & Wong, K. (2003). Complete axiomatization for reasoning about knowledge and branching time. Studia Logica, 75(1), 93–123.
van Ditmarsch, H., van der Hoek, W., & Kooi, B. (2007). Dynamic Epistemic Logic. Berlin: Springer.