K. Satoh and N. N. Iwayama. Computing abduction by using the TMS. In ICLP-91, pages 3--17, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....in detail in section 5.1. Recently, 78] compared SLDNFAC with di#erent other approaches for solving constraint problems including CLP, ACLP and the Smodels system [74] and shows that in many problems the system is competitive. Bottom up Abduction. This approach was proposed originally in [107] and aims to develop e#cient techniques for computing abductive solutions under the generalized stable model semantics [52] by translating the abductive logic program to a standard logic program and applying e#cient bottom up stable model generators to this translation. This approach is based on a ....

....stable model semantics [52] by translating the abductive logic program to a standard logic program and applying e#cient bottom up stable model generators to this translation. This approach is based on a translation of Abductive logic programs into pure logic programs with stable model semantics [107]. Abductive solutions w.r.t. the original abductive logic program correspond to stable models of its translation 8 . To compute abductive solutions, 107] also proposed a procedure for bottom up stable model computation based on truth maintenance techniques. It is an extension of the procedure ....

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Satoh, K. and Iwayama, N. Computing Abduction by Using the TMS. Proc. of ICLP'91, pp. 505 -- 518, 1991.

....the computational aspects of abduction using constraint solving extensively to control the abductive search and enhance its computational behaviour. On a more abstract level our work is related to Answer Set Programming(ASP) Gelfond and Lifschitz, 1991] Strong connections have been established [Satoh and Iwayama, 1991] between ALP and ASP. At the level of semantics these two frameworks are for a large class of theories (ASP admits only a special type of integrity constraints) equivalent. At the level of computation our construction of an abductive solution System corresponds to the generation of a model ....

K. Satoh and N. Iwayama. Computing abduction by using the tms. In Proc. of ICLP'91, pages 505--518, 1991.

....is introduced and the rules: p not p p not p This methodology can be seen easily as a way of encoding an ID logic theory by a stable logic program. I sketch how this compilation works. The idea is taken from Satoh and Iwayama s transformation of Abductive Logic Programming to pure LP [35]. I present it here in the context of an ID logic theory. An ID logic theory consisting of a set of rst order axioms T and a de nition D de ning a set of predicates P d in terms of open predicates P o by some set of rules P , is transformed to a logic program: keep the set of rules P (and ....

K. Satoh and N. Iwayama. Computing Abduction by Using the TMS. In Proc. of the International Conference on Logic Programming 91, page 504, 1991.

....LP framework. Bottom up Abduction This work aimed to develop ecient abductive inference procedures for ALP under Kakas and Mancarella s generalized stable model semantics [45] The approach was based on a translation of Abductive logic programs into pure logic programs with stable model semantics [93]. Abductive solutions w.r.t. the original abductive logic program correspond to stable models of its translation. 93] developed a 10 system for bottom up stable model computation and used the resulting system to compute abductive solutions. This system is an extension of the procedure for ....

....and Mancarella s generalized stable model semantics [45] The approach was based on a translation of Abductive logic programs into pure logic programs with stable model semantics [93] Abductive solutions w.r.t. the original abductive logic program correspond to stable models of its translation. [93] developed a 10 system for bottom up stable model computation and used the resulting system to compute abductive solutions. This system is an extension of the procedure for computing well founded models of [27, 82] and dynamically checks integrity constraints during the computation of stable ....

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Satoh, K. and Iwayama, N. Computing Abduction by Using the TMS. Proc. of ICLP'91, pp. 505 - 518, 1991.

....3. For any literal a # A # P , the following rule is in UR: a # not a . Here, a and a are uniquely associated with any a # A and are called update atoms. The atom a becomes true i# a is not true. Then, a pair of rules in abd(a) specify the situation that an abducible a is true or not [15, 10]. The rule a # a derives the atom a if an abducible a which is not in P is to be true. In contrast, the rule a # not a derives the atom a if an abducible a which is in P is not to be true. The set of all update atoms associated with A is denoted by UA. We define that UA = UA ....

K. Satoh and K. Iwayama. Computing abduction by using the TMS. In: Proc. 8th Int'l Conf. Logic Programming, pages 505--518, MIT Press, 1991.

