Stickel, M.: A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California (1988)  Home/Search   Document Details and Download   Summary   Related Articles   Check

....however, is the lack of a precisely defined semantics of weights. We do not attempt to provide a formal definition of its semantics in this paper, instead we use ad hoc heuristics that are applicable to our particular application. Following the weighted abductive inference algorithm described in [16], our abductive prover, Tacitus lite , is a collection of rules where each rule is expressed as a Horn clause p w 1 # #p wn n r, where each conjunct p i has a weight w i associated with it. The weight is used to calculate the cost of assuming p i instead of proving it where cost(p i ) ....

Mark Stickel. A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California, 1988.

....however, is the lack of a precisely defined semantics of weights. We do not attempt to provide a formal definition of its semantics in this paper, instead we use ad hoc heuristics that are applicable to our particular application. Following the weighted abductive inference algorithm described in [14], our abductive prover, Tacitus lite , is a collection of rules where each rule is expressed as a Horn clause p w1 1 p wn n r where each conjunct p i has a weight w i associated with it. The weight is used to calculate the cost of assuming p i instead of proving it where cost(p i ) ....

Mark Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California, 1988.

....Bylander et al. BATJ91] has formulated abduction in order to analyze the computational complexity of abduction for propositional logic and for the diagnosis problem. In computational linguistics, Hobbs et al. HSME88] has introduced abduction in order to interpret natural language. Stickel [Sti91] has also investigated abduction deeply, and suggested a Prolog like inference system to interpret natural language. 1.4 Classification of Abduction In order to systematically understand the above mentioned various researches of abduction in computer science and clearly discuss abduction, we ....

....Peirce s abduction. Abduction for explanation based generalization by Genest et al. GMP90] is a kind 30 of rule selecting abduction. However, it depends on heuristics which makes the surprising fact surprising . Abduction for natural language interpretation by Hobbs et al. HSME88] and Stickel [Sti91] is a kind of rule selecting abduction. In the formulation of Hobbs et al. HSME88] they have dealt with first order formulas with costs as the logical forms of abduction. On the other hand, Stickel [Sti91] has dealt with function free definite programs as the logical forms of abduction. ....

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Stickel, M. E.: A Prolog-like inference system for computing minimumcost abductive explanation in natural language interpretation, Annals of Mathematics and Artificial Intelligence 4, 89--106, 1991.

....the behaviour of the system is not normal. Abduction can be used to perform high level vision [15] The hypotheses are the objects to be recognised, and the observations are partial descriptions of objects. Abduction can be used in natural language understanding to interpret ambiguous sentences [9, 40, 53, 127]. The abductive explanations correspond to the various possible interpretations of such sentences. In planning problems, plans can be viewed as explanations of the given goal state to be reached [30, 125] These applications of abduction can all be understood as generating hypotheses which are ....

Stickel, M.E., A prolog-like inference system for computing minimumcost abductive explanations in natural-language interpretation. Proc. International Computer Science Conference (Artificial Intelligence: Theory and Applications), Honk Kong, Lassez and Chin eds. (1988) 343--350

....paper we are interested in a particular type of inference, known as abductive reasoning or diagnostic reasoning. In fact, is in the field of diagnostic where abductive reasoning has its most clear application [3] 4] 5] although other applications exist in natural language understanding [6] [7], vision [8] legal reasoning [9] plan recognition [10] 11] planning [12] and learning [13] Abduction [14] is defined as the process of generating a plausible explanation for a given set of observations or facts. In the context of probabilistic reasoning, abductive inference corresponds to ....

M.E. Stickel, "A prolog-like inference system for computing minimum-cost abductive explanations in natural language interpretation," Tech. Rep. 451, AI Center, SRI International, 1988.

