NOCLID is a research project funded by the Czech Science Foundation within the Junior Project scheme between January 2018 and December 2020. The project is based at the Institute of Computer Science of the Czech Academy of Sciences in Prague, Czech Republic.

Team

• Igor Sedlár (principal investigator)
• Vít Punčochář

We have an open 2-year post-doc position! A call for applications will be published and circulated soon.

Research objectives

Non-classical modal logic is an area of contemporary logic focusing on the study of modal reasoning in contexts where the assumptions of classical logic prove to be inappropriate. For example, various substructural modal logics formalize resource-sensitive and relevance-sensitive modal reasoning, and fuzzy modal logics formalize modal reasoning with graded notions. A special sort of modal reasoning not investigated in much detail so far is reasoning about information dynamics, i.e. processes that lead to changes in the information available to cognitive agents.

This project studies some of the modal logics for information dynamics based on non-classical logic. We focus on versions of Propositional Dynamic Logic, Public Announcement Logic, Logics for Soft Information Update and Dynamic Inquisitive Logic. On the non-classical side, we are interested in dynamic logics based on substructural logics including fuzzy logics. We study these logics in the context of relational (Kripke) semantics.

Work packages

WP 1, Internal models of information dynamics. The work package focuses on non-classical versions of Propositional Dynamic Logic, a prime example of a logic that models information dynamics "internally" in relational models by accessibility relations. We investigate (i) the relational semantics for substructural logics enriched by the PDL accessibility relations; (ii) lattice-valued versions of PDL extending the relational semantics for lattice-valued modal logics, and (iii) fuzzy versions of PDL.

WP 2, External models of information dynamics. In this WP we focus on non-classical versions of logics that model information dynamics "externally" by means of model transformations. This means, mainly, an investigation of Public Announcement Logic and Logics for Soft Information Update in the context of relational semantics for substructural logics, lattice-valued modal logics and fuzzy modal logics. Another task within this WP is an investigation of non-classical Dynamic Inquisitive Logic.