The validity degree vectors of formulae in two-valued predicate logic
By means of infinite product of uniformly distributed probability spaces of cardinal , the concept of -validity degrees and validity degree vectors of formulae in two-valued predicate logic are introduced. It is proved that the validity degree vectors of formulae can preserve the logical relation be...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Springer
2015-09-01
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| Series: | International Journal of Computational Intelligence Systems |
| Subjects: | |
| Online Access: | https://www.atlantis-press.com/article/25868633.pdf |
| _version_ | 1811301182838145024 |
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| author | Xiaoyan Qin Yang Xu Yi Liu |
| author_facet | Xiaoyan Qin Yang Xu Yi Liu |
| author_sort | Xiaoyan Qin |
| collection | DOAJ |
| description | By means of infinite product of uniformly distributed probability spaces of cardinal , the concept of -validity degrees and validity degree vectors of formulae in two-valued predicate logic are introduced. It is proved that the validity degree vectors of formulae can preserve the logical relation between formulae. Moreover, a consistency theorem is obtained which says that the -validity degree () of the quantifierfree first-order formula without any repeated predicate symbols or terms is independent of the natural number , and is a constant equal to the validity degree () of the corresponding proposition 0 in classical propositional logic. |
| first_indexed | 2024-04-13T07:04:18Z |
| format | Article |
| id | doaj.art-649eb8f78d334eaa92b0cf75e5057723 |
| institution | Directory Open Access Journal |
| issn | 1875-6883 |
| language | English |
| last_indexed | 2024-04-13T07:04:18Z |
| publishDate | 2015-09-01 |
| publisher | Springer |
| record_format | Article |
| series | International Journal of Computational Intelligence Systems |
| spelling | doaj.art-649eb8f78d334eaa92b0cf75e50577232022-12-22T02:57:01ZengSpringerInternational Journal of Computational Intelligence Systems1875-68832015-09-018510.1080/18756891.2015.1063245The validity degree vectors of formulae in two-valued predicate logicXiaoyan QinYang XuYi LiuBy means of infinite product of uniformly distributed probability spaces of cardinal , the concept of -validity degrees and validity degree vectors of formulae in two-valued predicate logic are introduced. It is proved that the validity degree vectors of formulae can preserve the logical relation between formulae. Moreover, a consistency theorem is obtained which says that the -validity degree () of the quantifierfree first-order formula without any repeated predicate symbols or terms is independent of the natural number , and is a constant equal to the validity degree () of the corresponding proposition 0 in classical propositional logic.https://www.atlantis-press.com/article/25868633.pdftwo-valued predicate logic-validity degreevalidity degree vectorconsistency theorem |
| spellingShingle | Xiaoyan Qin Yang Xu Yi Liu The validity degree vectors of formulae in two-valued predicate logic International Journal of Computational Intelligence Systems two-valued predicate logic -validity degree validity degree vector consistency theorem |
| title | The validity degree vectors of formulae in two-valued predicate logic |
| title_full | The validity degree vectors of formulae in two-valued predicate logic |
| title_fullStr | The validity degree vectors of formulae in two-valued predicate logic |
| title_full_unstemmed | The validity degree vectors of formulae in two-valued predicate logic |
| title_short | The validity degree vectors of formulae in two-valued predicate logic |
| title_sort | validity degree vectors of formulae in two valued predicate logic |
| topic | two-valued predicate logic -validity degree validity degree vector consistency theorem |
| url | https://www.atlantis-press.com/article/25868633.pdf |
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