....the behaviour of the system is not normal. Abduction can be used to perform high level vision [15] The hypotheses are the objects to be recognised, and the observations are partial descriptions of objects. Abduction can be used in natural language understanding to interpret ambiguous sentences [9, 40, 53, 127]. The abductive explanations correspond to the various possible interpretations of such sentences. In planning problems, plans can be viewed as explanations of the given goal state to be reached [30, 125] These applications of abduction can all be understood as generating hypotheses which are ....

Stickel, M.E., A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Proc. International Computer Science Conference (Articial Intelligence: Theory and Applications), Honk Kong, Lassez and Chin eds. (1988) 343-350

....[Poo89a] Given a set of al5 ternative assumption sets A 1 , A n that are solutions to the abduction problem T #A = #, assumption set A i is less presumptive than assumption set A j if T #A j = A i . This corresponds rather directly to what Stickel refers to as least specific abduction [Sti88a]. Stickel argues that least specific abduction is a good evaluation criterion for certain types of natural language interpretation tasks. For example, in ordinary discourse, if a speaker says My car won t start, it is likely that what the speaker intends the hearer to believe is that the car ....

....conditions that would lead one to prefer either a most specific or a least specific explanation. 3 Weighted Abduction We now turn to a more detailed description of weighted abduction. The algorithm for weighted abduction was introduced by Stickel, but without any theoretical analysis [Sti88a]. The key idea behind weighted abduction is that the process of making an assumption during inference should incur a cost. Thus every conjunct in conjunct in each rule in a weighted abduction theory is assigned an assumption cost, and this cost is propogated through rules, from consequents to ....

M. E. Stickel (1988). A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. In International Computer Science Conference, Hong Kong, 343-350.

....A [ T j= O. The assumptions A are said to explain the observation. Legal assumptions are frequently restricted, such as allowing only instances of certain predicates (predicate specific abduction) or requiring that assumptions not be provable from more basic assumptions (most specific abduction) [43]. In order to focus on leaf rules, Either s abductive component backchains as far as possible before making an assumption (most specific abduction) The consistency constraint is removed in order to allow assumptions to be viewed as antecedent retractions. Since an observation states that an ....

M. E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report Technical Note 451, SRI International, Menlo Park, CA, September 1988.

....as the best diagnoses. We can map a GSC diagnostic problem into an abduction problem in Accel as follows: Let the domain theory T be the set of axioms fd mj(d; m) 2 Cg, and let the input atoms O = V m2M m. Suppose only atoms d 2 D are assumable (i.e. we use predicate specific abduction [ Stickel, 1988 ] in which only atoms with certain predicates are assumable) It can be easily proved that the set of covers of GSC is the same as the set of explanations in Accel [ Ng, 1992 ] 3 The logical abduction approach, being based on a more expressive representation language, can accommodate more ....

Mark E. Stickel. A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Note 451, SRI International, September 1988.

....In first order logic, the important operation of unifying assumptions (factoring) becomes relevant. Frequently, simple and coherent explanations can only be constructed by unifying initially distinct assumptions so that the resulting combined assumption explains several observations [Pople, 1973, Stickel, 1988, Ng and Mooney, 1990] This important problem does not arise in the propositional case. The second problem is efficiency. The general purpose abduction algorithm proposed in [Stickel, 1988] can perform a great deal of redundant work in that partial explanations are not cached and shared among ....

....distinct assumptions so that the resulting combined assumption explains several observations [Pople, 1973, Stickel, 1988, Ng and Mooney, 1990] This important problem does not arise in the propositional case. The second problem is efficiency. The general purpose abduction algorithm proposed in [Stickel, 1988] can perform a great deal of redundant work in that partial explanations are not cached and shared among multiple explanations. The ATMS algorithm, though it caches and reuses partial explanations in order to avoid redundant work, has not been extended to perform general first order abduction. ....

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Mark E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Note 451, SRI International, September 1988.

