This approach led to comprehensive provability semantics for a broad class of modal logics. Gödel's use of modal logic to describe provability, gave the first exact semantics of modality. There are two major ideas that dominate the landscape of modal logic application in mathematics: Gödel's provability semantics and Tarski's topological semantics. Mathematics is one of modal logic's oldest application areas. Propositional modal logic offers a new paradigm of applying logical methods: instead of using the traditional languages with quantification to describe a structure, an appropriate quantifier-free language with additional logic operators that represent the phenomenon at hand, is used. Mathematics normally finds a proper language and level of abstraction for the study of its objects. This chapter presents a wide variety of mathematical techniques developed over decades of studying the intricate details of modal logic.
501–504.Formal modal logic is mostly mathematical in its methods, regardless of area of application. In: Proceedings of the 5th Congress Mathematicians, pp. Zermelo, E.: Über eine anwendung der mengenlehre auf die theorie des schachspiels. Walukiewicz, I.: Completeness of Kozen’s axiomatization of the propositional mu-calculus. Renmin University in Beijing, China (2008) Venema, Y.: Lectures on the modal μ-calculus. 218–319 (2002)ĭe Rijke, M.: A note on graded modal logic. In: Handbook of Philosophical Logic, 2nd edn., vol. IV, pp. Prakken, H., Vreeswijk, G.: Logics for defeasible argumentation. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference (KR 2010), May 9–13. In: Lin, F., Sattler, U., Truszczynski, M. Oikarinen, E., Woltran, S.: Characterizing strong equivalence for argumentation frameworks. Modgil, S., Caminada, M.: Proof theories and algorithms for abstract argumentation frameworks. (eds.) Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), IFAAMAS, pp. In: van der Hoek, W., Kaminka, G., Lespérance, Y., Sen, S. Grossi, D.: On the logic of argumentation theory.
#Ways to use the modal logic playground series#
ILLC Prepublication Series PP-2009-24, Institute for Logic, Language and Computation (2009) Grossi, D.: Doing argumentation theory in modal logic.
Studies in Logic and Practical Reasoning, vol. 3, pp. In: Blackburn, P., van Benthem, J., Wolter, F. Goranko, V., Otto, M.: Model theory of modal logic. For example, the formula 232p says that it is necessarily the case. Notre Dame Journal of Formal Logic 13, 516–520 (1972) We can express quite complicated statements in a straightforward way using this language. Technical report, University of Liverpool (2001)įine, K.: Propositional quantifiers in modal logic.
Artificial Intelligence 77(2), 321–358 (1995)ĭunne, P., Bench-Capon, T.: Complexity and combinatorial properties of argument systems. Springer, Heidelberg (2007)ĭung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Van Ditmarsch, H., Kooi, B., van der Hoek, W.: Dynamic Epistemic Logic. Cambridge University Press, Cambridge (1990) 121–130 (2006)ĭavey, B.A., Priestley, H.A.: Introduction to Lattices and Order. (eds.) Proceedings of Computational Models of Argument, COMMA 2006, pp. Cambridge University Press, Cambridge (2001)Ĭaminada, M.: Semi-stable semantics. Cambridge University Press, Cambridge (forthcoming)īlackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Van Benthem, J.: Logical Dynamics of Information and Interaction. 10 He makes the distinction this way: 9 impossible is used in one way of whatever cannot be true now or in the. This text is generally credited as being the source of the use of this distinction in modern philosophy and modal logic. (eds.) Mechanizing Mathematical Reasoning. Aquinas's text divides modal propositions into those which are modal de dicto and those which are modal de re. Van Benthem, J.: An essay on sabotage and obstruction.
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