Abstract
We develop an algebraic modal logic that combines epistemic and dynamic modalities with a view to modelling information acquisition (learning) by automated agents in a changing world. Unlike most treatments of dynamic epistemic logic, we have transitions that “change the state” of the underlying system and not just the state of knowledge of the agents. The key novel feature that emerges is the need to have a way of “inverting transitions” and distinguishing between transitions that “really happen” and transitions that are possible.
Our approach is algebraic, rather than being based on a Kripke-style semantics. The semantics are given in terms of quantales. We study a class of quantales with the appropriate inverse operations and prove properties of the setting. We illustrate the ideas with toy robot-navigation problems. These illustrate how an agent learns information by taking actions.
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References
Abramsky, S., Vickers, S.: Quantales observational logic and process semantics. Mathematical Structures in Computer Science 3, 161–227 (1993)
Aucher, G., Herzig, A.: From DEL to EDL: Exploring the Power of Converse Events. In: Mellouli, K. (ed.) ECSQARU 2007. LNCS (LNAI), vol. 4724, pp. 199–209. Springer, Heidelberg (2007)
Baltag, A., Coecke, B., Sadrzadeh, M.: Epistemic actions as resources. Journal of Logic and Computation 17, 555–585 (2007) (arXiv:math/0608166)
Desharnais, J., Müller, B., Struth, G.: Kleene algebra with domain. ACM Trans. Comput. Log. 7, 798–833 (2006)
Dunn, M.: Positive modal logic. Studia Logica 55, 301–317 (2005)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning About Knowledge. MIT Press, Cambridge (1995)
van Ditmarsch, H.P., van der Hoek, W., Kooi, B.P.: Dynamic Epistemic Logic with Assignment. In: Proceedings of AAMAS, pp. 141–148 (2005)
Gehrke, M., Nagahashi, H., Venema, Y.: A Sahlqvist theorem for distributive modal logic. Annals of Pure and Applied Logic 131, 65–102 (2005)
Harel, D., Kozen, D., Tiuryn, J.: Propositional Dynamic Logic. MIT Press, Cambridge (2000)
Halpern, J.Y., Moses, Y.: Knowledge and common knowledge in a distributed environment. In: Proceedings of the Third ACM Symposium on Principles of Distributed Computing, pp. 50–61 (1984); A revised version appears as IBM Research Report RJ 4421 (August 1987)
Halpern, J., Moses, Y.: Knowledge and common knowledge in a distributed environment. JACM 37, 549–587 (1990)
Kripke, S.: Semantical analysis of modal logic. Zeitschrift fur Mathematische Logik und Grundlagen der Mathematik 9, 67–96 (1963)
Panangaden, P., Sadrzadeh, M.: Learning in a changing world via algebraic modal logic, http://www.comlab.ox.ac.uk/files/2815/mehrnoosh_prakash.pdf and http://www.cs.mcgill.ca/~prakash/Pubs/mehrnoosh_prakash.pdf
Parikh, R.: The Completeness of Propositional Dynamic Logic. In: Winkowski, J. (ed.) MFCS 1978. LNCS, vol. 64, pp. 403–415. Springer, Heidelberg (1978)
Phillips, C.: An algebraic approach to dynamic epistemic logic. Master’s thesis, School of Computer Sciecne. McGill University (2009)
Sadrzadeh, M.: Actions and Resources in Epistemic Logic. PhD thesis, Université du Québec à Montréal (2006)
Sadrzadeh, M., Dyckhoff, R.: Positive logic with adjoint modalities: Proof theory, semantics and reasoning about information. ENTCS 23, 211–225 (2009)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer, Heidelberg (2008)
von Karger, B.: Temporal algebras. Mathematical Structures in Computer Science 8, 277–320 (1998)
Winskel, G.: Prime algebraicity. Theoretical Computer Science 410, 4160–4168 (2009)
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Panangaden, P., Sadrzadeh, M. (2011). Learning in a Changing World, an Algebraic Modal Logical Approach. In: Johnson, M., Pavlovic, D. (eds) Algebraic Methodology and Software Technology. AMAST 2010. Lecture Notes in Computer Science, vol 6486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17796-5_8
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DOI: https://doi.org/10.1007/978-3-642-17796-5_8
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