Abstract
In this work we lay a theoretical framework for developing dynamic epistemic logics in a many-valued setting. We consider in particular the logic of Public Announcements, which is one of the simplest and best-known dynamic epistemic systems in the literature. We show how to develop a Public Announcement Logic based on finite-valued Łukasiewicz modal logic. We define our logic through a relational semantics based on many-valued Kripke models, and also introduce an alternative but equivalent algebra-based semantics using MV-algebras endowed with modal operators. We provide a Hilbert-style calculus for our logic and prove completeness with respect to both semantics.
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Notes
- 1.
The multi-agent case is a straightforward generalization of the single-agent one: one just needs to index the static modal operator by the agents. At this point we do not deal with more complicated operators such as those for common knowledge; these may provide interesting lines for future research.
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Cabrer, L., Rivieccio, U., Rodriguez, R.O. (2016). Łukasiewicz Public Announcement Logic. In: Carvalho, J., Lesot, MJ., Kaymak, U., Vieira, S., Bouchon-Meunier, B., Yager, R. (eds) Information Processing and Management of Uncertainty in Knowledge-Based Systems. IPMU 2016. Communications in Computer and Information Science, vol 611. Springer, Cham. https://doi.org/10.1007/978-3-319-40581-0_10
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DOI: https://doi.org/10.1007/978-3-319-40581-0_10
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