A Non-uniform View of Craig Interpolation in Modal Logics With Linear Frames
Year: 2025
Type: article
Abstract: Normal modal logics extending the logic K 4.3 $\mathsf {K4.3}$ sans serif upper K Baseline sans-serif 4.3 of linear transitive frames are known to lack the Craig interpolation property (CIP), except some logics of bounded depth such as S 5 $\mathsf {S5}$ sans serif upper S Baseline sans-serif 5 . We turn this ‘negative’ fact into a research question and pursue a non-uniform approach to Craig interpolation by investigating the following interpolant existence problem: decide whether there exists a Craig interpolant between two given formulas in any fixed logic above K 4.3 $\mathsf {K4.3}$ sans serif upper K Baseline sans-serif 4.3 . Using a bisimulation-based characterisation of interpolant existence for descriptive frames, we show that this problem is decidable and coNP -complete for all finitely axiomatisable normal modal logics containing K 4.3 $\mathsf {K4.3}$ sans serif upper K Baseline sans-serif 4.3 . It is thus not harder than entailment in these logics, which is in sharp contrast to other recent non-uniform interpolation results. We also extend our approach to Priorean temporal logics (with both past and future modalities) over the standard time flows—the integers, rationals, reals, and finite strict linear orders—none of which is blessed with the CIP.
Source: Journal of Symbolic Logic
Authors: AGI KURUCZ, FRANK WOLTER, MICHAEL ZAKHARYASCHEV
Language: English
Subfield: Artificial Intelligence
Field: Computer Science
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,550
OpenAlex ID: W7101425137
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