Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National ConferenceonArtificial Intelligence, pages 923--928, Boston, MA, 1990.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....problem to be solved (a theorem to be proved) this algorithm reformulates the original problem into more abstract ones. The original problem may be mentioned in the further text also as the base problem, because it is determined at the lowest abstraction level. The ordered monotonicity property [55] is used as the basis for generating abstraction hierarchies. This property captures the idea that as an abstract solution is re ned, the structure of the abstract solution should be maintained. The process of re ning an abstract solution requires inserting additional steps to achieve the ....

....solution is re ned, the structure of the abstract solution should be maintained. The process of re ning an abstract solution requires inserting additional steps to achieve the literals ignored at more abstract level. The ordered monotonicity property of an abstraction hierarchy is de ned in [55] as follows. De nition 2.4.1 Ordered monotonic re nement is a re nement of an abstract solution that leaves the truth value of every literal in an abstract space unchanged. De nition 2.4.2 Ordered monotonic hierarchy is an abstraction hierarchy with the property that for every solvable ....

C. A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Arti cial Intelligence, Boston, MA, AAAI Press, pp. 923-928, 1990.

....as well as helping to explore and refine the engineering of the domain. One particular area that seems to be neglected is of pre compiling domain specifications to extract the goal structure within them (notable exceptions include analysis of goal interactions in REFLECT [4] STATIC [6] and ALPINE [8], as well as our own earlier work [11] Indeed, Barrett and Weld conclude that a domain compiler which identified good and bad orderings would have considerable benefits [1, pp 103] In this paper we extend our work reported in [11] and present the framework for an analysis of goal establishment ....

.... planning ffl use of type (iii) interactions to debug the domain model We have extensively tested the impact of using type (i) goal orders in plan generation in conjunction with a macro operator generator called PROPOSE and a method for generating possible orders between goals based on [8]. In this section we will present the results of a selection of these tests to give a feel for the potential of our approach. STRIPS world Results We used two variants of Sacerdoti s STRIPS world [16] Firstly, a STRIPS world consisting of 7 rooms connected by 10 doors in which a robot is ....

C. A. Knoblock. Learning Abstraction Hierarchies for Problem Solving. In Proc. AAAI, 1990.

....axioms and a sequent to be proved this algorithm reformulates the original problem into more abstract ones. The original problem is referred to in the subsequent text also as the base problem, because it is determined at the lowest abstraction level. The ordered monotonicity property [6] is used as the basis for generating abstraction hierarchies. This property captures the idea that as an abstract solution is re ned, the structure of the abstract solution should be maintained. The ordered monotonicity property of an abstraction hierarchy is de ned in [6] as follows. The ....

....monotonicity property [6] is used as the basis for generating abstraction hierarchies. This property captures the idea that as an abstract solution is re ned, the structure of the abstract solution should be maintained. The ordered monotonicity property of an abstraction hierarchy is de ned in [6] as follows. The ordered monotonic re nement is de ned as a re nement of an abstract solution that leaves the truth value of every literal in an abstract space unchanged. Algorithm DetermineConstraints(graph; axioms; goal) output: constraints, which guarantee ordered monotonicity for a given ....

C. A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Arti cial Intelligence, Boston, MA, 1990.

....succeeding steps (in a state space encoding) or apply a restriction on the number of steps before an action can assert a new value for the variable (in a causal encoding) 4. 1 Related Work There are a variety of other systems for creating and exploiting abstraction hierarchies [ Sacerdoti, 1974; Knoblock, 1990; Allen et al. 1991 ] ALPINE in particular has the ordered monotonicity property [ Knoblock, 1990 ] So, ALPINE s lower level plans will not disturb any predicates at steps committed at higher abstraction levels. Although this property restricts the abstraction steps ALPINE can take, using a ....

....action can assert a new value for the variable (in a causal encoding) 4. 1 Related Work There are a variety of other systems for creating and exploiting abstraction hierarchies [ Sacerdoti, 1974; Knoblock, 1990; Allen et al. 1991 ] ALPINE in particular has the ordered monotonicity property [ Knoblock, 1990 ] So, ALPINE s lower level plans will not disturb any predicates at steps committed at higher abstraction levels. Although this property restricts the abstraction steps ALPINE can take, using a system with this property in CPlan would have a substantial benefit. With the ordered monotonicity ....

C. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928. Menlo Park, Calif.: AAAI Press, August 1990.

