Lukasiewicz, T.: 1999c, `Probabilistic and truth-functional many-valued logic programming '. In: Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic. pp. 236--241.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....logics closer to truth functional logics [16] In detail, our many valued disjunctive logic programs have a probabilistic semantics in probabilities over possible worlds. Furthermore, the truth values of all clauses are truthfunctionally de ned on the truth values of atoms. We showed in [16] and [17] that many valued de nite logic programming with this probabilistic semantics has a model and xpoint characterization and a proof theory similar to classical de nite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same ....

....quantitative deduction [30] can be given a probabilistic semantics by probabilities over possible worlds under the additional axiom. However, van Emden s quantitative deduction is based on a conditional INFSYS RR 1843 99 09 3 probability semantics of the implication connective, while [16] [17], and the present paper use the material implication semantics. Interestingly, it turns out that the material implication is much closer to classical logic programming. In particular, the material implication is more suitable for additionally handling disjunction and nonmonotonic negation. It is ....

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T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proc. of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236-241, 1999. INFSYS RR 1843-99-09 19

....particular, can we gain tractability of deciding lukasiewicz.tex; 1 09 2001; 20:56; p. 42 Probabilistic Default Reasoning with Conditional Constraints 43 consistency and consequence in the literal Horn case under syntactic or semantic restrictions (for example, in the spirit of [26] and [64, 60, 61]) Acknowledgements I am very grateful to Salem Benferhat, Angelo Gilio, and Jurg Kohlas for their constructive comments and useful questions during the discussion of an earlier version of this paper at Electronic Transactions on Artificial Intelligence. I also want to thank John Pollock for ....

Lukasiewicz, T.: 1999c, `Probabilistic and truth-functional many-valued logic programming '. In: Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic. pp. 236--241.

....probabilistic approaches) and a nice probabilistic semantics. The latter is expressed in the fact that our many valued disjunctive logic programming under the minimal model and the least model state semantics is an approximation of purely probabilistic disjunctive logic programming. We showed in [6, 7] that many valued definite logic programming with this probabilistic semantics has a model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same ....

....model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same computational complexity as their classical counterparts. Interestingly, our approach in [6, 7] is closely related to van Emden s quantitative deduction [19] which interprets the implication connective as conditional probability, while our work uses the material implication. The main contributions of this paper can be summarized as follows. We introduce the least model state semantics for ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings ISMVL-99, pp. 236--241. IEEE Computer Society, 1999.

....probabilistic approaches) and a nice probabilistic semantics. The latter is expressed in the fact that our many valued disjunctive logic programming under the minimal model and the least model state semantics is an approximation of purely probabilistic disjunctive logic programming. We showed in [14, 15] that many valued definite logic programming with this probabilistic semantics has a model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same ....

....model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same computational complexity as their classical counterparts. Interestingly, our approach in [14, 15] is closely related to van Emden s quantitative deduction [30] which interprets the implication connective as conditional probability, while our work uses the material implication. The main contributions of this paper can be summarized as follows. We introduce the least model state semantics for ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236-- 241. IEEE Computer Society, 1999.

....probabilistic approaches) and a nice probabilistic semantics. The latter is expressed in the fact that our many valued disjunctive logic programming under the minimal model and the least model state semantics is an approximation of purely probabilistic disjunctive logic programming. We showed in [14, 15] that many valued definite logic programming with this probabilistic semantics has a model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same ....

....model and fixpoint characterization and a proof theory similar to classical definite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same computational complexity as their classical counterparts. Interestingly, our approach in [14, 15] is closely related to van Emden s quantitative deduction [30] which interprets the implication connective as conditional probability, while our work uses the material implication. The main contributions of this paper can be summarized as follows. We introduce the least model state semantics ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236-- 241. IEEE Computer Society, 1999.

....Another interesting question is whether there are tractable cases of reasoning under the new formalisms. In particular, can we gain tractability of deciding consistency and z consequence in the literal Horn case under syntactic or semantic restrictions (for example, in the spirit of [22] and [54, 57, 58]) A Appendix: Proofs for Section 5 Proof of Lemma 5.1. Assume that is admissible with T , and consider any default d 2D. The admissibility of implies that D d is under P not in conflict with d. That is, d is tolerated by D d under P . Assume that every d 2D is tolerated under P by ....

