Abstract
This work proposes an alternative definition of the so-called program transformers, used to obtain reduction axioms in the Logic of Communication and Change. Our proposal uses an elegant matrix treatment of Brzozowski’s equational method instead of Kleene’s translation from finite automata to regular expressions. The two alternatives are shown to be equivalent, with Brzozowski’s method having the advantage of being computationally more efficient.
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References
Arden, D.N.: Delayed-logic and finite-state machines. In: SWCT (FOCS), pp. 133–151. IEEE Computer Society (1961)
Baltag, A., Moss, L.S.: Logics for epistemic programs. Synthese 139(2), 165–224 (2004)
Baltag, A., Moss, L.S., Solecki, S.: The logic of public announcements and common knowledge and private suspicions. In: Gilboa, I. (ed.) TARK, pp. 43–56. Morgan Kaufmann, San Francisco (1998)
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press (2011)
van Benthem, J., van Eijck, J., Kooi, B.: Logics of communication and change. Information and Computation 204(11), 1620–1662 (2006)
van Benthem, J., Gerbrandy, J., Hoshi, T., Pacuit, E.: Merging frameworks for interaction. Journal of Philosophical Logic 38(5), 491–526 (2009)
van Benthem, J., Kooi, B.: Reduction axioms for epistemic actions. In: Schmidt, R., Pratt-Hartmann, I., Reynolds, M., Wansing, H. (eds.) Advances in Modal Logic (Number UMCS-04-09-01 in Technical Report Series), pp. 197–211. Department of Computer Science, University of Manchester (2004)
Brzozowski, J.A.: Derivatives of regular expressions. Journal of the ACM 11(4), 481–494 (1964)
Conway, J.H.: Regular Algebra and Finite Machines. Chapman and Hall (1971)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library Series, vol. 337. Springer (2007)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about knowledge. The MIT Press, Cambridge (1995)
Harel, D., Kozen, D., Tiuryn, J.: Dynamic Logic. MIT Press, Cambridge (2000)
Kleene, S.: Representation of events in nerve nets and finite automata. In: Shannon, C.E., McCarthy, J. (eds.) Automata Studies, pp. 3–41. Princeton University Press, Princeton (1956)
Kozen, D.: On kleene algebras and closed semirings. In: Rovan, B. (ed.) MFCS 1990. LNCS, vol. 452, pp. 26–47. Springer, Heidelberg (1990)
Parikh, R., Ramanujam, R.: A knowledge based semantics of messages. Journal of Logic, Language and Information 12(4), 453–467 (2003)
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Pardo, P., Sarrión-Morillo, E., Soler-Toscano, F., Velázquez-Quesada, F.R. (2014). Efficient Program Transformers for Translating LCC to PDL . In: Fermé, E., Leite, J. (eds) Logics in Artificial Intelligence. JELIA 2014. Lecture Notes in Computer Science(), vol 8761. Springer, Cham. https://doi.org/10.1007/978-3-319-11558-0_18
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DOI: https://doi.org/10.1007/978-3-319-11558-0_18
Publisher Name: Springer, Cham
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