Many−Valued First−Order Logics with Probabilistic Semantics
<p>We present n-valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n-valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics L_n. Within...
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| Materialtyp: | Conference item |
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Springer
1999
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| _version_ | 1826268752460644352 |
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| author | Lukasiewicz, T |
| author_facet | Lukasiewicz, T |
| author_sort | Lukasiewicz, T |
| collection | OXFORD |
| description | <p>We present n-valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n-valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics L_n. Within this semantics, closed formulas of classical first-order logics that are logically equivalent in the classical sense also have the same truth value under all n-valued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, n-valued logical consequence in disjunctive logic programs with n-valued disjunctive facts can be reduced to classical logical consequence in n-1 layers of classical disjunctive logic programs. Moreover, we show that n-valued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in n-valued logic programs have the same computational complexity like their classical counterparts.</p> |
| first_indexed | 2024-03-06T21:14:25Z |
| format | Conference item |
| id | oxford-uuid:3f4670a7-da2a-4f41-9a6e-5db35d7c8fdb |
| institution | University of Oxford |
| last_indexed | 2024-03-06T21:14:25Z |
| publishDate | 1999 |
| publisher | Springer |
| record_format | dspace |
| spelling | oxford-uuid:3f4670a7-da2a-4f41-9a6e-5db35d7c8fdb2022-03-26T14:31:03ZMany−Valued First−Order Logics with Probabilistic SemanticsConference itemhttp://purl.org/coar/resource_type/c_5794uuid:3f4670a7-da2a-4f41-9a6e-5db35d7c8fdbDepartment of Computer ScienceSpringer1999Lukasiewicz, T<p>We present n-valued first-order logics with a purely probabilistic semantics. We then introduce a new probabilistic semantics of n-valued first-order logics that lies between the purely probabilistic semantics and the truth-functional semantics of the n-valued Lukasiewicz logics L_n. Within this semantics, closed formulas of classical first-order logics that are logically equivalent in the classical sense also have the same truth value under all n-valued interpretations. Moreover, this semantics is shown to have interesting computational properties. More precisely, n-valued logical consequence in disjunctive logic programs with n-valued disjunctive facts can be reduced to classical logical consequence in n-1 layers of classical disjunctive logic programs. Moreover, we show that n-valued logic programs have a model and a fixpoint semantics that are very similar to those of classical logic programs. Finally, we show that some important deduction problems in n-valued logic programs have the same computational complexity like their classical counterparts.</p> |
| spellingShingle | Lukasiewicz, T Many−Valued First−Order Logics with Probabilistic Semantics |
| title | Many−Valued First−Order Logics with Probabilistic Semantics |
| title_full | Many−Valued First−Order Logics with Probabilistic Semantics |
| title_fullStr | Many−Valued First−Order Logics with Probabilistic Semantics |
| title_full_unstemmed | Many−Valued First−Order Logics with Probabilistic Semantics |
| title_short | Many−Valued First−Order Logics with Probabilistic Semantics |
| title_sort | many valued first order logics with probabilistic semantics |
| work_keys_str_mv | AT lukasiewiczt manyvaluedfirstorderlogicswithprobabilisticsemantics |