Modal Matters for Interpretability Logics

Modal Matters for Interpretability Logics

This paper is the first in a series of three related papers on modal methods in interpretability logics and applications. In this first paper the fundaments are laid for later results. These fundaments consist of a thorough treatment of a construction method to obtain modal models. This construction method is used to reprove some known results in the area of interpretability like the modal comp...

Modal Matters in Interpretability Logics

In this paper we expose a method for building models for interpretability logics. The method can be compared to the method of taking unions of chains in classical model theory. Many applications of the method share a common part. We isolate this common part in a main lemma. Doing so, many of our results become applications of this main lemma. We also briefly describe how our method can be gener...

Modal Logics for Coalgebras

This presentation is to introduce basic notions and recent results on an approach to specify behaviors of coalgebras by means of modal logics, based on the lecture by Dirk Pattinson (Pattinson, 2003) in NASSLLI 2003.

Modal Logics for Computer

Provability and Interpretability Logics with Restricted Realizations

The provability logic of a theory T is the set of modal formulas, which under any arithmetical realization are provable in T . We slightly modify this notion by requiring the arithmetical realizations to come from a specified set Γ. We make an analogous modification for interpretability logics. We first studied provability logics with restricted realizations, and show that for various natural c...