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.
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
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.
References
Baltag, A., Moss, L., Solecki, A.: The logic of public announcements, common knowledge, and private suspicions, CWI technical report SEN-R9922 (1999)
van Benthem, J.: Logical Dynamics of Information and Interaction. Cambridge University Press, Cambridge (2011)
Cignoli, R., D’Ottaviano, I.M.L., Mundici, D.: Algebraic Foundations of Many-Valued Reasoning. Trends in Logic—Studia Logica Library, vol. 7. Kluwer Academic Publishers, Dordrecht (2000)
Grigolia, R.S.: Algebraic analysis of Łukasiewicz-Tarski’s n-valued logical systems. In: Wójciki, R., Malinowski, G. (eds.) Selected Papers on Łukasiewicz Sentential Calculi, Ossolineum, Wronclaw, pp. 81–92 (1977)
Hansoul, G., Teheux, B.: Extending Łukasiewicz logics with a modality: algebraic approach to relational semantics. Studia Logica 101(3), 505–545 (2013)
Kurz, A., Palmigiano, A.: Epistemic updates on algebras. Logical Methods Comput. Sci. 9(4:17), 1–28 (2013)
Ma, M., Palmigiano, A., Sadrzadeh, M.: Algebraic semantics and model completeness for Intuitionistic Public Announcement Logic. Ann. Pure Appl. Logic 165, 963–995 (2014)
Teheux, B.: A duality for the algebras of a Łukasiewicz \(n+1\)-valued modal system. Studia Logica 87(1), 13–36 (2008)
Rivieccio, U.: Algebraic semantics for bilattice public announcement logic. In: Indrzejczak, A., Kaczmarek, J., Zawidzki, M. (eds.) Proceedings of Trends in Logic XIII, Lodz, Poland, 2–5 July 2014, pp. 199–215. Lodz University Press (2014)
Rivieccio, U.: Bilattice public announcement logic. In: Goré, R., Kooi, B., Kurucz, A. (eds.) Advances in Modal Logic, vol. 10. College Publications, pp. 459–477 (2014)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2016 Springer International Publishing Switzerland
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/978-3-319-40581-0_10
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-40580-3
Online ISBN: 978-3-319-40581-0
eBook Packages: Computer ScienceComputer Science (R0)