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arXiv · 2603.29424

Loop-Checking and Counter-Model Extraction for Intuitionistic Tense Logics via Nested Sequents

Tim S. Lyon
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Abstract

This paper develops a novel nested sequent proof-search methodology for intuitionistic tense logics (ITLs), supporting finite counter-model extraction. We introduce a new loop-checking method that detects repeating nested sequents using homomorphisms, thereby bounding the height of derivations during proof-search. Due to the non-invertibility of some inference rules, the algorithm does not construct a single derivation, but a generalized structure we call a 'computation tree.' We show how proofs and counter-models can be extracted from computation trees when proof-search succeeds or fails, respectively. This establishes the finite model property for each ITL of the form IKt + A with A a subset of {T,B,D}.

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Tim S. Lyon. 2026-03-31. Loop-Checking and Counter-Model Extraction for Intuitionistic Tense Logics via Nested Sequents. https://arxiv.org/abs/2603.29424

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