Łukasiewicz Public Announcement Logic

Cabrer, Leonardo Manuel; Rivieccio, Umberto; Rodríguez, Ricardo Óscar

doi:10.1007/978-3-319-40581-0_10

Cited by 4 publications

(3 citation statements)

References 6 publications

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“…The papers [32,29,38,39,9] have shown that a uniform methodology, with few ad hoc adjustments, can be extended from the classical setting to those of intuitionistic, bilattice and finite-valued Lukasiewicz modal logics. Other logics are likely to be easily dealt with, for example positive (i.e.…”

Section: Conclusion and Future Researchmentioning

confidence: 99%

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Bilattice logic of epistemic actions and knowledge

Bakhtiari

Ditmarsch

Rivieccio

2020

Annals of Pure and Applied Logic

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Baltag, Moss, and Solecki proposed an expansion of classical modal logic, called logic of epistemic actions and knowledge (EAK), in which one can reason about knowledge and change of knowledge. Kurz and Palmigiano showed how duality theory provides a flexible framework for modelling such epistemic changes, allowing one to develop dynamic epistemic logics on a weaker propositional basis than classical logic (for example an intuitionistic basis). In this paper we show how the techniques of Kurz and Palmigiano can be further extended to define and axiomatize a bilattice logic of epistemic actions and knowledge (BEAK).Our propositional basis is a modal expansion of the well-known four-valued logic of Belnap and Dunn, which is a system designed for handling inconsistent as well as potentially conflicting information. These features, we believe, make our framework particularly promising from a computer science perspective.

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Section: Conclusion and Future Researchmentioning

confidence: 99%

“…Such problems can be addressed in an algebraic framework. An elegant and versatile approach to the algebraic treatment of dynamic epistemic logic has been developed in a recent series of papers [29,32,38,39,9], in which the authors define non-classical counterparts of dynamic logics.…”

Section: Introductionmentioning

confidence: 99%

Bilattice logic of epistemic actions and knowledge

Bakhtiari

Ditmarsch

Rivieccio

2020

Annals of Pure and Applied Logic

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“…Similarly to akin logical systems (cf. References [10,34,36,41] [2,7,14]), the proof relies on a reduction procedure of IPDEL-formulas to formulas of the static fragment of IPDEL (referred to in what follows as IPEL), which preserves provable equivalence. This reduction procedure is effected using the interaction axioms and the rule of substitution of equivalent formulas.…”

Section: Proof Of the Completeness Of Ipdelmentioning

confidence: 99%

Probabilistic Epistemic Updates on Algebras

Conradie

Frittella

Palmigiano

et al. 2019

ACM Trans. Comput. Logic

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The present article contributes to the development of the mathematical theory of epistemic updates using the tools of duality theory. Here, we focus on Probabilistic Dynamic Epistemic Logic (PDEL). We dually characterize the product update construction of PDEL-models as a certain construction transforming the complex algebras associated with the given model into the complex algebra associated with the updated model. Thanks to this construction, an interpretation of the language of PDEL can be defined on algebraic models based on Heyting algebras. This justifies our proposal for the axiomatization of the intuitionistic counterpart of PDEL.

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Situated Epistemic Updates

Sedlár

Tedder

2021

Logic, Rationality, and Interaction

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Łukasiewicz Public Announcement Logic

Cited by 4 publications

References 6 publications

Bilattice logic of epistemic actions and knowledge

Bilattice logic of epistemic actions and knowledge

Probabilistic Epistemic Updates on Algebras

Situated Epistemic Updates

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