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Geometric theories in inquisitive modal logic.

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Title: Geometric theories in inquisitive modal logic.
Authors: Müller, Valentin1 (AUTHOR)
Source: Journal of Logic & Computation. Apr2026, Vol. 36 Issue 3, p1-36. 36p.
Subjects: Modal logic, Completeness theorem, Axioms, Conditionals (Logic)
Abstract: We provide sound and complete axiomatizations for a large class of inquisitive modal logics. Inquisitive modal logic can be regarded as an extension of standard modal logic that allows to reason about informative and interrogative aspects of meaning in a uniform way. After introducing a suitable frame language for inquisitive modal logic, we construct modular labelled sequent calculi for all inquisitive modal logics characterized by a certain type of frame conditions called geometric implications. The construction is based on a general method developed by Negri. Each of our calculi is shown to satisfy cut-admissibility, height-preserving admissibility of weakening and contraction and height-preserving invertibility of all rules. The completeness of our proof systems is established by a countermodel construction in the style of Takeuti. [ABSTRACT FROM AUTHOR]
Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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Header DbId: egs
DbLabel: Engineering Source
An: 193363968
AccessLevel: 6
PubType: Academic Journal
PubTypeId: academicJournal
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  Data: Geometric theories in inquisitive modal logic.
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  Data: <searchLink fieldCode="AR" term="%22Müller%2C+Valentin%22">Müller, Valentin</searchLink><relatesTo>1</relatesTo> (AUTHOR)
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Logic+%26+Computation%22">Journal of Logic & Computation</searchLink>. Apr2026, Vol. 36 Issue 3, p1-36. 36p.
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  Data: <searchLink fieldCode="DE" term="%22Modal+logic%22">Modal logic</searchLink><br /><searchLink fieldCode="DE" term="%22Completeness+theorem%22">Completeness theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink><br /><searchLink fieldCode="DE" term="%22Conditionals+%28Logic%29%22">Conditionals (Logic)</searchLink>
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  Data: We provide sound and complete axiomatizations for a large class of inquisitive modal logics. Inquisitive modal logic can be regarded as an extension of standard modal logic that allows to reason about informative and interrogative aspects of meaning in a uniform way. After introducing a suitable frame language for inquisitive modal logic, we construct modular labelled sequent calculi for all inquisitive modal logics characterized by a certain type of frame conditions called geometric implications. The construction is based on a general method developed by Negri. Each of our calculi is shown to satisfy cut-admissibility, height-preserving admissibility of weakening and contraction and height-preserving invertibility of all rules. The completeness of our proof systems is established by a countermodel construction in the style of Takeuti. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
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  Data: <i>Copyright of Journal of Logic & Computation is the property of Oxford University Press / USA and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Type: doi
        Value: 10.1093/logcom/exaf082
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      – Code: eng
        Text: English
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        PageCount: 36
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      – SubjectFull: Modal logic
        Type: general
      – SubjectFull: Completeness theorem
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      – SubjectFull: Axioms
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      – SubjectFull: Conditionals (Logic)
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      – TitleFull: Geometric theories in inquisitive modal logic.
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              M: 04
              Text: Apr2026
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              Y: 2026
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