....on different layers, each one equipped with a suitable planner. Each planner is allowed to use only the operators available at the corresponding level. It is worth pointing out that, whereas typical hierarchical planners use a fixed (a priori) decomposition strategy (e.g. HTN [8] ABSTRIPS [9]) in the proposed architecture, the decomposition is performed at runtime and distributed on several layers. Each layer is devoted to perform a (local) planning on any goal imposed by its overlying planner (if any) or to perform a re planning activity, if needed. Thus, a goal to be attained at ....

Knoblock, C.A., "Learning Abstraction Hierarchies for Problem Solving", in Proceedings of the Height National Conference on AI, pp. 993928, AAAI Press, Menlo Park, CA, 1991.

....1993) Others have studied re using plans under other conditions (Hammond, 1990) including multiple actors (Suguwara, 1995) An actor can also create a plan from scratch using a given set of STRIPS like operators (Fikes Nilsson, 1971) in a hierarchical planner (c.f. Sacerdoti, 1974; Knoblock, 1990) The situation calculus (McCarthy, 1958: 1968) is used to represent the planner s expectations about changes in the situation that result from a given kind of action. Each actor maintains a representation of the probability of success for di#erent actions in di#erent contexts. When planning ....

Knoblock, C. A. (1990). Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928.

....lower level tools. Actually, we have to learn how we can formally represent, generate, and investigate a mathematical model based on the abstract images extracted from the expert vision of the problem. implemented for many problems with varying degrees of success (see, e.g. Albus, 1991; Knoblock, 1990; Mesarovich et al., 1989; Botvinnik, 1984) Implementations based on the formal theories of linear and nonlinear planning meet hard efficiency problems (McAllester and Rosenblitt, 1991; Chapman, 1987; Nilsson, 1980; Stefik, 1981; Sacerdoti, 1975) An efficient planner requires an intensive use of ....

Knoblock, C.A. (1990). Learning Abstraction Hierarchies for Problem Solving, Proc. of the 8th AAAI Conf., (pp.923-928), Menlo Park, CA.

....2. Tools used primarily for compiling a domain model into a more efficient or operational form. These include: a) macro generation (see section 4.1 below) b) generation of various types of goal orderings (see section 4. 2 below) c) abstraction hierarchy generation (for example ALPINE in [35, 36]) At present our environment contains a number of tools of category 1 (a, b, e and f) as follows: ffl a tool that uses the substate class definitions to: check the syntax of the domain operator set; check that all substates that should be achievable are indeed achievable by operator action; help ....

....the orders were generated. For example, there is no precondition to do 42 with inflating a tyre before putting it on a hub in the operators, yet this might be a valid constraint. 5.3. 3 Generation of Possible Goal Orderings ABGEN is an implementation based on the ALPINE algorithm presented in [35, 36], which generates goal orders on the basis of possible interactions between goals (ABGEN was described in section 4.2) We included it in the tests as it complements necessary orders when choosing which goal to establish next during planning: given a set of goal predicates, necessary orders reduce ....

C. A. Knoblock. Learning Abstraction Hierarchies for Problem Solving. In Proc. AAAI, 1990.

....incorporating hierarchies into reinforcement learning algorithms. Research in classical planning has shown that hierarchical methods such as hierarchical task networks (Currie Tate, 1991) macro actions (Fikes, Hart, Nilsson, 1972; Korf, 1985) and state abstraction methods (Sacerdoti, 1974; Knoblock, 1990) can provide exponential reductions in the computational cost of finding good plans. However, all of the basic algorithms for probabilistic planning and reinforcement learning are flat methods they treat the state space as one huge flat search space. This means that the paths from the start ....

Knoblock, C. A. (1990). Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pp. 923--928 Boston, MA. AAAI Press.

.... one with conditional effects and universal quantification Inadequate emphasis on task decomposition has also had an unfortunate effect on machine learning research for planning, e.g. explanation based learning (Minton 1988) static domain analysis (Etzioni 1993, Smith Peot 1993) abstraction (Knoblock 1990, Yang Tenenberg 1990) case based planning (Hammond 1990) and derivational analogy (Veloso Carbonell 1993) It is unfortunate that the vast majority 1 of research on speedup learning has ignored taskdecomposition planners, since defining and using tasks provides a very successful form of ....

....steps respectively. The purpose of our experiment was to explore interactions between plan parsing and three different search strategies: vanilla best first; best first search with a search space structured according to an abstraction hierarchy generated by the alpine machine learning algorithm (Knoblock 1990); and domain dependent, hand coded rules. To create our Tyreworld parser we defined 5 tasks for getting tools, inflating tires, removing tires, installing tires, and cleaning up. The Process Planning parser was created out of a set of 12 schemata defining tasks like setting up drill presses and ....