.... Gar88, Gra91, KM91, Mar91, MS86, Neb91, RdK87, Win90] So, normally we are forced to make a choice and almost all the update mechanisms proposed in the literature make a choice or leave it to the user to make a choice, where s he may have no way of knowing apriori which is the correct choice [BKSW91, Dec90, GL90, KM90, RB92, SI91, Tom88, TA91, Wut93]. There are severe problems with making a choice. Suppose we chose alternative (i) in our example. Then, we also believe that r is true. However, suppose that after some time, more information concerning the world is known. Say, an update request to add s is received. It can be seen that, if ....

K. Satoh and N. Iwayama. Computing abduction by using the tms. In K. Furukawa, editor, Proc. 8th Int. Conf. on Logic Programming (ICLP 91), pages 505-- 518, 1991.

....do not exploit a set oriented fact processing as we do. 4] considers no negation in view definitions and the only constraints are functional and key dependencies; 23] provides a method for handling Horn rules and constraints which are functional dependencies over extensional predicates alone; [21, 13] discuss the case where the updates, rules and constraints are propositional formulas; the studies [19, 25] do not consider constraints. We do not thoroughly discuss here methods for filtering possible solutions (see [11, p.72] for references, and [25] Nor do we do discuss schema design ....

K. Satoh and N. Iwayama, "Computing Abduction by Using the TMS," Int Conf on Logic Programming, pp. 505- 518, 1991.

....and is uniquely associated with 8 [20] provides another simpler transformation, but it still needs the introduction of extra symbols. 23 each L. Then it is shown that there is a one to one correspondence between the belief sets of # and the answer sets of the transformed ELP. Satoh and Iwayama [38] introduce a similar transformation from ANLP to NLP. These results imply the following fact. Theorem 7.1 (set membership problem for the belief sets of an AELP) Deciding whether there is a belief set of an AELP satisfying an observation is NP complete. Proof. It is known that deciding whether a ....

....3.1) and AEDPs are reducible to EDPs (Theorem 5.1) In other words, under the answer set semantics abducibles are equivalently specified by disjunctions, but not vice versa. Also, as presented in Section 7. 1, AELPs ANLPs are reducible to ELPs NLPs under the answer set stable model semantics [19,38]. That is, abducibles are expressed using negation as failure. 11 The authors in [13,18] introduce program transformations from the stable models of NLPs and NDPs to the minimal models of PDPs. This fact implies that negation as failure is equivalently specified by disjunctions (plus integrity ....

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K. Satoh and K. Iwayama, Computing abduction by using the TMS, in: Proceedings of the 8th International Conference on Logic Programming (MIT Press, Cambridge, MA, 1991) 505--518.

....constraints as the semantics of a transformed logic program, without integrity constraints, using all the contrapositive variants of the original program rules. The idea of using the contrapositives is also explored by Jonker [12] but considering the well founded semantics. Satoh and Iwayama [41] use TMS techniques to maintain consistency while computing stable models of general logic programs with integrity constraints, and apply it to compute abduction in an abductive framework (c.f. 4, 15] In [18] Kowalski et al. suggest an extension (e answer sets) based on stable model semantics, ....

Ken Satoh and Noboru Iwayama. Computing abduction by using the TMS. In Koichi Furukawa, editor, International Conference on Logic Programming, pages 505--518. MIT Press, 1991.

....of [EK89] However, this transformation inherits the difficulty of computation from Eshghi and Kowalski s abductive interpretation of negation as failure, and their procedure suffers from the soundness problem with respect to the generalized stable model semantics. Alternatively, Ino91] and [SI91] show that an abductive general logic program h P; 0 i can be transformed to a single general logic program. For each atom A(x) from 0, they introduce the negative literal :A(x) and a pair of clauses: A(x) not :A(x) A(x) not A(x) 14) Then, there is a 1 1 correspondence between the ....

....from 0, they introduce the negative literal :A(x) and a pair of clauses: A(x) not :A(x) A(x) not A(x) 14) Then, there is a 1 1 correspondence between the generalized stable models of h P; 0 i and the stable models of the transformed program. Using this transformation, Satoh and Iwayama [SI91] propose a bottom up, TMS style procedure for computing stable models of a general logic program, which is similar to [SZ90] s procedure and performs an exhaustive search with backtracking. At this point, we can use any procedure to compute stable models. Comparing each procedure, the MGTP based ....

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K. Satoh and N. Iwayama. Computing abduction by using the TMS. In: Proc. 8th Int. Conf. Logic Programming, pages 505--518, 1991.