....have dealt with the problem of choosing the best hypotheses from a set of alternatives for explaining an agent s behavior. In general, they have introduced various coherence criteria for checking the validity of the selected hypotheses (for a classification of some of these criteria, see [ Stickel, 1988 ] Kautz adopted the simplicity criterion and tried to explain an agent s behavior with a minimal set of higher level hypotheses that justify the observed actions [ Kautz, 1990 ] Ng and Mooney [ Ng and Mooney, 1990 ] observed that the simplicity criterion does not capture in a satisfactory way ....

M.E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. In Proc. Int. Computer Science Conference, Hong Kong, 1988.

....can serve as an explanation for the evidence. For example, assuming that no one is home is a possible explanation for the house being dark and quiet. Abductive explanation has been formalized in AI as the process of searching for some set of assumptions that can prove the things to be explained [7, 26, 60, 64, 73, 31, 20, 43, 41]. We call each such set an explanation for the given evidence. A basic problem which naturally arises is that there maybe many different possible 3 For a good general discussion of abduction, see [29] explanations available. From traditional symbolic logic, the only measure of a set s ....

....preferential ordering on the explanations is necessary. This would serve to precisely define the notion of a best explanation as well as subsequent next best which is critical to have in domains such as medical diagnosis. Several ordering measures are available such as least specific abduction [26, 73], cost based abduction [7] parsimonious covering theory [43] and belief revision [41] Each approach offers different perspectives on the problem and provides individual frameworks capable of modeling certain aspects of abductive reasoning. The complexity of abduction quickly becomes apparent ....

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Mark E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report Technical Note 451, SRI International, 1988.

....is true or not; all we have is probabilities and evidence to work out what is most likely true. Similar considerations motivated the addition of probabilities to consistency based diagnosis [ de Kleer and Williams, 1989 ] Perhaps the closest work to that presented here is that of Stickel [ Stickel, 1988 ] His is an iterative deepening search for the lowest cost explanation. He does not consider probabilities. 6 Using existing logic programming technology In this section we show how the branch and bound search can be compiled into Prolog. The basic idea is that when we are choosing a partial ....

M. E. Stickel. A Prolog-like inference system for computing minimum-cost abductive explanations in natural language interpretations. Technical Note 451, SRI International, Menlo Park, CA, September 1988.

....cannot be intermediate assumptions that are themselves provable by assuming some other (more basic) assumptions. This is the approach used in the diagnosis work of [Cox and Pietrzykowski, 1987] In least specific abduction, the only allowable assumptions are literals in the input observations. [Stickel, 1988] claims that least specific abduction is best suited for natural language interpretation. He argues that what one learns from reading a piece of text is often close to its surface form, and that assuming deeper causes is unwarranted. In weighted abduction [Hobbs et al. 1988] weights (or costs) ....

....is best suited for natural language interpretation. He argues that what one learns from reading a piece of text is often close to its surface form, and that assuming deeper causes is unwarranted. In weighted abduction [Hobbs et al. 1988] weights (or costs) are assigned to the antecedents of 5 [Stickel, 1988] describes yet another form of abduction known as predicate specific abduction, which has been used primarily in planning and design synthesis tasks. In predicate specific abduction, the predicate of any assumption made must be one of a pre specified set of predicates. inst w working) inst ....

Mark E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Note 451, SRI International, September 1988.

....T 0 (T 0 = T [ A) The observations O should now be contained within the deductive closure T 0 c while (representing inconsistency) should not. Typically, in AI applications, this task is achieved using a backward chaining reasoner that is allowed to make assumptions where necessary [Stickel, 1988; Ng and Mooney, 1991] We will look briefly at the Accel algorithm [Ng and Mooney, 1991] upon which our work is based. The algorithm is similar to the inference procedure of Prolog but with the added ability to make assumptions out of subgoals or to unify them with previous assumptions or ....

M. E. Stickel. A Prolog-like inference system for computing minimumcost abductive explanations in natural-language interpretation. Technical Report Technical Note 451, SRI International, Menlo Park, CA, September 1988.

