Multi-modal and Temporal Logics with Universal Formula--Reduction of Admissibility to Validity and Unification.
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| Title: | Multi-modal and Temporal Logics with Universal Formula--Reduction of Admissibility to Validity and Unification. |
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| Authors: | RYBAKOV, V.1 v.rybakov@mmu.ac.uk |
| Source: | Journal of Logic & Computation. Aug2008, Vol. 18 Issue 4, p509-519. 11p. |
| Subjects: | Mathematical logic, Combinatory logic, Logic machines, Nonclassical mathematical logic, Model theory, Set theory |
| Abstract: | The article studies multi-modal (in particular temporal, tense, logics) possessing universal formulas. We prove (Theorems 11 and 12) that the admissibility problem for inference rules (inference rules with parameters) is decidable for all decidable multi-modal (in particular, temporal) logics possessing an universal formula and decidable w.r.t. unification (unification with parameters). These theorems use characterizations of admissible rules in terms of valid rules and unifiable formulas. Results are applied to wide range of multi-modal logics, including all linear transitive temporal logics, all temporal logics with bounded zigzag, all multi-modal logics with explicit universal modality. As consequence, we show that the admissibility problem for all such logics is decidable (e.g. for all logics of the series S4nU, nϵN). [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 | Links: – Type: pdflink Text: Availability: 0 |
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| Header | DbId: egs DbLabel: Engineering Source An: 34034890 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Multi-modal and Temporal Logics with Universal Formula--Reduction of Admissibility to Validity and Unification. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22RYBAKOV%2C+V%2E%22">RYBAKOV, V.</searchLink><relatesTo>1</relatesTo><i> v.rybakov@mmu.ac.uk</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Logic+%26+Computation%22">Journal of Logic & Computation</searchLink>. Aug2008, Vol. 18 Issue 4, p509-519. 11p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Mathematical+logic%22">Mathematical logic</searchLink><br /><searchLink fieldCode="DE" term="%22Combinatory+logic%22">Combinatory logic</searchLink><br /><searchLink fieldCode="DE" term="%22Logic+machines%22">Logic machines</searchLink><br /><searchLink fieldCode="DE" term="%22Nonclassical+mathematical+logic%22">Nonclassical mathematical logic</searchLink><br /><searchLink fieldCode="DE" term="%22Model+theory%22">Model theory</searchLink><br /><searchLink fieldCode="DE" term="%22Set+theory%22">Set theory</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: The article studies multi-modal (in particular temporal, tense, logics) possessing universal formulas. We prove (Theorems 11 and 12) that the admissibility problem for inference rules (inference rules with parameters) is decidable for all decidable multi-modal (in particular, temporal) logics possessing an universal formula and decidable w.r.t. unification (unification with parameters). These theorems use characterizations of admissible rules in terms of valid rules and unifiable formulas. Results are applied to wide range of multi-modal logics, including all linear transitive temporal logics, all temporal logics with bounded zigzag, all multi-modal logics with explicit universal modality. As consequence, we show that the admissibility problem for all such logics is decidable (e.g. for all logics of the series S4nU, nϵN). [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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| RecordInfo | BibRecord: BibEntity: Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 11 StartPage: 509 Subjects: – SubjectFull: Mathematical logic Type: general – SubjectFull: Combinatory logic Type: general – SubjectFull: Logic machines Type: general – SubjectFull: Nonclassical mathematical logic Type: general – SubjectFull: Model theory Type: general – SubjectFull: Set theory Type: general Titles: – TitleFull: Multi-modal and Temporal Logics with Universal Formula--Reduction of Admissibility to Validity and Unification. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: RYBAKOV, V. IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 08 Text: Aug2008 Type: published Y: 2008 Identifiers: – Type: issn-print Value: 0955792X Numbering: – Type: volume Value: 18 – Type: issue Value: 4 Titles: – TitleFull: Journal of Logic & Computation Type: main |
| ResultId | 1 |
