Abstract

In this article we establish interpolation for the minimal system of interpretability logic IL. We prove that arrow interpolation holds for IL and that turnstile interpolation and interpolation for the -modality easily follow from this. Furthermore, these properties are extended to the system ILP. The related issue of Beth Definability is also addressed. As usual, the arrow interpolation property implies the Beth property. From the latter it follows via an argumentation which is standard in provability logic, that IL has the fixed point property. Finally we observe that a general result of Maksimova [11] for provability logics can be extended to interpretability logics, implying that all extensions of IL have the Beth property. Keywords Interpretability Logic, Interpolation Properties, Beth Property, Fixed Point Property. 1 Introduction 1.1 Some History Interpretability logics are extensions of provability logics introduced by Visser in [15]. There the modal logics IL, ILM and ILP a...

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