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Intuitionistic monotone modal logic via translation.

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Title: Intuitionistic monotone modal logic via translation.
Authors: Groot, Jim de1 (AUTHOR)
Source: Journal of Logic & Computation. Jun2026, Vol. 36 Issue 4, p1-39. 39p.
Subjects: Modal logic, Intuitionistic mathematics, First-order logic, Axioms, Kripke semantics
Abstract: We introduce a monotone modal analogue of the intuitionistic (normal) modal logic |$\textsf{IK}$| using a translation into a suitable (intuitionistic) first-order logic. We axiomatize the logic and give a semantics by means of intuitionistic neighbourhood models, which contain neighbourhoods whose value can change when moving along the intuitionistic accessibility relation. We compare the resulting logic with other intuitionistic monotone modal logics and show how it can be embedded into a multimodal version of |$\textsf{IK}$|⁠. [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
FullText Text:
  Availability: 0
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DbLabel: Engineering Source
An: 194431601
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PubType: Academic Journal
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  Data: Intuitionistic monotone modal logic via translation.
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  Data: <searchLink fieldCode="AR" term="%22Groot%2C+Jim+de%22">Groot, Jim de</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>. Jun2026, Vol. 36 Issue 4, p1-39. 39p.
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  Data: <searchLink fieldCode="DE" term="%22Modal+logic%22">Modal logic</searchLink><br /><searchLink fieldCode="DE" term="%22Intuitionistic+mathematics%22">Intuitionistic mathematics</searchLink><br /><searchLink fieldCode="DE" term="%22First-order+logic%22">First-order logic</searchLink><br /><searchLink fieldCode="DE" term="%22Axioms%22">Axioms</searchLink><br /><searchLink fieldCode="DE" term="%22Kripke+semantics%22">Kripke semantics</searchLink>
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  Data: We introduce a monotone modal analogue of the intuitionistic (normal) modal logic |$\textsf{IK}$| using a translation into a suitable (intuitionistic) first-order logic. We axiomatize the logic and give a semantics by means of intuitionistic neighbourhood models, which contain neighbourhoods whose value can change when moving along the intuitionistic accessibility relation. We compare the resulting logic with other intuitionistic monotone modal logics and show how it can be embedded into a multimodal version of |$\textsf{IK}$|⁠. [ABSTRACT FROM AUTHOR]
– Name: AbstractSuppliedCopyright
  Label:
  Group: Ab
  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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        Value: 10.1093/logcom/exag017
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      – Code: eng
        Text: English
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        PageCount: 39
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      – SubjectFull: Modal logic
        Type: general
      – SubjectFull: Intuitionistic mathematics
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      – SubjectFull: First-order logic
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      – SubjectFull: Axioms
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      – SubjectFull: Kripke semantics
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      – TitleFull: Intuitionistic monotone modal logic via translation.
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              M: 06
              Text: Jun2026
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              Y: 2026
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