....our approach exhibits a slower run time growth rate. This formulation also permits the natural generation of alternative explanations. 1 Introduction Abductive explanation has been formalized in AI as the process of searching for some set of assumptions that can prove the things to be explained [2,4,8,9,12, 16,17,18]. We call each such set an explanation for the given evidence. A basic problem which naturally arises is in choosing among the many different possible explanations available. We can easily see that some preferential ordering on the explanations are necessary. Early measures based on minimizing the ....

....[4,9] have been shown to 1 This work has been supported by the National Science Foundation under grant IRI 8911122 and by the Office of Naval Research, under contract N00014 88 K 0589. Special thanks to Eugene Charniak for important pointers and critical review of this paper. be inadequate [2,8,18] suggesting the use of a more sophisticated approach. One such approach proposed by Hobbs and Stickel [8,18] called weighted abduction involves levying numerical costs to making individual assumptions. The cost of an explanation is a function of the cost of the individual assumptions made in the ....

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Stickel, Mark E., "A Prolog-like Inference System for Computing Minimum-Cost Abductive Explanations in Natural-Language Interpretation," SRI International, Technical Note 451, 1988.

....information and common knowledge. iv) A general way of allowing these contexts to influence the interpretive process. In particular, contexts should influence the preferences that are assigned to interpretations. Our approach 6 uses a form of weighted abduction as the reasoning mechanism [Sti88, HSAM93] with contexts modeled as modal like operators. This allows contexts to be represented explicitly and reasoned about. 7 The abductive interpretation of an utterance will use a modal operator to limit the rules that are accessible and adjust the weights of assumptions. We can create ....

Mark Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California, 1988.

.... may be multiple answers to any query, and just because we ask a query does not mean we want to solve it (we may only want to bound the probability of the answer) One of the reasons that we wanted to present this at a high level of abstraction rather than as an iterative deepening version (such as [31]) is to allow for such ideas as creating lemmata. Based on our experience, there are some cases where the lemma version is faster than even one iteration of the depth bounded search needed for an iterative deepening solution. There is some connection between the idea of saving recomputing subgoals ....

....algorithm, the explicit use of the priority queue, the estimation of the prior and posterior probabilities (including error bounds) and the use of two explanations being found at once for conditional probabilities (Section 4. 2) Perhaps the closest work to that presented here is that of Stickel [31]. His is an iterative deepening search for the lowest cost explanation, and at that level can be seen as an iterative deepening version of the algorithm of Figure 1. The problem he is trying to solve is to find the least cost explanation. He does not consider probabilities (but Charniak and ....

M. E. Stickel. A Prolog-like inference system for computing minimumcost abductive explanations in natural language interpretations. Technical Note 451, SRI International, Menlo Park, CA, September 1988.

....for linear strategies, and the use of depth first iterative deepening search in deduction. Besides being useful for deduction, the model elimination procedure and PTTP can be extended for use in abductive reasoning in diagnosis [30, 6, 7] design synthesis [8] and natural language interpretation [11, 41, 42]. Adding the capability to skip and thereby assume literals instead of prove them permits this extension from deductive to abductive reasoning [24, 34, 13] The model elimination procedure and PTTP can then play a fundamental role in the computation of default logics [4, 29] circumscription ....

Stickel, M.E. A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. To appear in Annals of Mathematics and Artificial Intelligence.

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Stickel, M.: A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California (1988)

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Stickel, M.: 1988, `A Prolog-Like Inference System for Computing Minimum-Cost Abductive Explanations in Natural-Language Interpretation'. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California.

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M. E. Stickel. A prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretations. Annals of Mathematics and Artificial Intelligence, 4:89--106, 1991. 40

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Stickel, M.: A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California (1988)

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Stickel, Mark E., 1988. "A Prolog-like Inference System for Computing Minimum-Cost Abductire Explanations in Natural-Language Interpretation", forthcoming.

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Mark Stickel. 1988. A Prolog-like inference system for computing minimum-cost abductive explanations in natural-language interpretation. Technical Report 451, SRI International, 333 Ravenswood Ave., Menlo Park, California.

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