Interpretability logics and generalised Veltman semantics

Journal of Symbolic Logic 85 (2):749-772 (2020)
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Abstract

We obtain modal completeness of the interpretability logics IL $\!\!\textsf {P}_{\textsf {0}}$ and ILR w.r.t. generalised Veltman semantics. Our proofs are based on the notion of full labels [2]. We also give shorter proofs of completeness w.r.t. the generalised semantics for many classical interpretability logics. We obtain decidability and finite model property w.r.t. the generalised semantics for IL $\textsf {P}_{\textsf {0}}$ and ILR. Finally, we develop a construction that might be useful for proofs of completeness of extensions of ILW w.r.t. the generalised semantics in the future, and demonstrate its usage with $\textbf {IL}\textsf {W}^\ast = \textbf {IL}\textsf {WM}_{\textsf {0}}$.

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References found in this work

Modal Matters for Interpretability Logics.Evan Goris & Joost Joosten - 2008 - Logic Journal of the IGPL 16 (4):371-412.
Modal completeness of ILW.Dick De Jongh & Frank Veltman - 1999 - In Jelle Gerbrandy, Maarten Marx, Maarten de Rijke & Yde Venema (eds.), Essays Dedicated to Johan van Benthem on the Occasion of His 50th Birthday. Amsterdam University Press.
Filtrations of generalized Veltman models.Tin Perkov & Mladen Vuković - 2016 - Mathematical Logic Quarterly 62 (4-5):412-419.

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