Abstract
Starting off with Moss and Parikh’s investigation into knowledge and topology, we propose a logical system which is capable of formally handling endomorphisms of subset spaces. The motivation for doing so originates from dynamic agent logics. Usually, these logics comprise certain epistemic actions. Our aim is to show that an appropriate extension of the Moss-Parikh system can serve similar purposes. In fact, since the semantics of an action can be described as a function inducing a change of the knowledge states of the involved agents, such transformations are to be modeled accordingly. Due to the ambivalence of the framework used here, this has some quasi-topological impact, too, in so far as a certain notion of open mapping can be captured now. The main issues of this paper concern the basic logical properties of the arising system, in particular, completeness. Our main technical resource for that is hybrid logic.
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References
McKinsey, J.C.C.: A solution to the decision problem for the Lewis systems S2 and S4, with an application to topology. Journal of Symbolic Logic 6, 117–141 (1941)
McKinsey, J.C.C., Tarski, A.: The algebra of topology. Annals of Mathematics 45, 141–191 (1944)
Aiello, M., Pratt-Hartmann, I.E., van Benthem, J.F.A.K.: Handbook of Spatial Logics. Springer, Heidelberg (2007)
Dabrowski, A., Moss, L.S., Parikh, R.: Topological reasoning and the logic of knowledge. Annals of Pure and Applied Logic 78, 73–110 (1996)
Moss, L.S., Parikh, R., Steinsvold, C.: Handbook of Spatial Logics [3], pp. 299–341. Springer, Heidelberg (2007)
Heinemann, B.: Reasoning about knowledge and continuity. In: Goebel, R., Sutcliffe, G. (eds.) Proceedings 19th International Florida Artificial Intelligence Research Society Conference (FLAIRS 2006), pp. 37–42. AAAI Press, Menlo Park (2006)
Heinemann, B.: Reasoning about operations on sets. In: Kobti, Z., Wu, D. (eds.) Canadian AI 2007. LNCS, vol. 4509, pp. 308–319. Springer, Heidelberg (2007)
van Ditmarsch, H., van der Hoek, W., Kooi, B.: Dynamic Epistemic Logic. Synthese Library, vol. 337. Springer, Heidelberg (2007)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 53. Cambridge University Press, Cambridge (2001)
Heinemann, B.: A hybrid logic for reasoning about knowledge and topology. Journal of Logic, Language and Information 17(1), 19–41 (2008)
Areces, C., ten Cate, B.: Handbook of Modal Logic [12], pp. 821–868. Elsevier, Amsterdam (2007)
Blackburn, P., van Benthem, J., Wolter, F.: Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3. Elsevier, Amsterdam (2007)
Heinemann, B.: Topological nexttime logic. In: Kracht, M., de Rijke, M., Wansing, H., Zakharyaschev, M. (eds.) Advances in Modal Logic 1, Stanford, CA. CSLI Publications, vol. 87, pp. 99–113. CSLI Publications, Kluwer (1998)
Wang, Y.N.: A two-dimensional hybrid logic of subset spaces. In: Ramanujam, R., Sarukkai, S. (eds.) Logic and Its Applications, ICLA 2009. LNCS, vol. 5378, pp. 196–209. Springer, Heidelberg (2009)
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Heinemann, B. (2009). Observational Effort and Formally Open Mappings. In: Ono, H., Kanazawa, M., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2009. Lecture Notes in Computer Science(), vol 5514. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-02261-6_16
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DOI: https://doi.org/10.1007/978-3-642-02261-6_16
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