L. Console, D. Theseider Dupr'e, and P. Torasso. On the Relationship Between Abduction and Deduction. J. Logic and Computation, 1(5):661--690, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....explanations for a query = q from a Horn CNF , deciding whether there is an additional explanation is NP complete. Consequently, the existence of a polynomial total time algorithm for computing all explanations implies P=NP. However, for the well known class of acyclic Horn theories (see e.g. [5, 24, 21, 1]) we present an algorithm which enumerates all explanations for q with incremental polynomial delay (i.e. in time polynomial in the size of the input and output so far) and thus solves the problem in polynomial total time. Compared to explanations for an atomic query q, intuitively cyclic ....

....literal query is infeasible in general unless P=NP, it becomes an issue to find restricted input classes for which this is feasible. In this section, we show a positive result for the important class of acyclic Horn theories, which has been studied extensively in the literature (see, e.g. [5, 24, 21, 1]) We first recall the concept of acyclic Horn theories (see e.g. 5, 24] Definition 2. For any Horn CNF over atom set At, its dependency graph is the directed graph G( V; E) where V = At and E = fx i x j j c 2 ; x i 2 N(c) x j 2 P (c)g, i.e. E contains an arc from each atom in a ....

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L. Console, D. Theseider Dupre, and P. Torasso. On the relationship between abduction and deduction. J. Logic and Computation, 1(5):661--690, 1991.

.... programs with database updates as applications [18] Denecker and de Schreye proposed another much simpler translation of A into abductive normal logic programs with constraints [17] and showed that their translation is both sound and complete with respect to the predicate completion semantics [11] of abductive normal logic programs. All these results impress on us that the action description language A is really a good basis for systematical development of theories of actions. This paper is in line with the work related to the action description language A. We will examine the action ....

....as predicate symbols and sometimes as literals (with or without NAF) and onstraints can be formulas in first order or three valued or modal logic, etc. In this paper we will take abducibles to be a set of predicate symbols, and constraints to be a set of first order formulas. As per Console [11], the semantics of a normal logic program can be defined through deduction by completing the non abducible predicates together with Clark s Equality Theory (CET) 10] Let P be a normal logic program, and A a set of abducibles. We write COMP (P ; A) to denote the first order theory obtained by ....

Console, L., Dupre, D.T., and Torasso, P., On the relationship between abduction and deduction, J. of Logic and Computation, 1:5, 1991, 661--690

.... logic programs with database updates as applications [8] Denecker and de Schreye proposed another much simpler translation of A into abductive normal logic programs with constraints [7] and showed that their translation is both sound and complete with respect to the predicate completion semantics [4] of abductive normal logic programs. Baral and Gelfond [3] extended the action language A with concurrent actions. All these results impress us that the action description language A is a good basis for systematical development of theories of actions. This paper is in line with the work related to ....

....) are taken as abducible predicates used to capture the incomplete knowledge about the initial situation. The semantics of D is defined to be the union of the integrity constraints, the Clark Equality Theory, and the firstorder theory obtained by completing all the non abducible predicates [4]. The definition for abducible predicates initially true(F ) and initially false(F ) are left open. We will write COMP ( D) to denote the semantics of of D. The following two results justify the above semantics definition. Proposition 4.1 D is an acyclic program with first order constraints in ....

Console, L., Dupre, D.T., and Torasso, P., On the relationship between abduction and deduction, J. of Logic and Computation, 1:5, 1991, 661-- 690

....programs with abducibles. Section 5 presents a model generation procedure for computing generalized stable models. Some comparisons between our fixpoint theory and previous work are discussed in Section 6. 2 Model Theory for Abductive Logic Programs There are several definitions of abduction [PGA87, EK89, KM90, Bry90, Gel90, Ino91, CDT91, Ino92]. The semantics of abduction we use here is based on the generalized stable models defined by Kakas and Mancarella [KM90] As stated in Section 1, their abductive framework is given by a triple h P; 0; I i, where P is a general logic program, 0 is a set of abducible predicates, and I is a set of ....

....Compared with abduction based on first order logic by [PGA87, Ino92] Kakas and Mancarella define a program P not as first order formulas but as a general logic program with negation as failure. This definition covers a more general class of programs than Console et al. s object level abduction [CDT91] that is defined for hierarchical logic programs. Two different definitions by Gelfond [Gel90] and Inoue [Ino91] are more general than that by [KM90] in the sense that they allow more extended classes of programs for P and 0. We will revisit such an extension in Section 4. We define an abductive ....

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L. Console, D.T. Dupre and P. Torasso. On the relationship between abduction and deduction. J. Logic and Computation, 1:661--690, 1991.

....compete with specialized algorithms for these problems, and will be less efficient on large instances; it remains to see how it performs on small instances. Another class of queries involves advanced AI reasoning techniques on databases, in particular model based diagnosis. In abductive diagnosis [8], customarily the failure of a component shows up in effects , which are evoked by sets of causes. e.g. in the simple circuit in Figure 4, melting of a fuse (F1 or F2) is an effect, and high voltage of the battery (B) is a cause. C B F2 F1 R2 R1 Fig. 4. Electric circuit In abductive diagnosis, ....

L. Console, D. Theseider Dupr'e, and P. Torasso. On the Relationship Between Abduction and Deduction. J. Logic and Computation, 1(5):661--690, 1991.

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L. Console, D. Theseider Dupr'e, and P. Torasso. On the Relationship Between Abduction and Deduction. J. Logic and Computation, 1(5):661--690, 1991.

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Console, L., Dupre, D.T., and Torasso, P., On the relationship between abduction and deduction, J. of Logic and Computation, 1:5, 1991, 661--690

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