Probabilistic Epistemic Updates on Algebras

Willem Conradie (1) , Sabine Frittella (2) , Alessandra Palmigiano (3) , Apostolos Tzimoulis (3)

1 UJ - University of Johannesburg [South Africa]
2 LIF - Laboratoire d'informatique Fondamentale de Marseille
3 Applied Logic

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 characterise 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.

Mots clés: intuitionistic probabilistic dynamic epistemic logic; duality; intuitionistic modal logic; algebraic models; pointfree semantics

Domaines: Logique en informatique [cs.LO]

Willem Conradie, Sabine Frittella, Alessandra Palmigiano, Apostolos Tzimoulis. Probabilistic Epistemic Updates on Algebras. LORI V, Oct 2015, Taipei, Taiwan. ⟨10.1007/978-3-662-48561-3_6⟩. ⟨hal-01509403⟩