Handling Transitive Relations in First-Order Automated Reasoning.
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| Title: | Handling Transitive Relations in First-Order Automated Reasoning. |
|---|---|
| Authors: | Claessen, Koen1 koen@chalmers.se, Lillieström, Ann1 |
| Source: | Journal of Automated Reasoning. Dec2021, Vol. 65 Issue 8, p1097-1124. 28p. |
| Subjects: | Automatic theorem proving, Mathematical equivalence, Reasoning, Axiomatic design, Mathematical notation |
| Abstract: | We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations. [ABSTRACT FROM AUTHOR] |
| Copyright of Journal of Automated Reasoning is the property of Springer Nature 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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| Header | DbId: egs DbLabel: Engineering Source An: 153186653 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: Handling Transitive Relations in First-Order Automated Reasoning. – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Claessen%2C+Koen%22">Claessen, Koen</searchLink><relatesTo>1</relatesTo><i> koen@chalmers.se</i><br /><searchLink fieldCode="AR" term="%22Lillieström%2C+Ann%22">Lillieström, Ann</searchLink><relatesTo>1</relatesTo> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Journal+of+Automated+Reasoning%22">Journal of Automated Reasoning</searchLink>. Dec2021, Vol. 65 Issue 8, p1097-1124. 28p. – Name: Subject Label: Subjects Group: Su Data: <searchLink fieldCode="DE" term="%22Automatic+theorem+proving%22">Automatic theorem proving</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+equivalence%22">Mathematical equivalence</searchLink><br /><searchLink fieldCode="DE" term="%22Reasoning%22">Reasoning</searchLink><br /><searchLink fieldCode="DE" term="%22Axiomatic+design%22">Axiomatic design</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+notation%22">Mathematical notation</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: We present a number of alternative ways of handling transitive binary relations that commonly occur in first-order problems, in particular equivalence relations, total orders, and transitive relations in general. We show how such relations can be discovered syntactically in an input theory, and how they can be expressed in alternative ways. We experimentally evaluate different such ways on problems from the TPTP, using resolution-based reasoning tools as well as instance-based tools. Our conclusions are that (1) it is beneficial to consider different treatments of binary relations as a user, and that (2) reasoning tools could benefit from using a preprocessor or even built-in support for certain types of binary relations. [ABSTRACT FROM AUTHOR] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Journal of Automated Reasoning is the property of Springer Nature 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: Identifiers: – Type: doi Value: 10.1007/s10817-021-09605-z Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 28 StartPage: 1097 Subjects: – SubjectFull: Automatic theorem proving Type: general – SubjectFull: Mathematical equivalence Type: general – SubjectFull: Reasoning Type: general – SubjectFull: Axiomatic design Type: general – SubjectFull: Mathematical notation Type: general Titles: – TitleFull: Handling Transitive Relations in First-Order Automated Reasoning. Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Claessen, Koen – PersonEntity: Name: NameFull: Lillieström, Ann IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 12 Text: Dec2021 Type: published Y: 2021 Identifiers: – Type: issn-print Value: 01687433 Numbering: – Type: volume Value: 65 – Type: issue Value: 8 Titles: – TitleFull: Journal of Automated Reasoning Type: main |
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