Abstract
Previous research has shown that argumentation semantics can be described with Monadic Second Order Logic. While certain less expressive, modal, logics can also capture some of the semantics, the general issue of finding minimal modal logics that are able to describe certain argumentation semantics has not received a lot of attention in the literature so far. In this paper we show that full hybrid μ-calculus cannot describe the preferred semantics, thus providing a negative answer to an open question. We show that the same holds for the skeptical and credulous versions of the preferred semantics. Our result relies on the invariance of full hybrid μ-calculus with respect to a suitable notion of bisimulation. We provide a complete proof of this invariance in the paper.
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
Grossi, D.: On the logic of argumentation theory. In: van der Hoek, W., Kaminka, G., Lesperance, Y., Luck, M., Sandip, S. (eds.) Proceedings of the 9th International Conference on Autonomous Agents and Multiagent Systems (AAMAS 2010), pp. 409–416. IFAAMAS (2010)
Grossi, D.: An Application of Model Checking Games to Abstract Argumentation. In: van Ditmarsch, H., Lang, J., Ju, S. (eds.) LORI 2011. LNCS (LNAI), vol. 6953, pp. 74–86. Springer, Heidelberg (2011)
Sattler, U., Vardi, M.Y.: The Hybrid μ-Calculus. In: Goré, R.P., Leitsch, A., Nipkow, T. (eds.) IJCAR 2001. LNCS (LNAI), vol. 2083, pp. 76–91. Springer, Heidelberg (2001)
Bonatti, P.A., Lutz, C., Murano, A., Vardi, M.Y.: The complexity of enriched μ-calculi. Logical Methods in Computer Science 4(3:11), 1–27 (2008)
Areces, C., ten Cate, B.: Hybrid logics. In: Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 821–868. Elsevier (2007)
Bradfield, J., Stirling, C.: Modal μ-calculi. In: Handbook of Modal Logic. Studies in Logic and Practical Reasoning, vol. 3, pp. 721–756. El (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), 321–357 (1995)
Janin, D., Walukiewicz, I.: On the Expressive Completeness of the Propositional μ-Calculus with Respect to Monadic Second Order Logic. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 263–277. Springer, Heidelberg (1996)
Blackburn, P., de Rijke, M., Venema, Y.: Modal Logic. Cambridge Tracts in Theoretical Computer Science, vol. 27. Cambridge University Press (2001)
Baroni, P., Giacomin, M.: Semantics of abstract argument systems. In: Rahwan, I., Simari, G. (eds.) Argumentation in Artificial Intelligence, pp. 24–44. Springer (2009)
Baroni, P., Giacomin, M., Guida, G.: Scc-recursiveness: a general schema for argumentation semantics. Artificial Intelligence 168(1-2), 162–210 (2005)
Baroni, P., Giacomin, M.: On principle-based evaluation of extension-based argumentation semantics. Artificial Intelligence 171(10-15), 675–700 (2007)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gratie, C., Florea, A.M., Meyer, JJ.C. (2012). Full Hybrid μ-Calculus, Its Bisimulation Invariance and Application to Argumentation. In: Fisher, M., van der Torre, L., Dastani, M., Governatori, G. (eds) Computational Logic in Multi-Agent Systems. CLIMA 2012. Lecture Notes in Computer Science(), vol 7486. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32897-8_13
Download citation
DOI: https://doi.org/10.1007/978-3-642-32897-8_13
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-32896-1
Online ISBN: 978-3-642-32897-8
eBook Packages: Computer ScienceComputer Science (R0)