# Sound and Complete Tree-Sequent Calculus for Inquisitive Logic

• Katsuhiko Sano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5514)

## Abstract

We introduce a tree-sequent calculus for inquisitive logic (Groenendijk 2008) as a special form of labelled deductive system (Gabbay 1996). In particular, we establish that (i) our tree-sequent calculus is sound and complete with respect to Groenendijk’s inquisitive semantics and that (ii) our tree-sequent calculus is decidable and enjoys cut-elimination theorem. (ii) is semantically revealed by our argument for (i). The key idea which allows us to obtain these results is as follows: In Groenendijk’s inquisitive semantics, a formula of propositional logic is evaluated against a pair of worlds on a model. Given the appropriate pre-order on the set of such pairs, any inquisitive model can be regarded as a Kripke model for intuitionistic logic. This representation enables us to connect inquisitive semantics with the tree-sequent technique for non-classical logics (Kashima 1999).

## Keywords

Propositional Logic Intuitionistic Logic Kripke Model Sequent Calculus Hybrid Logic
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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## Authors and Affiliations

• Katsuhiko Sano
• 1
1. 1.Department of Humanistic Informatics Graduate School of LettersKyoto University / JSPSJapan