Denecker, M., De Schreye, D., On the Duality of Abduction and Model Generation. Proc. of the International Conference on Fifth Generation Computer Systems 1992, pp. 650--657, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....be a consequence of the equality theory. As a consequence, the explanation formula is unique up to equivalence in the equality theory, and the proof procedure is more complex than for the propositional case, because it needs to generate consequences of the equality theory. Denecker and De Schreye [19] compare the search spaces for reasoning backward using the if halves of definitions with those for reasoning forward using the only if halves for logic programs without NAF. They show a structural equivalence between the search spaces for SLD resolution extended with abduction and the search ....

Denecker, M., De Schreye, D., On the duality of abduction and model generation. Proc. International Conference on Fifth Generation Computer Systems, Tokyo (1992) 650--657

....be a consequence of the equality theory. As a consequence, the explanation formula is unique up to equivalence in the equality theory, and the proof procedure is more complex than for the propositional case, because it needs to generate consequences of the equality theory. Denecker and De Schreye [19] compare the search spaces for reasoning backward using the ifhalves of de nitions with those for reasoning forward using the only if halves for logic programs without NAF. They show a structural equivalence between the search spaces for SLD resolution extended with abduction and the search spaces ....

Denecker, M., De Schreye, D., On the duality of abduction and model generation. Proc. International Conference on Fifth Generation Computer Systems, Tokyo (1992) 650-657

....Then, comp 00 (P ) f p q; q p a g, and for an observation O = p, P [ fag j= p, while comp 00 (P ) fOg 6j= a. On the other hand, P 0 = f p q; q p; qa) Ka ; Kaa g is obtained by our transformation in Section 3.3, and fq; a; pg is in T P 0 . Denecker and De Schreye [DD92] recently proposed a model generation procedure for Console et al. s object level abduction. In contrast to us, they compute the models of the only if part of a completed program that is not range restricted in general, even if the original definite clauses are rangerestricted. To this end, they ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In: Proc. Int. Conf. Fifth Generation Computer Systems 1992, pages 650--657, 1992.

....other model generation approaches. These comparisons have indicated several possible directions for further developments, but other directions are possible as well: From a theorem proving and model generation perspective, an extension to be investigated and implemented is reasoning with equality [7, 13]. In addition, bidirectional search as in Satchmore [15] can accelerate refutation proofs of Satchmo. From a logic programming perspective, we would like to support nonmonotonic features such as aggregation and negation as failure, as well as access to predicates defined outside the clausal ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In I. Staff, editor, Proceedings, International Conference on Fifth Generation Computer Systems '92, pages 650--657. IOS Press, 1992.

....explanation for O. From this description and the previous discussion of direct proof method, we might conceivably use one of the computation mechanisms described above, tailored to compute the disjunction of explanations, W E i . An alternative is to use a model generation theorem prover ( 43] [21]) Since the abductive explanations for O are the abducible atoms in the minimal models of Sigma O, we can generate the set of minimal Herbrand models using a model generator and then retrieve the abducible atoms as our abductive explanations. 5 The Complexity of Abduction The task of ....

M. Denecker and D. de Schreye. On the duality of abduction and model generation. In Proceedings of the Fifth Generation Computer Systems Conference (FGCS'92), pages 650-- 657, 1992.

.... synthesis oriented (for an overview see for instance Lloyd, 1990) On the other side, synthetic aspects play a major role in a lot of problem classes, thus research is under way at many places on such topics as abduction (O Rorke (1990 1991) Lloyd, 1990) model generation (Manthey and Bry (1988) Denecker and DeSchreye (1992), Fujita et al. 1992) model elimination (Stickel (1985) Bowen and Bahler, 1991 1993) etc. which could provide a suitable formal platform for synthetic problem solving. The Constructive Problem Solving (CPS) has been developed in Klein (1991) as an expressive, well formalized approach to ....

....generation (see for instance Levesque (1989) O Rorke, 1990 1991) The great majority of research done in this field (up to now) is based on propositional calculi. Only a couple of systems using abduction on first order languages has been developed (Manthey and Bry (1988) Goebel (1992) Denecker and DeSchreye, 1992) but without realistic applications (as far as we know) Even at the propositional level abduction has been shown to be much more complex then the corresponding deductive approaches (Eiter and Gottlob, 1992) An interesting alternative approach to a formal treatment of design and ....

Denecker, M. and De Schreye, D.: 1992, On the duality of abduction and model generation, in: Proceedings of the International Conference on Fifth Generation Computer Systems, ICOT, Tokyo.

