Probabilistic epistemic updates on algebras

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

States of finite GBL-algebras with monoidal sum

Generalized BL-algebras, i.e. divisible residuated lattices, provide the semantics for a generalization of Basic Logic where the axiom of prelinearity does not hold. Informally, GBL-algebras generalize Heyting algebras in a similar way as MV-algebras generalize Boolean algebras. We introduce the operation of sum in finite GBL-algebras and we axiomatize the obtained finite structures, called GBL 95-algebras. We hence define states of GBL 95-algebras, extending MV-algebraic states, and we prove that they are determined by their restriction on the Heyting skeleton. Extremal states are also characterized in terms of densities concentrated in a unique join-prime idempotent