In this paper we consider IL0, the closed fragment of the basic interpretability logic IL. We show that we can translate GL1, the one variable fragment of Gödel-Löb’s provabilty logic GL, into IL0. Invoking a result on the PSPACE completeness of GL1 we obtain the PSPACE hardness of IL0.

In this paper we determine a characteristic class of ILsetframes for the principle F. Then we prove that the principle P is not provable in the system ILF. We use a generalized Veltman model.

In this paper, we develop a toolkit to derive principles for the interpetability logic of all reasonable theories by fine-tuning ILM and ILP proofs.

We show that the decision problem for the basic system of interpretability logic IL is PSPACE– complete. For this purpose we present an algorithm which uses polynomial space with respect to the length of a given formula. The existence of such algorithm, together with the previously known PSPACE–hardness of the closed fragment of IL, implies PSPACE–completeness.

David Guaspari [G] conjectured that a modal formula is essentially Σ1 (i.e., is is Σ1 under any arithmetical interpretation), if and only if it is provably equivalent to a disjunction of formulas of the form 2B. This conjecture was proved first by A. Visser. Then, in [DJP], the authors characterized essentially Σ1 formulas of languages with witness comparisons using the interpretability logic I...

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 logic is a nonstandard modal logic. Interpretability logic is an extension of provability logic. Generalized Veltman models are Kripke like semantics for interpretability logic. We consider generalized Veltman models with a root, i.e. r-validity, r-satisfiability and a consequence relation. We modify Fine’s and Rautenberg’s proof and prove non–compactness of interpretability logic.

This paper is a presentation of a status qu stionis, to wit of the problem of the interpretability logic of all reasonable arithmetical theories. We present both the arithmetical side and the modal side of the question.