A note on Trillas' CHC models
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| Title: | A note on Trillas' CHC models |
|---|---|
| Authors: | Qiu, Daowen1,2 issqdw@mail.sysu.edu.cn |
| Source: | Artificial Intelligence. Mar2007, Vol. 171 Issue 4, p239-254. 16p. |
| Subject Terms: | Orthomodular lattices, Mathematical models, Quantum logic, Contradiction |
| Abstract: | Abstract: Trillas et al. [E. Trillas, S. Cubillo, E. Castiñeira, On conjectures in orthocomplemented lattices, Artificial Intelligence 117 (2000) 255–275] recently proposed a mathematical model for conjectures, hypotheses and consequences (abbr. CHCs), and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic. We demonstrate that the orthomodular condition is not necessary for holding Watanabe''s structure theorem of hypotheses, and indeed, in some orthocomplemented but not orthomodular lattices, this theorem is still valid. We use the CHC operators to describe the theorem of deduction, the theorem of contradiction and the Lindenbaum theorem of classical logic, and clarify their existence in the CHC models; a number of examples is presented. And we re-define the CHC operators in residuated lattices, and particularly reveal the essential differences between the CHC operators in orthocomplemented lattices and residuated lattices. [Copyright &y& Elsevier] |
| Copyright of Artificial Intelligence is the property of Elsevier B.V. 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: | Education Research Complete |
| FullText | Text: Availability: 0 |
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| Header | DbId: ehh DbLabel: Education Research Complete An: 24302237 AccessLevel: 6 PubType: Academic Journal PubTypeId: academicJournal PreciseRelevancyScore: 0 |
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| Items | – Name: Title Label: Title Group: Ti Data: A note on Trillas' CHC models – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Qiu%2C+Daowen%22">Qiu, Daowen</searchLink><relatesTo>1,2</relatesTo><i> issqdw@mail.sysu.edu.cn</i> – Name: TitleSource Label: Source Group: Src Data: <searchLink fieldCode="JN" term="%22Artificial+Intelligence%22">Artificial Intelligence</searchLink>. Mar2007, Vol. 171 Issue 4, p239-254. 16p. – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22Orthomodular+lattices%22">Orthomodular lattices</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models%22">Mathematical models</searchLink><br /><searchLink fieldCode="DE" term="%22Quantum+logic%22">Quantum logic</searchLink><br /><searchLink fieldCode="DE" term="%22Contradiction%22">Contradiction</searchLink> – Name: Abstract Label: Abstract Group: Ab Data: Abstract: Trillas et al. [E. Trillas, S. Cubillo, E. Castiñeira, On conjectures in orthocomplemented lattices, Artificial Intelligence 117 (2000) 255–275] recently proposed a mathematical model for conjectures, hypotheses and consequences (abbr. CHCs), and with this model we can execute certain mathematical reasoning and reformulate some important theorems in classical logic. We demonstrate that the orthomodular condition is not necessary for holding Watanabe''s structure theorem of hypotheses, and indeed, in some orthocomplemented but not orthomodular lattices, this theorem is still valid. We use the CHC operators to describe the theorem of deduction, the theorem of contradiction and the Lindenbaum theorem of classical logic, and clarify their existence in the CHC models; a number of examples is presented. And we re-define the CHC operators in residuated lattices, and particularly reveal the essential differences between the CHC operators in orthocomplemented lattices and residuated lattices. [Copyright &y& Elsevier] – Name: AbstractSuppliedCopyright Label: Group: Ab Data: <i>Copyright of Artificial Intelligence is the property of Elsevier B.V. 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: 10.1016/j.artint.2006.12.002 Languages: – Code: eng Text: English PhysicalDescription: Pagination: PageCount: 16 StartPage: 239 Subjects: – SubjectFull: Orthomodular lattices Type: general – SubjectFull: Mathematical models Type: general – SubjectFull: Quantum logic Type: general – SubjectFull: Contradiction Type: general Titles: – TitleFull: A note on Trillas' CHC models Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Qiu, Daowen IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 03 Text: Mar2007 Type: published Y: 2007 Identifiers: – Type: issn-print Value: 00043702 Numbering: – Type: volume Value: 171 – Type: issue Value: 4 Titles: – TitleFull: Artificial Intelligence Type: main |
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