Knoblock, C. 1990. Learning abstraction hierarchies for problem solving. In Proc. 8th Nat. Conf. on A.I., 923--928.

....Carbonell, 1993) Others have studied re using past plans under other conditions (Hammond, 1990) including multiple actors (Suguwara, 1995) An actor can create a plan from scratch using a given set of STRIPS like operators (Fikes Nilsson, 1971) in a hierarchical planner (c.f. Sacerdoti, 1974; Knoblock, 1990) Depending on their type, di#erent actors have di#erent operations that they can perform. The special purpose operators for the actors in MOVERS WORLD are: lifter LIFT, LIFT TOGETHER, CARRY, CARRY TOGETHER, LOAD, LOAD TOGETHER, UNLOAD, UNLOAD TOGETHER, PUT DOWN, and PUT DOWN TOGETHER. ....

Knoblock, C. A. (1990). Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928.

.... previously satisfied prerequisites and its prerequisites might be already satisfied (the number of unsatisfied prerequisites decreases) Therefore regressing the mtc on the action schemas themselves is needed to predict some changes made by an action addition to the truth value of prerequisites [Knoblock 90] Smith Peot 93] Thus, the number of times the mtc must be called does not depend on the number of calls to GeneratePlan and not, in particular, to promotion, demotion, unification of separation. We use this property to add a condition on the evaluation of line 1 of GeneratePlan while ....

.... since depth first search is good for shallow solution paths in general [Langley 92] Many planners are propositional closed literals without any variables (SNLP, UCPOP) For example, abstractions based on time ordering have been shown to improve the efficiency of the search in general [Knoblock 90] But such propositional planners might perform arbitrarily poorly on particular individuals (see [Smith Peot 92] concerning propositional hierarchies and [Ginsberg 93] concerning propositional planning) Nevertheless, work of the late 70s showed that variables used as placeholders do improve ....

Craig Knoblock. Learning Abstraction Hierarchies for Problem Solving. In Proceedings of AAAI'90, Boston, MA, 1990.

....will use the routines to validate their own speedup learning experiments. z Affiliate Assistant Professor, Department of Biostatistics, University of Washington. 1 Motivation Speedup learning systems are systems that automatically generate search control knowledge (e.g. Etzioni, 1990b, Knoblock, 1990, Minton, 1988a, Mooney, 1989, O Rorke, 1989, Shavlik, 1990] The effectiveness of a speedup learning system is typically evaluated by comparing the performance of a problem solver, guided by the learned knowledge, with the performance of the problem solver given no control knowledge, or given ....

Knoblock, Craig A. 1990. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, Menlo Park, CA. AAAI Press.

....abstrips [Sac74] 1980 Plaisted Weak and Ordinary A. Pla80] 1986 Plaisted Generalisation A. Pla86] 1987 [Kor87] 1988 Tenenberg A. in Planning [Ten88] 1989 Giunchiglia Walsh Abstract T.P. GW90] 1990 Cremonini et al. A framework for A. CMS90] Pla90] Gamma Knoblock alpine [Kno90] 1991 Knoblock et al. A. for Planning [KTY91] KME91] 1992 Giunchiglia, Walsh T. of A. GW92] SP92] Gamma 1994 Bacchus et al. highpoint [BY94] 1995 Nakay, Levy Semantic T. of A. NL95] BJ95] Gamma 1996 Bundy et al. resistor prob. BGSW96] Giunchiglia et al. absfol [GV96] ....

C.A. Knoblock. Learning Abstraction Hierarchies for Problem Solving. In Proceedings AAAI-90, Boston, MA, 1990.

....to be explicitly stated, the problem solver is able to reason with them and to choose abstractions tailored for the specific task at hand, as opposed to being constrained by predefined abstraction hierarchies. The issue of automatically creating abstractions has received much attention lately [8, 9, 18, 6, 2, 13, 12, 5]. A promising direction is to use relevance claims to generate abstractions. In this approach, a system will be able to automatically generate model fragments needed for a certain task, rather than only choosing from a pre defined set. 11 The most important source of relevance heuristics has been ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, Los Altos, CA, 1990. Morgan Kaufmann.

