Paul, G.: 1993, `Approaches to abductive reasoning---an overview'.  Home/Search   Document Details and Download   Summary   Related Articles   Check

.... ABDUCTION Abduction has recently attracted a lot of attention as an appropriate form of reasoning for formulating many AI problems as such as diagnosis, temporal reasoning including planning, scheduling and temporal diagnosis, natural language processing and others (see the recent surveys [5] [8]) Also abductive reasoning has been proven suitable for capturing logically different kinds of inferences such as explanation, non monotonic and default reasoning, knowledge assimilation and belief revision. This versatility of abduction as a reasoning paradigm together with the high level ....

G. Paul, "Approaches to abductive reasoning: an overview", Artificial Intelligence Review, 7, 109-152, 1993.

....by Kakas et al. 56] for other relationships between abduction and truth maintenance systems. 3.3.4 Knowledge Level Approach to Abduction Levesque [63] presents a knowledge level approach to abduction which subsumes, to a certain extent, the approaches presented thus far. Some surveys (see Paul [95] for instance) identify this as an approach separate from both set cover and logic based approaches though it is essentially logical in nature. Levesque s approach is based on enriching the language to include a belief operator B . By varying this notion of belief, different notions of ....

....definition of abduction we shall investigate the role it plays in belief revision in subsequent chapters. 4.1 Defining Abduction We start with the definition of abduction given in the previous chapter. As noted there, this definition is one of the more common ones to be found in the literature [52, 95, 102]. Some of the work in this chapter has appeared in [90] Describing a metaphor by C. Lewis and R. Mack [66] 77 Definition 4.1.1 An abduction of a set of formulae F with respect to a set of background formulae G is a set Y such that G [ Y F G [ Y 6 Let us return to our example in the ....

Gabrielle Paul. Approaches to abductive reasoning: An overview. Artificial Intelligence Review, 7:109--152, 1993.

....a fundamental form of logical inference that allows us to find hypotheses that account for some observed facts. Its simplest form is: From A B, and B Infer A as a possible justification of B Most of the mechanisms for driving the generation of abductive hypotheses are based on resolution (see [12] or [11] for a survey on abduction mechanisms) However, most failed proof search spaces are huge and these mechanisms are severely affected by the combinatorial explosion phenomenon, see [16] Fortunately, the planning search spaces generated by proof plans are moderately small, see [1] This ....

Paul, G.: Approaches to Abductive Reasoning: an Overview. Artificial Intelligence Review, vol. 7, 109--152. Kluwer Academic Publisher (1993).

....the premises with necessity. That is, given a set of observations, many hypotheses (or conjunctive hypotheses) can be formed, each of which may have different degrees of plausibility. In general, how do we select a best one Many researchers (e.g. Josephson Josephson, 1994; Thagard, 1992a; Paul, 1993) distinguish two components of an abductive reasoning process. That is, abduction is a process that includes both hypothesis generation (forming a set of plausible hypotheses) and hypothesis evaluation (choosing a best one) Note that this distinction does not imply that abduction is a clean ....

Paul, G. (1993). Approaches to abductive reasoning: An overview. Artificial Intelligence Review, 7, 109-152.

....Planning, Natural Language Understanding and others such as Database Updates. Also abduction has been proved suitable for capturing logically different kinds of inferences such as explanation, non monotonic and default reasoning, knowledge assimilation and belief revision (see the recent surveys [4, 5]) This versatility of abduction as a reasoning paradigm together with the high level expressivity that it allows are the primary reasons for its success in formulating so many different problems. We therefore take it as given that the ACLP framework and system are appropriate for tackling NMR ....

Paul, G. : Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7, 109-152, 1993.

....entailed. These abducible assumptions are usually in terms of prespecified predicates, called abducibles, which are not (fully) defined in the general theory. In Artificial Intelligence abduction manifests itself as an important form of inference for addressing a variety of problems (e.g. [Poo88, CDT91, KKT93, DS97, Pau93, Ino94, JJ94, Bre96]) These problems include, amongst others, reasoning with incomplete information, updating a database or belief revision and formalizing and addressing application problems like that of planning, diagnosis, natural language understanding and user modeling. Several applications of abduction exist ....

G. Paul. Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7, 109-152, 1993.

....of evidence that are of interest here are not disbeliefs but plausibilities, and hence are consistent with the current knowledge. Since the result is in general stronger than classical expansion, it is closest to what has been called abduction or inference to the best explanation in the literature [11]. The following figure provides a visual representation of the abductive process suggested in [10] K] x] K x] Fig. 2. Minimality based Abduction Pagnucco has examined the properties of this abduction operation. Let K be the current belief set, x the evidence and the abductive expansion ....