....decision problem of the existence of explanations for a given observation in an abductive Horn program is NP complete. In other words, in an abductive Horn program, deciding whether there is a generalized stable model satisfying an observation is NP complete. Inoue [Ino91] and Satoh and Iwayama [SI91] show that an abductive logic program can be translated into a semantically equivalent normal logic program. For an abductive logic program h P; A i, consider a normal logic program obtained from P by adding the following clauses for each abducible A in A: A not A 0 ; A 0 not A ; where ....

Satoh, K. and Iwayama, K., Computing Abduction by using the TMS, Proc. 8th Int. Conf. on Logic Programming, 505-518, 1991.

....be translated into a propositional theory T Pi such that each model of the latter corresponds to a stable model of the former. It follows from this that the problem of finding all the stable models of a knowledge base corresponds to the problem of finding all the models of a propositional theory. Satoh and Iwayama (1991) provide a nondeterministic procedure for computing Ben Eliyahu the stable models of logic programs with integrity constraints. Junker and Konolige (1990) present an algorithm for computing TMS labels. Antoniou and Langetepe (1994) introduce a method for representing some classes of default ....

....stable model semantics. The algorithms developed by Marek and Truszczy nski (1993) for autoepistemic logic can also be adopted for computing stable models. The procedures by Marek and Truszczy nski (1993) Antoniou and Langetepe (1994) Pimentel and Cuadrado (1989) BenEliyahu and Dechter (1991) Satoh and Iwayama (1991), Bell et al. 1994) Subrahmanian et al. 1995) and Junker and Konolige (1990) do not take advantage of the structure of the knowledge base as reflected in its dependency graph, and therefore are not efficient for stratified knowledge bases. Sacc a and Zaniolo (1990) present a backtracking ....

Satoh, K., & Iwayama, N. (1991). Computing abduction by using the TMS. In Furukawa, K.

....To generate test cases we have exploited the Stanford GraphBase developed by Donald E. Knuth [ 1993 ] that is a portable software package for generating and processing graphs. There are several other proposals for computing stable models [ Bell et al. 1994; Chen and Warren, 1994; Eshghi, 1990; Satoh and Iwayama, 1991 ] In order to contrast the novel algorithm to existing approaches we wanted to use a special purpose implementation of the stable model semantics. As such a challenge system we employ the SLG system developed by Chen and Warren [ 1993 ] because it is freely available and because it seems to be a ....

K. Satoh and N. Iwayama. Computing abduction by using the TMS. In Proceedings of the 8th International Conference on Logic Programming, pages 505518, Paris, France, June 1991. The MIT Press.

....of O with respect to h P; 0 i iff I E is a 0 minimal belief model of h P [ f not Og; 0 i. Proof. a) Immediately follows from the observation that the addition of not O to P imposes the integrity constraint that O should be derived. This result is also stated by Satoh and Iwayama [35]. b) E is a minimal explanation of O with respect to h P; 0 i iff no E 0 ae E is an explanation of O with respect to h P; 0 i iff no belief model I E 0 of h P; 0 i in which O is true satisfies E 0 ae E iff no belief model I E 0 of h P [ f not Og; 0 i satisfies E 0 ae E iff I E is a ....

....to the belief model semantics by incorporating a special integrity checking into the procedure of [8, 22] To our best knowledge, no procedure other than ours has been developed so far as a sound procedure for abductive extended disjunctive programs. 6.2.3. Computation with TMS. Satoh and Iwayama [35] and Inoue [16] independently show that any abductive normal logic program h P; 0 i can be transformed into a single extended (or normal) logic program. For each atom A in 0, they introduce the negative literal :A and a pair of clauses: 8 For Example 3.10, the top down abductive procedure of [8] ....

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Satoh, K. and Iwayama, N., Computing Abduction by Using the TMS, in: K. Furukawa (ed.), Logic Programming: Proceedings of the Eighth International Conference, MIT Press, 1991, pp. 505--518.

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K. Satoh and N. N. Iwayama. Computing abduction by using the TMS. In ICLP-91, pages 3--17, 1991.

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K. Satoh and N. Iwayama. Computing abduction by using the TMS. In: Proceedings of the 8th International Conference on Logic Programming, pages 505--518, MIT Press, 1991.

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