Interpolation and the Interpretability Logic of PA

The interpretability logic ILF ∗

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.

Interpretability Logic

This is an overview a study of interpretability logic in Zagreb for the last twenty years: a brief history and some planes for further research. The idea of treating a provability predicate as a modal operator goes back to Gödel. The same idea was taken up later by Kripke and Montague, but only in the mid–seventies was the correct choice of axioms, based on Löb’s theorem, seriously considered b...

Unary Interpretability Logic

Let T be an arithmetical theory. We introduce a unary modal operator T to be interpreted arithmetically as the unary interpretability predicate over T. We present complete axiomatizations of the (unary) interpretability principles underlying two important classes of theories. We also prove some basic modal results about these new axiomatizations.

Bi-Unary Interpretability Logic

Complexity of the interpretability logic IL

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.