....than F 0 requires that F F 0 be a logical consequence of CET and that F 0 F not be a consequence of CET. The explanation formula is unique up to equivalence with respect to CET. The proof procedure is extended to take into account the equality theory CET. Denecker and De Schreye [33] compare the search space obtained by reasoning backward using the if half of the if and only if form of a definite program with that obtained by reasoning forward using the only if half. They show an equivalence between the search space for SLD resolution extended with abduction and the search ....

Denecker, M., De Schreye, D., On the duality of abduction and model generation. Proc. International Conference on Fifth Generation Computer Systems, Tokyo (1992) 650--657

....00 (P ) f p j q; q j p a g; and for an observation O = p, P [ fag j= p, while comp 00 (P ) fOg 6j= a. On the other hand, P 0 = f p q; q p; q a) Ka ; Ka a g is obtained by our transformation in Section 3.3, and fq; a; pg is in T P 0 . Denecker and De Schreye [5] propose a model generation procedure for Console et al. s object level abduction. In contrast to ours, their procedure computes the models of the only if part of a completed program that is not range restricted in general, even if the original definite clauses are range restricted. To this end, ....

Denecker, M. and De Schreye, D., On the Duality of Abduction and Model Generation, in: Proceedings of the International Conference on Fifth Generation Computer Systems 1992, Ohmsha, 1992, pp. 650--657.

....[11] In this view, the problem with non ground negative atoms is a subproblem of the problem with non ground abductive literals. Strong indications exist that the techniques incorporated in SLDNFA can solve the problem of oundering negation for positive goals but not for negative goals. In ([6]) we have formalised a procedural duality between abduction and model generation. A current limitation of the duality framework is its restriction to de nite abductive programs. In future work we intend to extend the framework to describe a duality between SLDNFA and an extended notion of model ....

Marc Denecker and Danny De Schreye. On the duality of abduction and model generation. In proceedings of FGCS, Tokyo, 1992.

....in the right the computed formula is called the explanation formula. Though such a procedure can be used to solve abductive problems, it is much weaker than an abductive procedure like SLDNFA because naive unfolding cannot guarantee the consistency of the right hand of the explanation formula. In [5, 9], we show that SLDNFA can be interpreted also as a kind of an unfolding procedure, but SLDNFA is equipped with a mechanism for checking the consistency of each of the disjuncts at the right hands of the generated explanation formula. In our opinion, this is absolutely necessary because even for ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In Proc. of the International Conference on Fifth Generation Computer Systems, 1992.

....it turns out that SLDNFA verifies the original integrity constraint in a bottom up way: an instance of the body of the rule is found and this fires the abduction of the head of the rule. A subject for future research is to compare with special purpose procedures (such as the one in [38] In [9, 11], we have formalised a procedural duality between abduction and an extension of Satchmo [28] for model generation under FEQ with equality atoms in the head of the rules. Interestingly, the duality framework indicates a close relation between Eshghi s approach of abducing equality facts [13] and ....

....approach of abducing equality facts [13] and the approach of Shanahan [41] Missiaen [32] and of section 5.2 of extending unification for dealing with skolem constants. Eshghi s problem of keeping a set of ground equality facts consistent wrt FEQ also occurs during model generation under FEQ. In [9, 11], we developed efficient techniques to do this, inspired by Term Rewriting. New equality atoms which are derived during model generation, are processed in a special way. In the first step, called dynamic completion, the derived equality atoms are transformed to a complete term rewriting system. In ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In Proc. of the International Conference on Fifth Generation Computer Systems, 1992.

....a rich functionality to a knowledge base with uncertainty. It has been used in AI diagnosis, for natural language interpretation, for temporal reasoning such as scheduling and planning, etc. We have shown that in the context of OLP FOL, abductive procedures can be used for model generation [29, 33], deduction and satisfiability proving [34] Others have shown the use of abduction for belief revision and assimilation and default reasoning [45] We are currently integrating SLDNFA with constraint solvers for real number arithmetic and finite domain solvers [2] and a constraint solver for the ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In Proc. of the International Conference on Fifth Generation Computer Systems, 1992.

....in the right the computed formula is called the explanation formula. Though such a procedure can be used to solve abductive problems, it is much weaker than an abductive procedure like SLDNFA because naive unfolding cannot guarantee the consistency of the righ hand of the explanation formula. In [5, 9], we show that SLDNFA can be interpreted also as a kind of an unfolding procedure, but SLDNFA is equiped with a mechanism for checking the consistency of each of the disjuncts at the right hands of the generated explanation formula. In our opinion, this is absolutely necessary because even for ....

M. Denecker and D. De Schreye. On the duality of abduction and model generation. In Proc. of the International Conference on Fifth Generation Computer Systems, 1992.

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Denecker, M., De Schreye, D., On the Duality of Abduction and Model Generation. Proc. of the International Conference on Fifth Generation Computer Systems 1992, pp. 650--657, 1992.

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