K. Eshghi and R.A. Kowalski. Abduction through deduction. Technical report, Imperial College, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....entailment and reasoning with respect to this entailment relation as abductive reasoning. Such entailments were used in [DDS93,Dun93] while formalizing reasoning about actions using abductive logic programming and one such entailment was formally defined using generalized stable models [KM90,EK88] with respect to abductive logic programming in [BG94] Shanahan in Chapter 17 of his book [Sha97] refers to such entailments as knowledge assimilation . 1 Pearl [Peab,Peaa] refers to such reasoning from evidence to explanation, and then from explanation to predictions as transduction. 2 ....

K. Eshghi and R. Kowalski. Abduction through deduction, 1988. unpublished paper.

....theory we need a new definition of explanation. Various (non equivalent) definitions can be found in the literature. For comparison of several of them see [Ino92a] Here we shell concentrate on the proposal by Kakas and Mancarella (based on the unpublished paper by Esghi and Kowalski [EK88]) In [KM90] they develop a semantics of abductive logic programs closely related to stable model semantics of general logic program. Let Pi; A; I be an abductive logic program. A set M of ground atoms is a generalized stable model of Pi; A; I if there is Delta ae atoms(A) such that M ....

....lies(a)g) ff lies(a) bird(a) penguin(a) hasbeak(a)g. In the first option, the resulting abductive program Pi 1 ; A; I [ X not only explains the observation f lies(a) by concluding bird(a) and :penguin(a) which can also be achieved by the standard approach of abductive logic programs [EK88, KM90]) but also entails the conclusion hasbeak(a) which is apparently not done by the standard approach. In the second option, the resulting abductive program Pi 1 [X; A; I only entails f lies(a) and does not entail any of the new conclusions entailed in the previous case. 2 61 Example 8.4 Let ....

K. Eshghi and R. Kowalski. Abduction through deduction, 1988. unpublished paper.

....of haswings(tweety) from the theory T and the observation ff ly(tweety)g as abductive entailment. Such entailments were used in [DDS93,Dun93] while formalizing reasoning about actions using abductive logic programming and one such entailment was formally defined using generalized stable models [KM90,EK88] with respect to abductive logic programming in [BG94] Shanahan in Chapter 17 of his book [Sha97] refers to such entailments as knowledge assimilation . In fact, throughout the book he views explanation as an aspect of knowledge assimilation. We believe abductive entailment and the ....

K. Eshghi and R. Kowalski. Abduction through deduction, 1988. unpublished paper.

....first order theory we need a new definition of explanation. Various (non equivalent) definitions can be found in the literature. For comparison of several of them see [Ino92a] Here we shell concentrate on the proposal by Kakas and Mancarella (based on the unpublished paper by Esghi and Kowalski [EK88]) In [KM90] they develop a semantics of abductive logic programs closely related to stable model semantics of general logic program. Let 5; A; I be an abductive logic program. A set M of ground atoms is a generalized stable model of 5; A; I if there is 1 ae atoms(A) such that M is a ....

....A(ff lies(a)g) ff lies(a) bird(a) penguin(a) hasbeak(a)g. In the first option, the resulting abductive program 5 1 ; A; I [ X not only explains the observation f lies(a) by concluding bird(a) and :penguin(a) which can also be achieved by the standard approach of abductive logic programs [EK88, KM90]) but also entails the conclusion hasbeak(a) which is apparently not done by the standard approach. In the second option, the resulting abductive program 5 1 [X; A; I only entails f lies(a) and does not entail any of the new conclusions entailed in the previous case. 2 Example 8.4 Let us now ....

K. Eshghi and R. Kowalski. Abduction through deduction, 1988. unpublished paper.

....used and successful in various domains such as semiotics [ 8 ] linguistics [ 9 ] and artificial intelligence, since [ 17 ] mainly in the perspective of diagnostic reasoning, see e.g. 11 ] for a general presentation. Abduction has also been introduced in Logic Programming by R. Kowalski in [ 13 ] and the combination of abductive capabilities within the rigorous framework of Logic Programming brings up to an elegant simple and powerful sytem, further developments of which can be found in [ 12 ] 2 Constraint based Reasonning A constraint is simply a logical relation between several ....