....in this paper, we extend the definition of irrelevance to other subjects, such as predicate and object distinctions. Recently, the issue of automatically generating abstractions and evaluating their utility has received much attention [ Ellman, 1988; Bennett, 1986; Giunchiglia and Walsh, 1992; Knoblock, 1990; Yoshida and Motoda, 1990; Yoshida and Motoda, 1992; Williams, 1990 ] and in the context of modeling of physical devices [ Falkenhainer and Forbus, 1991; Nayak, 1992 ] Space limitations enable us to discuss only one of these works in detail. Yoshida Motoda [ Yoshida and Motoda, 1990 ] also ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, Los Altos, CA, 1990. Morgan Kaufmann.

....and multiple levels of abstraction. He has shown that in the optimal case, abstraction can reduce the expected search time from exponential to linear. Knoblock has developed an approach to construct a hierarchy of abstraction spaces automatically from a given concrete level problem solving domain (Knoblock, 1990, 1993, 1994) These so called ordered monotonic abstraction hierarchies (Knoblock, Tenenberg, Yang, 1991b) have proven useful in many domains. Recently, Bacchus and Yang (1994) presented an improved method for automatically generating abstraction hierarchies based on a more detailed model of ....

....its simplicity, refinement is very easy because abstract states can directly be used as goals at the more detailed levels. Another very important property of abstraction by dropping sentences is that useful hierarchies of abstraction spaces can be constructed automatically from domain descriptions (Knoblock, 1990, 1993, 1994; Bacchus Yang, 1994) 2.2 Generating of Abstract Solutions from Scratch Another limiting factor of classical hierarchical problem solving can be the way abstract solutions are computed. As pointed out by Korf, a good abstract solution must lead to mostly independent subproblems of ....

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Knoblock, C. A. (1990). Learning abstraction hierarchies for problem solving. In Proceedings Eighth National Conference on Artificial Intelligence, Vol. 2, pp. 923--928 London.

.... in focusing the search, e.g. 66, 43] ffl Resource bounded search, e.g. 89, 91, 134] ffl Means ends analysis, e.g. 44] ffl Search for partially ordered plans, e.g. 137, 150, 160] ffl Least commitment approach, e.g. 142, 74] ffl Abstraction of plan and operator descriptions, e.g. [136, 85, 152, 46]; ffl Defaults and approximate planning, e.g. 41, 62] ffl Search space decomposition, e.g. 94, 109, 157] operator decomposition, e.g. 86] and competence level decomposition, e.g. 10] ffl Reactive planning via off line computation, e.g. 47, 55, 138] or use of deictic representations, e.g. ....

Knoblock, C. A., Learning Abstraction Hierarchies for Problem Solving. Proc. AAAI-90, Boston MA , 1990, pp. 923-928.

....transition function. States themselves are usually represented as a set of essential propositional sentences [Lifschitz, 1987] The operators of a domain can be modeled on several levels of abstraction, an idea already intensively investigated in research on hierarchical planning [Sacerdoti, 1974, Knoblock, 1990] On the lowest level of abstraction, we require e.g. the description of the raw cut( Area ) operation. This operation is applicable only if Area is accessible by the cutting tool and if Area specifies a part of the mold which is not already removed. As an effect of this operation, Area is ....

....[Bergmann and Wilke, 1993] An additional source of power of the explanation based similarity approach comes from its ability to abstract explanations on the basis of domain knowledge. Thereby, descriptions are transformed into a completely new abstract language. Other work on abstraction (e. g [Knoblock, 1990, Unruh and Rosenbloom, 1989] mostly focuses on abstraction by dropping parts of a description that are not assumed to be relevant on an abstract view. On the other hand, we require a more elaborated modeling of the domain knowledge. In [Birnbaum and Collins, 1988] an approach is described with ....

C. A. Knoblock. Learning abstraction hierarchies for problem solving. In MIT Press, editor, Proceedings Eighth National Conference on Artificial Intelligence, volume 2, pages 923--928, London, 1990. MIT Press.

....de caract eriser ces hi erarchies, divers crit eres ont et e d efinis. Les deux crit eres les plus etudi es sont respectivement la propri et e d affinement descendant (Downward Refinement Property ou DRP) 1, 2] et la propri et e de monotonie ordonn ee (Ordered Monotonicity Property ou OMP) 11] d ecrites informellement ci dessous. Dans ces d efinitions, un plan abstrait est un plan solution du probl eme de planification a un niveau d abstraction i donn e. Un plan P i Gamma1 est un affinement d un plan abstrait P i si P i Gamma1 est un plan abstrait qui ne diff ere de P i que par ....

