TY - JOUR
T1 - Probabilistic epistemic updates on algebras
AU - Conradie, Willem
AU - Frittella, Sabine
AU - Palmigiano, Alessandra
AU - Tzimoulis, Apostolos
AU - Wijnberg, Nachoem
PY - 2019/8
Y1 - 2019/8
N2 - 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.
AB - 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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U2 - 10.1145/3341725
DO - 10.1145/3341725
M3 - Article
AN - SCOPUS:85075573309
SN - 1529-3785
VL - 20
SP - 1
EP - 75
JO - ACM Transactions on Computational Logic
JF - ACM Transactions on Computational Logic
IS - 4
M1 - 24
ER -