K. Eshghi and R. A. Kowalski. Abduction through Deduction. Research report, Imperial college, March 1988.

....of abduction by concentrating in one framework, that of Abductive Logic Programming (ALP) Many of the ideas however are applicable, more generally, to other frameworks of abduction or hypothetical reasoning. The framework of ALP that we will adopt was originally proposed by Eshghi and Kowalski ([4,5]) and developed further by Kakas and Mancarella ( 12,13] The operational semantics for sequential execution of abduction is well defined within this framework and has been used in building meta interpreters on top of Prolog systems. However, as in ordinary (deductive) logic programming, ....

....Through Parallel Abduction Before closing this section it is worth mentioning that the parallel framework of abductive logic programming can, in fact, be used to enhance the computational efficiency of ordinary logic programming by applying it to the computation of NAF. Eshghi and Kowalski ([4]) show how NAF can be understood through abduction, where a negative literal not p is considered as a primitive abducible p with the constraint p, p . We also have a disjunctive integrity constraint p p which has the effect that whenever we require the absence of the abducible p in a ....

Eshghi K. and Kowalski R. A., Abduction Through Deduction, Technical Report, Department of Computer Science, Imperial College, 1988.

....and extended disjunctive deductive databases. They use bottom up incremental, backtrack free computation of the minimal models of positive disjunctive programs, together with integrity constraints over beliefs and disbeliefs. Gelfond and Lifschitz [GL92] extend the work of Eshghi and Kowalski [EK88], Evans [Eva89] and Apt and Bezem [AB90] on representing actions in logic programming languages with negation asfailure. Extended logic programs are used for this purpose. The method is applicable to temporal projection problems with incomplete information, as well as reasoning about the past. ....

K. Eshghi and R.A. Kowalski. Abduction through deduction. Technical Report, Dept. of Computing, Imperial College, London, 1988.

....the integrity of the explanations. There are, however, many ways of guaranteeing the integrity of a theory. The designer of the axiomatization can state integrity constraints, sentences describing conditions with which the information in a theory (knowledge base) must be consistent. This is known [EK88] as the consistency view of integrity constraints, which requires the theory consisting of the original axiomatization, the explanations and the integrity constraints, to be consistent. In principle, integrity constraints do not add anything but complexity to the consistency test problem (more ....

....axiomatization is internally consistent then the test of consistency could involve only the explanations and the integrity constraints. Alternatively, integrity contraints can be interpreted as goals to be achieved by the system. This is the theoremhood interpretation (of integrity constraints) EK88] which requires the integrity constraints to be entailed by the new theory (axiomatization plus explanations) The theoremhood interpretation is, in general, stronger (i.e. more restrictive) than the consistency view, although the two views coincide for theories of the form of the if and only ....

K. Eshghi and R. Kowalski. Abduction through deduction. Technical report, Deparment of Computing. Imperial College, London, UK, 1988.

.... the goal clause and Delta is a set of equalities (i.e. answer substitutions) By widening the notion of what can be contained in a Delta to include constraints (Jaffar and Lassez [9] by incorporating integrity checking (Sadri and Kowalski [13] and by allowing abduction (Eshghi and Kowalski [7]) a very powerful problem solving paradigm is obtained. But can a mechanism be built for this paradigm which exploits dependency information as effectively as it is exploited in an RMS The sets of assumptions manipulated by an RMS are a particular sort of logically structured entity. Their ....

Eshghi K. and Kowalski R.A., Abduction through Deduction, Technical Report, Imperial College, London (1988).

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K. Eshghi and R.A. Kowalski. Abduction through deduction. Technical report, Imperial College, 1988.

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Eshghi K., and R. Kowalski, Abduction through deduction, Technical Report, Department of Computing, Imperial College, University of London, 1988.

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Eshghi K. and Kowalski R. A., [1988]: Abduction through Deduction, Technical Report, Department of Computer Science, Imperial College, London.

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