Overview of Results Presented in "Trends in Logic XIII"

Book Reviews: Andrzej Indrzejczak, Janusz Kaczmarek, and Michał Zawidzki (editors), “Trends in Logic XIII. Gentzen’s and Jaśkowski’s Heritage. 80 Years of Natural Deduction and Sequent Calculi”, Wydawnictwo UŁ, Łódź (Poland), 2014, 269 pages, ISBN 978-83-7969-161-6

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

Ockham's razor and reasoning about information flow

What is the minimal algebraic structure to reason about information flow? Do we really need the full power of Boolean algebras with co-closure and de Morgan dual operators? How much can we weaken and still be able to reason about multi-agent scenarios in a tidy compositional way? This paper provides some answers.Comment: 15 page