Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems
By means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary con...
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Applied Computational Intelligence and Soft Computing |
| Online Access: | http://dx.doi.org/10.1155/2010/907298 |
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| _version_ | 1832566718440931328 |
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| author | Jiancheng Zhang |
| author_facet | Jiancheng Zhang |
| author_sort | Jiancheng Zhang |
| collection | DOAJ |
| description | By means of theory of truth degrees of formulas, according to deduction theorems
and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed. |
| format | Article |
| id | doaj-art-e0b504bc872d4cd88bfbd6671011d49a |
| institution | Kabale University |
| issn | 1687-9724 1687-9732 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Applied Computational Intelligence and Soft Computing |
| spelling | doaj-art-e0b504bc872d4cd88bfbd6671011d49a2025-02-03T01:03:29ZengWileyApplied Computational Intelligence and Soft Computing1687-97241687-97322010-01-01201010.1155/2010/907298907298Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic SystemsJiancheng Zhang0Department of Mathematics, Quanzhou Normal University, Quanzhou, Fujian 362000, ChinaBy means of theory of truth degrees of formulas, according to deduction theorems and completeness theorems, the new concepts of consistency degrees and polar index for general theories in Łukasewicz fuzzy and n-valued propositional logic systems are introduced. Moreover, sufficient and necessary conditions for a theory Γ to be consistent, inconsistent, and fully divergent are obtained. Finally, some important properties of truth degrees of formulas are proposed.http://dx.doi.org/10.1155/2010/907298 |
| spellingShingle | Jiancheng Zhang Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems Applied Computational Intelligence and Soft Computing |
| title | Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems |
| title_full | Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems |
| title_fullStr | Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems |
| title_full_unstemmed | Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems |
| title_short | Consistency Degrees of Theories in Łukasiewicz Fuzzy and n-Valued Propositional Logic Systems |
| title_sort | consistency degrees of theories in lukasiewicz fuzzy and n valued propositional logic systems |
| url | http://dx.doi.org/10.1155/2010/907298 |
| work_keys_str_mv | AT jianchengzhang consistencydegreesoftheoriesinłukasiewiczfuzzyandnvaluedpropositionallogicsystems |