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INTERPRETABILITY LOGICS AND GENERALISED VELTMAN SEMANTICS
- Part of
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- Journal:
- The Journal of Symbolic Logic / Volume 85 / Issue 2 / June 2020
- Published online by Cambridge University Press:
- 18 June 2020, pp. 749-772
- Print publication:
- June 2020
-
- Article
- Export citation
-
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
$\textbf {IL}\textsf {W}^\ast = \textbf {IL}\textsf {WM}_{\textsf {0}}$
.
