Implicational (dual) Residuated Semilinear Gaggle Logics.
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| Title: | Implicational (dual) Residuated Semilinear Gaggle Logics. |
|---|---|
| Authors: | YANG, EUNSUK1 eunsyang@jbnu.ac.kr |
| Source: | Journal of Multiple-Valued Logic & Soft Computing. 2025, Vol. 46 Issue 5/6, p419-438. 20p. |
| Subjects: | Completeness theorem, Residuated lattices, Kripke semantics, Logic, Implication (Logic) |
| Abstract: | Yang and Dunn [28] recently introduced implicational (dual) residuated partial gaggle logics. Here we extend those logics to semilinear ones. More precisely, this paper first defines the class of implicational (dual) residuated prelinear gaggle logics and shows that these logics are semilinear in an algebraic context, that is, they are semilinear in the sense that on linearly ordered matrices they are complete. We next introduce a relational semantics, called Routley-Meyer-style semantics, for finitary those logics and provide completeness for them using the semantics. We finally generalize the term "semilinear" to a notion applicable in both algebraic and set-theoretic contexts and show that finitary those logics are semilinear in this sense. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Multiple-Valued Logic & Soft Computing is the property of Old City Publishing, Inc. 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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| Items | – Name: Title Label: Title Group: Ti Data: Implicational (dual) Residuated Semilinear Gaggle Logics. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22YANG%2C+EUNSUK%22">YANG, EUNSUK</searchLink><relatesTo>1</relatesTo><i> eunsyang@jbnu.ac.kr</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Multiple-Valued+Logic+%26+Soft+Computing%22">Journal of Multiple-Valued Logic & Soft Computing</searchLink>. 2025, Vol. 46 Issue 5/6, p419-438. 20p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Completeness+theorem%22">Completeness theorem</searchLink><br /><searchLink fieldCode="DE" term="%22Residuated+lattices%22">Residuated lattices</searchLink><br /><searchLink fieldCode="DE" term="%22Kripke+semantics%22">Kripke semantics</searchLink><br /><searchLink fieldCode="DE" term="%22Logic%22">Logic</searchLink><br /><searchLink fieldCode="DE" term="%22Implication+%28Logic%29%22">Implication (Logic)</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Yang and Dunn [28] recently introduced implicational (dual) residuated partial gaggle logics. Here we extend those logics to semilinear ones. More precisely, this paper first defines the class of implicational (dual) residuated prelinear gaggle logics and shows that these logics are semilinear in an algebraic context, that is, they are semilinear in the sense that on linearly ordered matrices they are complete. We next introduce a relational semantics, called Routley-Meyer-style semantics, for finitary those logics and provide completeness for them using the semantics. We finally generalize the term "semilinear" to a notion applicable in both algebraic and set-theoretic contexts and show that finitary those logics are semilinear in this sense. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Multiple-Valued Logic & Soft Computing is the property of Old City Publishing, Inc. 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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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 20 StartPage: 419 Subjects: – SubjectFull: Completeness theorem Type: general – SubjectFull: Residuated lattices Type: general – SubjectFull: Kripke semantics Type: general – SubjectFull: Logic Type: general – SubjectFull: Implication (Logic) Type: general Titles: – TitleFull: Implicational (dual) Residuated Semilinear Gaggle Logics. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: YANG, EUNSUK IsPartOfRelationships: – BibEntity: Dates: – D: 15 M: 11 Text: 2025 Type: published Y: 2025 Identifiers: – Type: issn-print Value: 15423980 Numbering: – Type: volume Value: 46 – Type: issue Value: 5/6 Titles: – TitleFull: Journal of Multiple-Valued Logic & Soft Computing Type: main |
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