T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. In Proceedings CSL-98, LNCS 1584, pp. 415--429. Springer, 1999.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... To our knowledge, this paper is the first paper to contain a detailed analysis of complexity results in probabilistic logic programs, though [12] contains some results for probabilistic relational algebra, and [14] contains some results for a different probabilistic framework, and Lukasiewicz[20, 21, 22, 23] proves some elegant complexity results for a mix of multivalued and probabilistic logic programming. Finally, we have described a proof system for HPPs that guarantees that for every F : that is a ground logical consequence of an HPP P , we have a polynomially bounded proof of F : which in ....

T. Lukasiewicz. (1998) Many-Valued First-Order Logics with Probabilistic Semantics, in Proc. Computer Science Logic Conference, Brno, Czech Republic, Aug. 1998.

....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 ....

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T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. In Proceedings CSL-98, LNCS 1584, pp. 415--429. Springer, 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 ....

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T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. In Proceedings of the Annual Conference of the European Association for Computer Science Logic, volume 1584 of LNCS, pages 415--429. Springer, 1999.

....example, the requested least upper bound for u 1 = u 2 = u and x 1 = x 2 = x is shown in Fig. 5 for u; x 2 [0; 1] r 1 = r 2 = 0:15, v 1 = 0:8, y 1 = 0:8, and s 1 2 f0:05; 0:1g. The requested least upper bound for u 1 u 2 or x 1 x 2 is the maximum value over [u 1 ; u 2 ] Theta [x 1 ; x 2 ] Lukasiewicz s1=0.05 z2 0.99 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 u x s1=0.1 z2 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 ....

Lukasiewicz, T. (1998b). Many-valued first-order logics with probabilistic semantics. In Proceedings of the Annual Conference of the European Association for Computer Science Logic. To appear.

....example, the requested least upper bound for u 1 = u 2 = u and x 1 = x 2 = x is shown in Fig. 5 for u; x 2 [0; 1] r 1 = r 2 = 0:15, v 1 = 0:8, y 1 = 0:8, and s 1 2 f0:05; 0:1g. The requested least upper bound for u 1 u 2 or x 1 x 2 is the maximum value over [u 1 ; u 2 ] Theta [x 1 ; x 2 ] Lukasiewicz s1=0.05 z2 0.99 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 u x s1=0.1 z2 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 ....

Lukasiewicz, T. (1998b). Many-valued first-order logics with probabilistic semantics. In Proceedings of the Annual Conference of the European Association for Computer Science Logic. To appear.

.... programming under the conditional probability implication [14] Moreover, many valued logic programming in Pr n is related to the work on generalized annotated logic programming [9] and to signed formula logic programming [11] Many valued logic programming in Pr n itself was initiated in [12], where we already presented a model and fixpoint 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 ....

....in Pr n as a synonym for the problem of deciding whether Yes is the correct answer in Pr n for a given ground many valued query to a many valued logic program. 3.4. Model and fixpoint semantics We briefly discuss the model and fixpoint semantics of many valued logic programs in Pr n [12]. In the sequel, let P be an n valued logic program. We focus on Herbrand Pr n interpretations, which we identify with fuzzy sets. In detail, each Herbrand Pr n interpretation (I; is identified with the fuzzy set I : HB Phi TV , where I [A] for all A 2 HB Phi , is the sum of ....

T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. In Proc. of the Annual Conference of the European Association for Computer Science Logic, 1998.

....example, the requested least upper bound for u 1 = u 2 = u and x 1 = x 2 = x is shown in Fig. 5 for u; x 2 [0; 1] r 1 = r 2 = 0:15, v 1 = 0:8, y 1 = 0:8, and s 1 2 f0:05; 0:1g. The requested least upper bound for u 1 u 2 or x 1 x 2 is the maximum value over [u 1 ; u 2 ] Theta [x 1 ; x 2 ] Lukasiewicz s1=0.05 z2 0.99 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 u x s1=0.1 z2 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 0.1 0.2 0.3 ....

Lukasiewicz, T. (1998b). Many-valued first-order logics with probabilistic semantics. In Proceedings of the Annual Conference of the European Association for Computer Science Logic. To appear.

.... probability implication [30] Furthermore, many valued logic programming in Pr n is related to the important work on gen IFIG RR 9809 3 eralized annotated logic programming [21] and to signed formula logic programming [26] Many valued logic programming in Pr n itself was initiated in [27], where we introduced manyvalued first order logics with probabilistic semantics and already presented a model and fixpoint characterization. In this paper, many valued first order logics with probabilistic semantics are now analyzed more deeply from the logic programming viewpoint. The main new ....

....That is, some deduction problems that are P complete for classical logic programs are shown to be co NP complete for probabilistic many valued logic programs. ffl We show that probabilistic many valued logic programming is approximated by many valued logic programming in Pr n as introduced in [27]. ffl We present a proof theory for many valued logic programming in Pr n and show its soundness and completeness. The rest of this paper is organized as follows. In Section 2, we focus on probabilistic many valued logic programming. Section 3 concentrates on its approximation by many valued ....

[Article contains additional citation context not shown here]

T. Lukasiewicz. Many-valued first-order logics with probabilistic semantics. Presented at the Annual Conference of the European Association for Computer Science Logic, Brno, Czech Republic, 1998.

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