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INTERPRETABILITY LOGICS AND GENERALISED VELTMAN SEMANTICS

Part of: Proof theory and constructive mathematics General logic

Published online by Cambridge University Press:  18 June 2020

LUKA MIKEC  and
MLADEN VUKOVIĆ
LUKA MIKEC
Affiliation:
DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE, UNIVERSITY OF ZAGREB BIJENIčKA 30, ZAGREB, CROATIAE-mail: luka.mikec@math.hrE-mail: vukovic@math.hr
MLADEN VUKOVIĆ
Affiliation:
DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCE, UNIVERSITY OF ZAGREB BIJENIčKA 30, ZAGREB, CROATIAE-mail: luka.mikec@math.hrE-mail: vukovic@math.hr
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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 $\textbf {IL}\textsf {W}^\ast = \textbf {IL}\textsf {WM}_{\textsf {0}}$ .

Keywords

interpretability logicVeltman semanticscompletenessfinite model propertydecidability

MSC classification

Primary: 03B45: Modal logic (including the logic of norms)
Secondary: 03B60: Other nonclassical logic 03F45: Provability logics and related algebras (e.g., diagonalizable algebras)
Type
Articles
Information
The Journal of Symbolic Logic , Volume 85 , Issue 2 , June 2020 , pp. 749 - 772
Copyright
© The Association for Symbolic Logic 2020

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