Abstract
In the present paper we generalize two fundamental systems modelling the flow of time: the modal logic S4.3 and propositional linear time temporal logic. We allow to consider a whole set of states instead of only a single one at every time. Moreover, we assume that these sets increase in the course of time. Thus we get a basic formalism expressing a distinguished dynamic aspect of sets, growing. Our main results include completeness of the proposed axiomatizations and decidability of the set of all formally provable formulas.
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References
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Forthcoming; see URL http://turing/wins/uva/nl/~mdr/Publications/modal-logic.html
Chellas, B. F.: Modal Logic: An Introduction. Cambridge University Press, Cambridge (1980)
Dabrowski, A., Moss, L.S., Parikh, R.: Topological Reasoning and The Logic of Knowledge. Annals of Pure and Applied Logic 78 (1996) 73–110
Davoren, J.: Modal Logics for Continuous Dynamics. PhD dissertation, Department of Mathematics, Cornell University (1998)
Fagin, R., Halpern, J.Y., Moses, Y., Vardi, M.Y.: Reasoning about Knowledge. MIT Press, Cambridge (Mass.) (1995)
Georgatos, K.: Knowledge on Treelike Spaces. Studia Logica 59 (1997) 271–301
Goldblatt, R.: Logics of Time and Computation. CSLI Lecture Notes 7, Stanford, CA (1987)
Halpern, J.Y., Vardi, M.Y.: The Complexity of Reasoning about Knowledge and Time. I. Lower Bounds. Journal of Computer and System Sciences 38 (1989) 195–237
Hansen, M.R., Chaochen, Z.: Duration Calculus: Logical Foundations. Formal Aspects of Computing 9 (1997) 283–330
Heinemann, B.: Topological Nexttime Logic. In: Kracht, M., de Rijke, M., Wansing, H., Zakharyaschev, M. (eds.): Advances in Modal Logic, Vol. 1. CSLI Publications 87, Stanford, CA (1998) 99–113
Heinemann, B.: Temporal Aspects of the Modal Logic of Subset Spaces. Theoretical Computer Science 224(1–2) (1999) 135–155
McKinsey, J.C.C.: A Solution to the Decision Problem for the Lewis Systems S2 and S4, with an Application to Topology. J. Symbolic Logic 6(3) (1941) 117–141
Nutt, W.: On the Translation of Qualitative Spatial Reasoning Problems into Modal Logics. Lecture Notes in Computer Science Vol. 1701 (1999) 113–125
Ono, H., Nakamura, A.: On the Size of Refutation Kripke Models for Some Linear Modal and Tense Logics. Studia Logica 39 (1980) 325–333
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Heinemann, B. (2000). Generalizing the Modal and Temporal Logic of Linear Time. In: Rus, T. (eds) Algebraic Methodology and Software Technology. AMAST 2000. Lecture Notes in Computer Science, vol 1816. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45499-3_6
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DOI: https://doi.org/10.1007/3-540-45499-3_6
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