Probabilistic Epistemic Updates on Algebras

Willem Conradie 1 Sabine Frittella 2 Alessandra Palmigiano 1, 3 Apostolos Tzimoulis 3 Nachoem Wijnberg 4
2 SDS
LIFO - Laboratoire d'Informatique Fondamentale d'Orléans
3 Applied Logic
TU Delft - Delft University of Technology
Abstract : The present paper 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, of which prove soundness and completeness with respect to algebraic probabilistic epistemic models.
Type de document :
Pré-publication, Document de travail
2017
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https://hal.archives-ouvertes.fr/hal-01509416
Contributeur : Sabine Frittella <>
Soumis le : lundi 17 avril 2017 - 18:21:27
Dernière modification le : jeudi 12 juillet 2018 - 12:31:18

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  • HAL Id : hal-01509416, version 1
  • ARXIV : 1612.05267

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Willem Conradie, Sabine Frittella, Alessandra Palmigiano, Apostolos Tzimoulis, Nachoem Wijnberg. Probabilistic Epistemic Updates on Algebras. 2017. 〈hal-01509416〉

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