Eshghi, K.: 1993, `A tractable class of abduction problems'. In: Proceedings 13th International Joint Conference on Artificial Intelligence. Chambery, France, pp. 3--8.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....has been a growing literature on this subject, indicating the need for efficient abductive procedures. We refer to [18] which gives an excellent survey on intimately closely related problems in computational logic. Note that much effort has been spent on studying various input restrictions, cf. [14, 4, 13, 25, 8, 7, 10, 23, 24]. While computing some explanation of a query has been studied extensively in the literature, the issue of computing multiple or even all explanations for has received less attention. This problem is important since often one would like to select one out of a set of alternative explanations ....

K. Eshghi. A tractable class of abduction problems. In Proc. IJCAI-93, pp. 3--8, 1993.

....has been a growing literature on this subject, indicating the need for efficient abductive procedures. We refer to [17] which gives an excellent survey on intimately closely related problems in computational logic. Note that much effort has been spent on studying various input restrictions, cf. [13, 4, 12, 24, 8, 7, 10, 22, 23]. While computing some explanation of a query has been studied extensively in the literature, the issue of computing multiple or even all explanations for has received less attention. This problem is important since often one would like to select one out of a set of alternative explanations ....

K. Eshghi. A tractable class of abduction problems. In Proceedings IJCAI-93, pages 3--8, Chambery, France, August 1993.

..... The first constraint is [p # p # ] where p # means the opposite of p, following the approach described in [8, 6] Belief revision in Bayesian networks can be accurately modeled by cost based abduction [12] Polynomial algorithms exist for some useful classes of abductive problems [5]. Since weighted abduction is not yet one of them, we are still exploring the best heuristics to use for our domain and application. This is known as the consistency view of integrity constraints (see for example [8] horizontal velocity of pumpkin is constant Rule 24: The magnitude of a ....

Kave Eshghi. A tractable class of abduction problems. In Proceedings 13th International Joint Conference on Artificial Intelligence, pages 3--8, Chambery, France, 1993.

....then p is velocity of pumpkin is non constant . In other words, the abductive explanation satisfies this constraint iff Belief revision in Bayesian networks can be accurately modeled by cost based abduction [11] Polynomial algorithms exist for some useful classes of abductive problems [6]. Since weighted abduction is not yet one of them, we are still exploring the best heuristics to use for our domain and application. This is most closely related to the consistency view (see for example [7] horizontal velocity of pumpkin is constant Rule 24: The magnitude of a vector is ....

Kave Eshghi. A tractable class of abduction problems. In Proc. 13th International Joint Conference on Artificial Intelligence, pages 3--8, Chambery, France, 1993.

....with regard to the notion of explanation. What accounts for an explanation What determines the quality of an explanation What is a best explanation What is a process of inference to the best explanation [48] Numerous works on abduction adopt the following general definition of explanation [18, 19, 46, 58, 59, 66, 76]. 1 Definition 1.1 Given a system S, and an observation Obs, an explanation of Obs in S is a formula expl(S; Obs) that satisfies the following conditions: i) S [ fexpl(S; Obs)g j= Obs; ii) expl(S; Obs) is consistent with S. Usually several refinements of this definition are considered. 1) ....

Eshghi, K., 1993, A tractable class of abduction problems. In Proceedings, 13th International Joint Conference on Artificial Intelligence, Chambery, France, 3--8.

....from classical propositional theories, which has also been discussed for restricted cases by Selman and Levesque [74] Bylander [8] and Friedrich et al. 24] who focussed on Horn and definite Horn theories and the minimality preference criterion. In this context, Eshghi has identified in [23] a subclass of Horn theories for which finding a minimal solution is tractable. The results of [19] and this paper show that abduction from logic programs has complexity quite different than abduction from classical theories. Notice that in the abductive framework of [19] the inference ....

K. Eshghi. A Tractable Class of Abduction Problems. In Proc. International Joint Conference on Artificial Intelligence (IJCAI '93), pp. 3--8, 1993.

....of logic based abduction has only been partially investigated. Selman and Levesque [69] Bylander [4] and Friedrich et al. 28] studied the particular case where T is a propositional Horn theory and where the subsetminimality measure is used (for definitions, see Sections 2 and 5) Eshghi [24] studied abduction under further restriction of T to a subclass of Horn theories. The complexity of abductive reasoning in the general propositional case was left open, and it was also unclear how different minimality criteria would affect the complexity in both the general and the Horn case. It ....

....in our terms, finding a solution as well as finding any solution to a Horn PAP P is NP hard, and that the same holds if the solution must contain a certain hypothesis h. 5 These results are shown by a reduction from an NP complete problem on graphs; we give new proofs. Eshghi has shown in [24], where the notion of solution slightly stricter than in this paper, that finding a minimal solution is tractable if T is acyclic Horn and its pseudo completion is unit refutable. Friedrich et al. studied complexity issues for definite Horn PAPs [28] They showed that under this restriction, ....

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K. Eshghi. A Tractable Class of Abduction Problems. In Proceedings IJCAI-93, pages 3--8, 1993.

....about logical consequences of the theory can be answered in polynomial time. We map tractable satisfiability classes to tractable entailment classes, including hierarchies of tractable problems; and show that some initially promising conditions for tractability of entailment, proposed by Esghi [13] and del Val [10] surprisingly only identify a subset of renamable Horn. We then consider a potential application of tractable entailment, through a reduction due to Esghi [13] of certain abduction problems to a sequence of entailment problems. Besides clarifying the range of applicability of ....

