This paper gives an overview of what we call Verbrugge Semantics which so far in the
literature has been called Generalised Veltman semantics. Interpretability logics are …

Interpretability logics are endowed with relational semantics\a la Kripke: Veltman semantics.
For certain applications though, this semantics is not fine-grained enough. Back in 1992, in …

The notion of a critical successor 5 in relational semantics has been central to most classic
modal completeness proofs in interpretability logics. In this paper we shall work with a more …

We introduce a modal logic FIL for Feferman interpretability. In this logic both the provability
modality and the interpretability modality can come with a label. This label indicates that in …

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[eng] In the central part of this thesis we study for different interpretability logics the following
aspects: completeness for modal semantics, decidability and algorithmic complexity. In …

The notion of a critical successor [dJV90] has been central to almost all modal completeness
proofs in interpretability logics. In this paper we shall work with an alternative notion, that of …

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 …

In is paper we present a labelled tableau proof system that serves a wide class of
interpretability logics. The system is proved sound and complete for any interpretability logic …

Sufficiently strong arithmetical theories such as PA can formalize their interpretability
predicate. This predicate expresses the concept of relativized interpretability between finite …