Author:
MIKEC LUKA,VUKOVIĆ MLADEN
Abstract
AbstractWe 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
$\textbf {IL}\textsf {W}^\ast = \textbf {IL}\textsf {WM}_{\textsf {0}}$
.
Publisher
Cambridge University Press (CUP)
Reference17 articles.
1. The Principles of Interpretability
2. A new principle in the interpretability logic of all reasonable arithmetical theories
3. [12] Verbrugge, L.C. , Verzamelingen-Veltman frames en modellen (set Veltman frames and models). Unpublished manuscript, Amsterdam, 1992.
4. Modal Matters for Interpretability Logics
5. Two new series of principles in the interpretability logic of all reasonable arithmetical theories;Goris;this Journal,2020
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