Abstract
The paper presents a study of abstract argumentation theory from the point of view of modal logic. The key thesis upon which the paper builds is that argumentation frameworks can be studied as Kripke frames. This simple observation allows us to import a number of techniques and results from modal logic to argumentation theory, and opens up new interesting avenues for further research. The paper gives a glimpse of the sort of techniques that can be imported, discussing complete calculi for argumentation, adequate model-checking and bisimulation games, and sketches an agenda for future research at the interface of modal logic and argumentation theory.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
van Benthem, J.: An essay on sabotage and obstruction. In: Hutter, D., Stephan, W. (eds.) Mechanizing Mathematical Reasoning. LNCS (LNAI), vol. 2605, pp. 268–276. Springer, Heidelberg (2005)
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (forthcoming)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge University Press, Cambridge (2001)
Caminada, M.: Semi-stable semantics. In: Dunne, P.E., Bench-Capon, T. (eds.) Proceedings of Computational Models of Argument, COMMA 2006, pp. 121–130 (2006)
Davey, B.A., Priestley, H.A.: Introduction to Lattices and Order. Cambridge University Press, Cambridge (1990)
van Ditmarsch, H., Kooi, B., van der Hoek, W.: Dynamic Epistemic Logic. Synthese Library Series, vol. 337. Springer, Heidelberg (2007)
Dung, P.M.: On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games. Artificial Intelligence 77(2), 321–358 (1995)
Dunne, P., Bench-Capon, T.: Complexity and combinatorial properties of argument systems. Technical report, University of Liverpool (2001)
Fine, K.: Propositional quantifiers in modal logic. Theoria 36, 336–346 (1936)
Fine, K.: In so many possible worlds. Notre Dame Journal of Formal Logic 13, 516–520 (1972)
Goranko, V., Otto, M.: Model theory of modal logic. In: Blackburn, P., van Benthem, J., Wolter, F. (eds.) Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 249–329. Elsevier, Amsterdam (2007)
Grossi, D.: Doing argumentation theory in modal logic. ILLC Prepublication Series PP-2009-24, Institute for Logic, Language and Computation (2009)
Grossi, D.: On the logic of argumentation theory. In: van der Hoek, W., Kaminka, G., Lespérance, Y., Sen, S. (eds.) Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), IFAAMAS, pp. 409–416 (2010)
Modgil, S., Caminada, M.: Proof theories and algorithms for abstract argumentation frameworks. In: Rahwan, Y., Simari, G. (eds.) Argumentation in AI. Springer, Heidelberg (2009)
Oikarinen, E., Woltran, S.: Characterizing strong equivalence for argumentation frameworks. In: Lin, F., Sattler, U., Truszczynski, M. (eds.) Principles of Knowledge Representation and Reasoning: Proceedings of the Twelfth International Conference (KR 2010), May 9–13. AAAI Press, Toronto (2010)
Prakken, H., Vreeswijk, G.: Logics for defeasible argumentation. In: Handbook of Philosophical Logic, 2nd edn., vol. IV, pp. 218–319 (2002)
de Rijke, M.: A note on graded modal logic. Studia Logica 64(2), 271–283 (2000)
Venema, Y.: Lectures on the modal μ-calculus. Renmin University in Beijing, China (2008)
Walukiewicz, I.: Completeness of Kozen’s axiomatization of the propositional mu-calculus. Information and Computation 157, 142–182 (2000)
Zermelo, E.: Über eine anwendung der mengenlehre auf die theorie des schachspiels. In: Proceedings of the 5th Congress Mathematicians, pp. 501–504. Cambridge University Press, Cambridge (1913)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2011 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Grossi, D. (2011). Argumentation in the View of Modal Logic. In: McBurney, P., Rahwan, I., Parsons, S. (eds) Argumentation in Multi-Agent Systems. ArgMAS 2010. Lecture Notes in Computer Science(), vol 6614. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21940-5_12
Download citation
DOI: https://doi.org/10.1007/978-3-642-21940-5_12
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21939-9
Online ISBN: 978-3-642-21940-5
eBook Packages: Computer ScienceComputer Science (R0)