In [Sas01], it was given a cut-free sequent system for the smallest interpretability logic IL. He first gave a cut-free system for IK4, a sublogic of IL, whose ✄-free fragment is the modal logic K4. Here, using the method in [Sas01], we give sequent systems for the interpretability logic ILP obtained by adding the persistence axiom P : (p✄ q) ⊃ ✷(p✄ q) to IL and for the logic IK4+P obtained by ...

In a recent reply to our article, “What is Interpretability?,” Prasetya argues against position that artificial neural networks are explainable. It claimed indefeasibility thesis—that adding complexity an explanation of phenomenon does not make the any less explainable—is false. More precisely, unificationist explanations defeasible increasing complexity, and thus, we may be able provide such h...

Interpretability logic is a modal description of the interpretability predicate. The modal system IL is an extension of the provability logic GL (Gödel–Löb). Bisimulation quotients and largest bisimulations have been well studied for Kripke models. We examine interpretability logic and consider how these results extend to Veltman models. REPORTS ON MATHEMATICAL LOGIC 40 (2006), 59–73 Domagoj VR...

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...

In this paper we study IL(PRA), the interpretability logic of PRA. As PRA is neither an essentially reflexive theory nor finitely axiomatizable, the two known arithmetical completeness results do not apply to PRA: IL(PRA) is not ILM or ILP. IL(PRA) does of course contain all the principles known to be part of IL(All), the interpretability logic of the principles common to all reasonable arithme...