Gabrielle Paul. Approaches to abductive reasoning: An overview. Artificial Intelligence Review, 7:109--152, 1993.

....the model, with an example of its application. Finally, the paper discusses some advantages of the introduced model over other approaches. Explanation Models All explanation systems must reason from effect to cause; this process is known as abduction (Charniak McDermott 1985; Konolige 1990; Paul 1993). Harman (Harman 1965) describes abduction as inference to the best explanation which suggests two aspects to the abductive process; 1) the construction of candidate explanations that explain a given event, and, 2) the evaluation of these candidates to select the best explanation. Explanation ....

....candidates to select the best explanation. Explanation Construction Two main approaches to explanation construction have emerged: ffl candidate explanations are constructed by backward chaining, starting from scratch, from the fact to be explained ( Charniak McDermott 1985; Konolige 1990; Paul 1993) provide an introduction to the basic abductive process while (Ng Mooney ) illustrates its use in various applications) In this paper, this method will be referred to as the chaining based approach. ffl the second is referred to in the literature as CaseBased Explanation (Schank 1986) This ....

Paul, G. 1993. Approaches to abductive reasoning: an overview. In Yazdani, M., and Dodd, T., eds., Artificial Intelligence Review 7, (2). Kluwer Academic. 109--152.

....follow simply from the causal theory) tries to find an explanation of the observed facts. An explanation is a set of hypothetical facts which, along with the causal theory, justifies the presence of the observed facts. Recently there has been various formal characterisations of abduction (see [Paul 93] for a complete overview on this subject) The following is a logic based account for abduction. Let L be a first order language and T be a logical theory defined over the language L. Let A and W be sets of sentences of L respectively called abducible and observable. A logic based abduction ....

Gabriele Paul, Approaches to abductive reasoning: an overview, Artificial Intelligence Review, 7, 109-152, Kluwer Academic Publishers, 1993

....and persistence problems. The enriched specification is obtained from the previous one adding new initial conditions over the attribute values and or new restrictions on the enabling of actions and or fairness requirements over action occurrences. This kind of problem has an abductive flavour [11, 10]: the fact that the property does not follow from the specification is seen as an abduction problem and the set of new specification axioms is seen as an explanation for that problem. The techniques we use to generate the explanations are based on proof techniques in the context of temporal ....

G. Paul. Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7:109--152, 1993.

....a correlation between a speaker s mental state and his uttering a certainsentence44 3. to recognize the syntactic and semantic features of an utterance and, eventually, 4. to define a partial order of plausibility overmental8 18 , then, having received an utterance, the hearer canuse415 166 (see [3,4] for a good review on this subject) to update his image of the speaker s mental state. Even if the speaker would be aware of the way the hearer s updates his own image of the speaker s mental state, he could not completely foresee the effects of his utterances because his image ofe hearer s mental ....

G. Paul, Approaches to abductive reasoning: an overview, Artificial Intelligence Review, Kluwer Academic Publishers, 7, 109-152, 1993.

....We will assume Sigma to be a consistent set of sentences in a finite propositional language L and Ab a set of propositional letters from L. Any formula built using only letters from Ab will be an abducible formula in AbF orm. Given an observation ff, the process of abduction is usually defined ([14, 17, 3, 11, 20, 4]) as the task of finding a consistent subset Delta of AbF orm such that Sigma [ Delta ff . In our example above, Sigma will be the implication (1) ff will be grass is wet and Delta the set frained last nightg. However, this formal description covers only part of the effects one can ....

G. Paul. Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7:109--152, 1993.

....OE are not reasons for ff. ff, fi, fl, ffi :j are reasons for ff. ff is the only strong reason for ff. ffi :j is a more plausible explanation for ff than fi or fl. 6 Abductive Reasoning One method currently gaining popularity for defining the notion of explanation is that of abductive reasoning [Paul, 1993; Stickel, 1991] Abduction is a form of logical inference that aims to derive plausible explanations for information and is, in fact, often described as inference to the best explanation. An abductive inference proceeds by proposing or generating hypotheses which would account for, or explain a ....

....for information and is, in fact, often described as inference to the best explanation. An abductive inference proceeds by proposing or generating hypotheses which would account for, or explain a group of facts. A common way of defining explanation as an abductive inference is the following (see [Paul, 1993], for example however, note that we do not adopt his restriction to abducibles) Definition:An abductive explanation of a sentence fi with respect to a set of sentences T is a sentence ff such that (i) T [ fffg fi, and (ii) T [ fffg 6 . Part (i) of the definition corresponds to having ....

