Theory and application of labelling techniques for interpretability logics

Mathematical Logic Quarterly 68 (3):352-374 (2022)
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Abstract

The notion of a critical successor [5] in relational semantics has been central to most classic modal completeness proofs in interpretability logics. In this paper we shall work with a more general notion, that of an assuring successor. This will enable more concisely formulated completeness proofs, both with respect to ordinary and generalised Veltman semantics. Due to their interesting theoretical properties, we will devote some space to the study of a particular kind of assuring labels, the so‐called full labels and maximal labels. After a general treatment of assuringness, we shall apply it to obtain a completeness result for the modal logic w.r.t. generalised semantics for a restricted class of frames.

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Joost Joosten
Universitat de Barcelona

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References found in this work

The interpretability logic of peano arithmetic.Alessandro Berarducci - 1990 - Journal of Symbolic Logic 55 (3):1059-1089.
The formalization of interpretability.Albert Visser - 1991 - Studia Logica 50 (1):81 - 105.
On Logics and Semantics for Interpretability.Luka Mikec - 2022 - Bulletin of Symbolic Logic 28 (2):265-265.

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