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236--241, 1999.

....focus on more specific probabilistic interpretations in order to bring probabilistic logic programming closer to classical logic programming. More precisely, we just have to increase the axioms of probability by an additional axiom that brings probabilistic logics closer to truth functional logics [45, 46, 44]. We will see that under this more restricted probabilistic semantics, ordinary probabilistic logic programs (in which probabilistic program clauses have only atoms in their heads and are assigned only probability intervals of the form [c; 1] have similar computational properties as classical ....

....logic program to the problem of solving two linear programs. Again, the generated linear programs have a small size when P contains few relevant purely probabilistic knowledge. We show that ordinary probabilistic logic programming under a more restricted probabilistic semantics as presented in [45, 46, 44] is characterized by van Emden s quantitative deduction. It thus has the same computational properties as classical logic programming. We present an efficient approximation technique for probabilistic logic programming, which uses van Emden s quantitative deduction to compute a candidate for a ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236--241, 1999. INFSYS RR 1843-00-01 55

....the notion of 0 entailment by some inheritance mechanism. Finally, an interesting question is whether it is possible to regain tractability of deciding consistency and z consequence in the literal Horn case by assuming a more restricted probabilistic semantics (similar to, for example, [35, 36]) Appendix A Proofs for Section 4 Proof of Lemma 4.2. a) Clearly, z is a mapping from D to the set of all nonnegative integers. Assume now that z is not admissible with T . That is, there exists a default d 2D and a set of defaults D 0 D such that D 0 is under P in conflict with d and that ....

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proceedings of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236--241, 1999. INFSYS RR 1843-00-02 25

....logics closer to truth functional logics [17] In detail, our many valued disjunctive logic programs have a probabilistic semantics in probabilities over possible worlds. Furthermore, the truth values of all clauses are truth functionally de ned on the truth values of atoms. We showed in [17] and [18] that many valued de nite logic programming with this probabilistic semantics has a model and xpoint characterization and a proof theory similar to classical de nite logic programming. Moreover, special cases of many valued logic programming with this semantics were shown to have the same ....

....More precisely, van Emden s quantitative deduction [31] can be given a probabilistic semantics by probabilities over possible worlds under the additional axiom. However, van Emden s quantitative deduction is based on a conditional probability semantics of the implication connective, while [17] [18], and the present paper use the material implication semantics. Interestingly, it turns out that the material implication is much closer to classical logic programming. In particular, the material implication is more suitable for additionally handling disjunction and nonmonotonic negation. It is ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Probabilistic and truth-functional many-valued logic programming. In Proc. of the 29th IEEE International Symposium on Multiple-Valued Logic, pages 236-241, 1999.

....characterization. The rest of this paper is organized as follows. Section 2 deals with probabilistic many valued logic programming. In Section 3, we concentrate on many valued logic pro gramming in Pr n . Section 4 summarizes the main results. This paper is an extract from a longer version [13], which includes in full detail all the proofs missing here. 2. Many valued logic programming in Prn 2.1. Technical preliminaries We briefly summarize how classical first order logics can be given a probabilistic n valued semantics with n 3 in which probabilities are defined over a set of ....

.... correct answer substitutions for 9(re(h; U ) 8;1] to P are given by fU=ag and fU=bg) Finally, the unique tight answer substitution for 9(re(h; o) X; 1] to P is given by fX= 7g : Like classical logic programs, many valued logic programs have the nice property that they are always satisfiable [13]. Furthermore, ground many valued formulas are logically entailed in Pr n interpretations iff they are logically entailed in Herbrand Pr n interpretations [13] In the sequel, we use probabilistic many valued logic programming as a synonym for the problem of deciding whether Yes is the correct ....

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T. Lukasiewicz. Probabilistic and truth-functional manyvalued logic programming. Technical Report 9809, Institut fur Informatik, Universitat Gießen, 1998.

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