....tractable problems; and show that some initially promising conditions for tractability of entailment, proposed by Esghi [13] and del Val [10] surprisingly only identify a subset of renamable Horn. We then consider a potential application of tractable entailment, through a reduction due to Esghi [13] of certain abduction problems to a sequence of entailment problems. Besides clarifying the range of applicability of Esghi s results from the semantic point of view, we show that the reduction can almost trivially fail to be in any of the basic tractable classes discussed in the first part of the ....

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Kave Esghi. A tractable class of abduction problems. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence, 1993.

....Because pure literals will never be resolved upon, they can be put first in the ordering for the purposes of the FP I 1 procedure. 5 What other ordering strategies are available to reduce the number of merges stored by FP I 1 A promising concept is that of a tied chain, introduced in [ Esghi, 1993 ] Definition 6 A tied chain in a set of clauses Sigma is a sequence of triples (x 1 ; C 1 ; y 1 ) xn ; Cn ; y n ) such that: ffl For 1 i n: C i 2 Sigma, x i ; y i 2 C i , and x i 6= y i ; ffl For 1 i n: y i and x i 1 (the link literals of the chain) are complementary ....

....2 C i , and x i 6= y i ; ffl For 1 i n: y i and x i 1 (the link literals of the chain) are complementary literals; ffl x 1 = y n , called the tied literal of the chain. For example, Sigma = fp q r; r s; s pg contains a tied chain with p as tied literal and r and s as link symbols. In [ Esghi, 1993 ] it is shown that the absence of tied chains is a sufficient condition for unit refutation completeness. This result can be rederived (and, in a sense, explained) using the concept of merges, as an easy consequence of the next lemma and theorem 1. Lemma 6 Suppose there is a resolution deduction ....

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Esghi, Kave 1993. A tractable class of abduction problems. In Proceedings of the Thirteenth International Joint Conference on Artificial Intelligence.

....diagnosis systems can isolate the faulty components that can explain the abnormal behavior being observed. The model based mechanism is more complete because of the use of the deep knowledge, but may suffer from computational complexity. Many efforts have been made to overcome the disadvantage [1,2,3,4,5]. In 1993, Raiman, de Kleer and Saraswat proposed an architecture, IMPLODE [5] which uses a sensitivity analysis of assumptions to assign a critical level to assumptions. With the criticality, IMPLODE represents the environments, conflicts and diagnoses with critical environments, critical ....

Kave Eshghi, " A Tractable Class of Abduction Problems ", in Proceedings of IJCAI-93, Vol.1, PP.3-8, 1993.

.... Horn theories [6] More surprisingly, abduction can be performed in polynomial time using a set of characteristic models, whereas abduction using Horn theories is NP complete [23] This result is particularly interesting because very few other tractable classes of abduction problems are known [3,8,24]. The final part of this paper examines the problem of converting a set of models into an efficient representation. This general task can be viewed as identifying meaningful, computationally attractive structures in a set of empirical data, where each model represents a data point [5] As such ....

K. Eshghi, A tractable class of abduction problems, in: Proceedings IJCAI-93 , Chamb'ery, France (1993) 3--8.

....that the computational complexity of model based diagnosis makes the mechanism impractical to use for real world diagnostic tasks. Many efforts have been made to reduce the computational complexity. Among them, focusing the diagnostic reasoning on a reduced diagnosis space is a promising way[1,2,3,4,5]. The critical reasoning architecture IMPLODE proposed by Raiman, de Kleer and Saraswat[5] is such a kind of method, which uses a sensitivity analysis of assumptions to assign a critical level to assumptions. With the criticality, IMPLODE represents the environments, conflicts and diagnoses with ....

Kave Eshghi, A Tractable Class of Abduction Problems, Proceedings of IJCAI-93, pp. 3-8, 1993.

....side and root clauses by a link edge which represents the literal to be resolved upon in the resolution with C i . Definition 9 A merge cycle is a resolution chain such that the first literal of the chain and the last are the same. It is the same concept as the one of tied chain developed in [3]. However, we prefer the term merge cycle which is more representative of what is the main property of this object, in our opinion. 3] used tied chains to build a sufficient test of completeness for unit refutability. Since forward chaining is a kind of unit resolution, it is not surprising to ....

....merge cycle is a resolution chain such that the first literal of the chain and the last are the same. It is the same concept as the one of tied chain developed in [3] However, we prefer the term merge cycle which is more representative of what is the main property of this object, in our opinion. [3] used tied chains to build a sufficient test of completeness for unit refutability. Since forward chaining is a kind of unit resolution, it is not surprising to find the same concept in both contexts. Definition 10 A tautological cycle is a resolution chain such that the first literal of the ....

Kave Eshghi, `A tractable class of abduction problems', in Proceedings of the 30th International Joint Conference of Artificial Intelligence, pp. 3--8, (1993).

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Eshghi, K.: 1993, `A tractable class of abduction problems'. In: Proceedings 13th International Joint Conference on Artificial Intelligence. Chambery, France, pp. 3--8.

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K. Eshghi. A tractable class of abduction problems. In Proc. 13th International Joint Conference on Artificial Intelligence (IJCAI-93), pp. 3--8, 1993.

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, Chambéry , pp. 3-8, 1993.

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