Probabilistic and Truth−Functional Many−Valued Logic Programming
<p>We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problem...
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| Format: | Conference item |
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IEEE
1999
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| _version_ | 1826263029708226560 |
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| author | Lukasiewicz, T |
| author_facet | Lukasiewicz, T |
| author_sort | Lukasiewicz, T |
| collection | OXFORD |
| description | <p>We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-valued logic programs. We then focus on many-valued logic programming in Pr_n* as an approximation of probabilistic many-valued logic programming. Surprisingly, many-valued logic programs in Pr_n* have both a probabilistic semantics in probabilities over a set of possible worlds and a truth-functional semantics in the finite-valued Lukasiewicz logics L_n. Moreover, many-valued logic programming in Pr_n* has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming.</p> |
| first_indexed | 2024-03-06T19:45:12Z |
| format | Conference item |
| id | oxford-uuid:220e9f1a-dd1d-4c21-8279-c33586075f14 |
| institution | University of Oxford |
| last_indexed | 2024-03-06T19:45:12Z |
| publishDate | 1999 |
| publisher | IEEE |
| record_format | dspace |
| spelling | oxford-uuid:220e9f1a-dd1d-4c21-8279-c33586075f142022-03-26T11:36:39ZProbabilistic and Truth−Functional Many−Valued Logic ProgrammingConference itemhttp://purl.org/coar/resource_type/c_5794uuid:220e9f1a-dd1d-4c21-8279-c33586075f14Department of Computer ScienceIEEE1999Lukasiewicz, T<p>We introduce probabilistic many-valued logic programs in which the implication connective is interpreted as material implication. We show that probabilistic many-valued logic programming is computationally more complex than classical logic programming. More precisely, some deduction problems that are P-complete for classical logic programs are shown to be co-NP-complete for probabilistic many-valued logic programs. We then focus on many-valued logic programming in Pr_n* as an approximation of probabilistic many-valued logic programming. Surprisingly, many-valued logic programs in Pr_n* have both a probabilistic semantics in probabilities over a set of possible worlds and a truth-functional semantics in the finite-valued Lukasiewicz logics L_n. Moreover, many-valued logic programming in Pr_n* has a model and fixpoint characterization, a proof theory, and computational properties that are very similar to those of classical logic programming.</p> |
| spellingShingle | Lukasiewicz, T Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title | Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title_full | Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title_fullStr | Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title_full_unstemmed | Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title_short | Probabilistic and Truth−Functional Many−Valued Logic Programming |
| title_sort | probabilistic and truth functional many valued logic programming |
| work_keys_str_mv | AT lukasiewiczt probabilisticandtruthfunctionalmanyvaluedlogicprogramming |