ML-1998-11: The Interpolation Theorem for IL and ILP

ML-1998-11: Areces, Carlos and de Jongh, Dick and Hoogland, Eva (1998) The Interpolation Theorem for IL and ILP. [Report]

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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 \Lambda­
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.

Item Type: Report
Report Nr: ML-1998-11
Series Name: Mathematical Logic and Foundations (ML)
Year: 1998
Uncontrolled Keywords: Interpretability Logic, Interpolation Properties, Beth Property, Fixed Point Property.
Date Deposited: 12 Oct 2016 14:40
Last Modified: 12 Oct 2016 14:40

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