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.
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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
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DOI: https://doi.org/10.1007/978-3-642-32897-8_13
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