On Logics and Semantics for Interpretability

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...

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...

Semantics and logics for signals

On Fibring Semantics for BDI Logics

This study examines BDI logics in the context of Gabbay’s fibring semantics. We show that dovetailing (a special form of fibring) can be adopted as a semantic methodology to combine BDI logics. We develop a set of interaction axioms that can capture static as well as dynamic aspects of the mental states in BDI systems, using Catach’s incestual schema Ga,b,c,d . Further we exemplify the constrai...