Bounded Inquisitive Logics: Sequent Calculi and Schematic Validity

2025/07/18 by Litak, Tadeusz, Sano, Katsuhiko · 1 citation
#FOS: Computer and information sciences #Logic in Computer Science (cs.LO)

paper · doi:10.48550/arxiv.2507.13946

Abstract

Propositional inquisitive logic is the limit of its n-bounded approximations. In the predicate setting, however, this does not hold anymore, as discovered by Ciardelli and Grilletti, who also found complete axiomatizations of n-bounded inquisitive logics InqBQ_n, for every fixed n. We introduce cut-free labelled sequent calculi for these logics. We illustrate the intricacies of schematic validity in such systems by showing that the well-known Casari formula is atomically valid in (a weak sublogic of) predicate inquisitive logic InqBQ, fails to be schematically valid in it, and yet is schematically valid under the finite boundedness assumption. The derivations in our calculi, however, are guaranteed to be schematically valid whenever a single specific rule is not used.

Citations

• Axiomatizing Propositional Dependence Logics
• Inquisitive Logic

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• A Deep-Inference Sequent Calculus for Basic Propositional Team Logic (Without Delving Too Deep)

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