## Relation- and Domain-Changing Modal Operators (2015)

(Guillaume Hoffmann, CONICET - Universidad Blas Pascal, AR)

This talk presents two families of dynamic modal operators. We are interested in these operators because of their connection with hybrid logics and dynamic epistemic logics. We are driven by their semantic definitions and properties. In both cases the axiomatization of these logics is currently unknown.

First, we present a family of dynamic modal operators that can change the accessibility relation of a Kripke model during the evaluation of a modal formula (Relation-Changing, RC). In particular, these operators are able to delete, add or swap an edge between pairs of elements of the domain. We show these RC modal logics are fragments of classical logics and can also be translated to hybrid logics with binders. We also show that their satisfiability problems is undecidable.

Then, we present the dynamic modal operators Copy and Remove (C&R). The Copy operator replicates a given model, and the Remove operator removes paths in a given model. We show that the product update by an action model in dynamic epistemic logic decomposes in C&R operations. We also show that C&R operators with paths of length 1 can be expressed by action models with post-conditions. We investigate the expressive power of the logic with copy and remove operations, and prove decidability of the satisfiability problems of some of its syntactic fragments.

Click for slides.

Due to technical difficulties, the lecture had to be split into two parts and some minutes of the talk may be missing.

Below is a playlist:

First, we present a family of dynamic modal operators that can change the accessibility relation of a Kripke model during the evaluation of a modal formula (Relation-Changing, RC). In particular, these operators are able to delete, add or swap an edge between pairs of elements of the domain. We show these RC modal logics are fragments of classical logics and can also be translated to hybrid logics with binders. We also show that their satisfiability problems is undecidable.

Then, we present the dynamic modal operators Copy and Remove (C&R). The Copy operator replicates a given model, and the Remove operator removes paths in a given model. We show that the product update by an action model in dynamic epistemic logic decomposes in C&R operations. We also show that C&R operators with paths of length 1 can be expressed by action models with post-conditions. We investigate the expressive power of the logic with copy and remove operations, and prove decidability of the satisfiability problems of some of its syntactic fragments.

Click for slides.

Due to technical difficulties, the lecture had to be split into two parts and some minutes of the talk may be missing.

Below is a playlist: