# Epistemic Updates on Algebras

## Alessandra Palmigiano

### Delft University of Technology

The present talk reports on some recent developments in the mathematical theory of epistemic updates, a very fruitful line of research initiated in [4, 3] and further pursued in [2, 5, 1]. This line of research is motivated by the observations that ‘dynamic phenomena’ are independent of their underlying static logic being classical, and that this assumption is unrealistic in many important contexts; for instance, in all those contexts (such as scientific experiments, acquisition of legal evidence, verification of programs, etc.) where the notion of truth is procedural. Desirable and conceptually important as it is, the more general problem of identifying the right intuitionistic (or more generally nonclassical) counterparts of (modal-like) expansions of classical logic (such as modal logics themselves, or hybrid logics, etc.) has proven to be difficult, and for most of these logics, this question is still open. Indeed, different axiomatizations which in the presence of classical tautologies define the same logic become nonequivalent against a weaker propositional background. Hence, each classical axiomatization might have infinitely many nonequivalent nonclassical potential counterparts. We introduce a uniform methodology for defining the nonclassical counterparts of dynamic logics, which is grounded on semantics rather than on syntax. This methodology is based on the dual characterizations of the transformations of models which interpret the actions. This dual characterization makes it possible to define epistemic updates on algebras, thanks to which an algebraic semantics for (e.g.) the intuitionistic counterpart of Baltag-Moss-Solecki’s dynamic epistemic logic can be defined e.g. on Heyting algebras.

References

[1] Z. Bakhtiari, U. Rivieccio. Epistemic Updates on Bilattices. Proceedings of the Fifth International Workshop on Logic, Rationality and Interaction – LORI, LNCS 9394, pp. 426-8 (2015).

[2] W. Conradie, S. Frittella, A. Palmigiano, A. Tzimoulis, Probabilistic Epistemic Updates on Algebras, Proceedings of the Fifth International Workshop on Logic, Rationality and Interaction – LORI, LNCS 9394, pp. 64-76 (2015).

[3] Alexander Kurz and Alessandra Palmigiano. Epistemic updates on algebras. Logical Methods in Computer Science, 2013. arXiv:1307.0417. 1

[4] Minghui Ma, Alessandra Palmigiano, and Mehrnoosh Sadrzadeh. Algebraic semantics and model completeness for intuitionistic public announcement logic. Annals of Pure and Applied Logic, 165 (2014) 963-995.

[5] U. Rivieccio, Bilattice Public Announcement Logic, Proc. AiML 10 (2014).

Alessandra Palmigiano received her doctorate from the University of Barcelona in 2005. She is currently the head the research group of applied logic at TU Delft and has been part of the Institute for Logic, Language and Computation (ILLC) of the University of Amsterdam. Her interests include technical research of modal and epistemic logics, which models, formalizes and analyzes human cognition.