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Paul, G., Approaches to Abductive Reasoning: An Overview, Artificial Intelligence Review, 7:109--152, 1993.

....either fl 6 Sigma fl 1 or fl 6 Sigma fl 2 , so by using E1 and RLE we have (ff fi) fl i for i = 0 or i = 1. Thus from cases (a) or (b) we conclude fl i Sigma ae for i = 0 or i = 1, therefore fl Sigma ae 2 When the language is finite there is a principle stronger than E1 mentioned in [9] as one of the simplicity criteria used to select preferred explanations. It says that preferred explanations have to be complete formulas. E Comp: ff fl ; 6 fl :fi fl fi Under the presence of RLE, it is clear that E Comp implies E1. One could strengthen E Comp by allowing Sigma ....

G. Paul. Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7:109--152, 1993.

....following representation theorem characterises expansion functions in terms of Cn. Theorem 2.1 (AGM [4] The expansion function satisfies (K 1) K 6) iff K ff = Cn(K [ fffg) 2. 2 Abduction We adopt a definition of abduction similar to ones commonly found in the literature [9, 16, 17]. Definition 2.1 An abduction of a formula ff with respect to a domain theory G is a formula fi such that: i) G [ ffig ff; ii) G [ ffig is consistent (i.e. G [ ffig 6 ) For example, suppose G = frain wet grass, sprinkler wet grass, cloud dewpoint reached rain g and ff = wet ....

....we are interested in a general framework capturing all expansions via abduction, we do not impose any further restrictions on abductions here. Different forms of restrictions, however, may be of some interest; for instance, criteria related to syntax, minimality, triviality and specificity (see [16] for an overview) 3 Abductive Expansion In this section we begin our investigation of the proposed belief change operation of abductive expansion in a manner analogous to the development of expansion, contraction and revision within the AGM framework. We begin with an overview of Pagnucco et ....

G. Paul. Approaches to abductive reasoning: An overview. Artificial Intelligence Review, 7:109--152, 1993.

....and argue that our approach could provide a useful link between abduction and machine learning. 1 INTRODUCTION Overthe lastdecade manyauthors havepointedoutthe importance of abductive reasoning in problems of Artifi cial Intelligence and other areas of Computer Science (see the surveys [5] [9] and references therein) Abduction has been shown to be a useful form of reasoning for many applications ranging from diagnosis and planning to database updates andusermodeling. Althoughrecently there hasbeen somework trying to relate abductionandlearning (orinduction)there has been very little ....

G. Paul. Approaches to abductive reasoning: an overview. Artifi cial IntelligenceReview, 7:109-152, 1993.

....such, this review is presented from the perspective of the problem of relating abduction to learning. In many cases the review is (deliberately) simplified to a level sufficient for the purposes of this paper. For more extensive reviews the reader can refer to various existing surveys, e.g. 25] [40]. As in the rest of this paper we will confine ourselves within the logic based approach to abduction and the role of abduction in logic programming 1 . Abduction is reasoning to an explanation according to a given known theory. We explain the observation that the grass is wet by rain ....

G. Paul. Approaches to abductive reasoning: an overview. Artificial Intelligence Review, 7, 109-152, 1993.

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G. Paul. Approaches to abductive reasoning -- an overview. AI Review, 1993. to appear.

....to cope with ambiguity and to allow qualified help. It seems reasonable to constrain the set of all feasible plan hypotheses in order to prevent over or undercommitment or loss of information by adopting a more abstract plan rather than a 1 For a detailed overview on abduction see [KKT92] or [Pau93] disjunction. In order to be able to force a decision among the various hypotheses if, for example, the user directly asks for help to complete his plan, there must be a criterion to judge the quality of a plan hypothesis which enables the best guess of the actually pursued plan to be ....

G. Paul. Approaches to abductive reasoning---an overview. Artificial Intelligence Review, 7:109--152, 1993.

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Paul, G.: 1993, `Approaches to abductive reasoning---an overview'.

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Paul G., Approaches to abductive reasoning: an overview, Artificial Intelligence Review, Kluwer Academic Publishers, 7, 109-152 (1993).

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Paul G., Approaches to abductive reasoning: an overview, Artificial Intelligence Review, Kluwer Academic Publishers, 7, 109-152 (1993).

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