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A Family of Graded Epistemic Logics

Authors: Benevides, Mario R. F.; Madeira, Alexandre; Martins, Manuel A.;

A Family of Graded Epistemic Logics

Abstract

Abstract Multi-Agent Epistemic Logic has been investigated in Computer Science [Fagin, R., J. Halpern, Y. Moses and M. Vardi, “Reasoning about Knowledge,” MIT Press, USA, 1995] to represent and reason about agents or groups of agents knowledge and beliefs. Some extensions aimed to reasoning about knowledge and probabilities [Fagin, R. and J. Halpern, Reasoning about knowledge and probability, Journal of the ACM 41 (1994), pp. 340–367] and also with a fuzzy semantics have been proposed [Fitting, M., Many-valued modal logics, Fundam. Inform. 15 (1991), pp. 235–254; Maruyama, Y., Reasoning about fuzzy belief and common belief: With emphasis on incomparable beliefs, in: IJCAI 2011, Proceedings of the 22nd International Joint Conference on Artificial Intelligence, Barcelona, Catalonia, Spain, July 16–22, 2011, 2011, pp. 1008–1013]. This paper introduces a parametric method to build graded epistemic logics inspired in the systematic method to build Multi-valued Dynamic Logics introduced in [Madeira, A., R. Neves and M. A. Martins, An exercise on the generation of many-valued dynamic logics, J. Log. Algebr. Meth. Program. 85 (2016), pp. 1011–1037. URL http://dx.doi.org/10.1016/j.jlamp.2016.03.004 ; Madeira, A., R. Neves, M. A. Martins and L. S. Barbosa, A dynamic logic for every season, in: C. Braga and N. Marti-Oliet, editors, Formal Methods: Foundations and Applications – 17th Brazilian Symposium, SBMF 2014, Maceio, AL, Brazil, September 29-October 1, 2014. Proceedings, Lecture Notes in Computer Science 8941 (2014), pp. 130–145. URL http://dx.doi.org/10.1007/978-3-319-15075-8_9 ]. The parameter in both methods is the same: an action lattice [Kozen, D., On action algebras, Logic and Information Flow (1994), pp. 78–88]. This algebraic structure supports a generic space of agent knowledge operators, as choice, composition and closure (as a Kleene algebra), but also a proper truth space for possible non bivalent interpretation of the assertions (as a residuated lattice).

Keywords

Epistemic Logic, Modal logics, Action lattice, Epistemic logic, Action Lattice, Modal Logics

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citations
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
6
Average
Average
Average
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