....nous avons men ee sur la hi erarchisation. Ces r esultats ont et e montr es dans le cadre du syst eme I XTET mais, dans la mesure o u ils reposent essentiellement sur Domaines facteur d G n G =p G nombre nombre taille de gain attributs taches plan Hilares 1.4 2 1.5 3 3 10 Iares 2.7 3 1. 5 5 11 19 Columbus prob. 1 1.7 4 1.7 16 11 10 prob. 2 2.3 4 1.7 16 11 12 Ariane 3.9 6 6 6 0 56 Finition 8.8 6 4 18 12 18 pi ece Table 2: Gains globaux li es a la hi erarchisation hi erarchie ordonn ee hi erarchie hors ligne: dynamique: Noeuds 305 59 Retour arri eres 14 0 Temps CPU 14.1 s 2.8 s ....

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C.A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings AAAI-90, pages 923--928, 1990.

....different from ours. Feldman and Morris discuss the distinction between filters and subgoals in [2] but their analysis focuses on the detection of loops in planning search and leaves the question of hierarchy unaddressed. Knoblock discusses the automatic derivation of a planning hierarchy in [10], but the methods used are primarily syntactic and are concerned with the development of a static hierarchy in any event. Smith and Peot suggest that Knoblock s analysis should focus on more semantic features in [14] but they, too, limit their attention to static hierarchies. This is to be ....

C. A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

....non localized domain description. We have identified two domain independent criteria for forming these localizations: abstraction and scope. Knoblock s method for generating planning abstraction levels for STRIPS based frameworks is based on an analysis of problem goals and operator descriptors [3]. We were able to graft Knoblock s technique onto Collage s action based framework by recognizing that the relationship between state literals he derived was based on a type of activation relationship i.e. how planning to achieve one literal could lead to (activate) planning to achieve another. ....

....regional collapse. In particular, both of the abstraction based localizations contain an extremely large region due to potential constraint activation relationships. Thus, although the abstraction based localizations do result in a monotonic reasoning space that searches each region only once [3, 9], they do so at a price. In contrast, scoped takes advantage of Collage s highly flexible localizing abilities i.e. its ability to allow for a variety of localization structures and to flow back and forth among regional search spaces while still assuring consistency. It thus benefits from ....

Knoblock, C.A. "Learning Abstraction Hierarchies for Problem Solving," in Seventh International Workshop on Machine Learning, pp. 923-928 (1990).

....Towell90] Several non learning techniques can also be viewed from this perspective. Forexample several reactive planningsystems transform a causal theory into a set of reactive rules [Drummond90, Schoppers87] Automatic abstraction systems can also be viewed as transformational processes [Knoblock90 ]. Thetransformations available to a learner define its vocabulary of transformations. These are essentially learning operators and collectively they define a transformationspace. For instance, acquiring a macro operator can be viewed as transforming the initial system (the original planner) into ....

C.Knoblock, "Learning Abstraction Hierarchies for Problem Solving," AAAI90, Boston, MA, 1990.

....It is interesting to compare this work with similar research on subgoal ordering discussed earlier in the section on Solution Extraction as Constraint Satisfaction. Problemspace graphs [25] and operator graphs [97, 98] share many resemblances to causal graphs. Knoblock s ALPINE abstraction system [58] can be viewed as finding a serialization ordering, and it can eliminate most search when given a problem with acyclic structure such as the towers of Hanoi [60] 25 The causal graph is constructed offline from a compiled version of the domain theory which eliminates all reference to dependent ....

C. Knoblock. Learning abstraction hierarchies for problem solving. In Proc. 8th Nat. Conf. AI, pages 923--928, August 1990.

....plans produced by the planner. The algorithm presented in the paper is novel in that it automatically finds primary effects. The learner may be integrated with an algorithm presented in [Fink and Yang, 1992b] to increase the number of levels of ordered abstraction hierarchies generated by ALPINE [ Knoblock, 1990 ] while preserving the completeness of planning and ensuring a small cost increase. ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

....important not only for the purpose of optimizing plans, but also for abstract problem solving. Several important concepts describing the algorithms for generating abstraction hierarchies are defined via justified plans. For example, the theoretical concepts underlying Knoblock s planner ALPINE [ Knoblock, 1990 ] are based on the notions of justified plans. Other results that depend on this notion are presented in [ Tenenberg and Yang, 1990 ] Knoblock et al. 1991 ] and [ Bacchus and Yang, 1991 ] In spite of the importance of the concept of justified plans, relatively few efforts have been made ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....the encapsulated event subsets at the same hierarchical level to be partially ordered as a constant number of chains. We present an abstraction technique to exploit temporal locality in a hierarchical way, using a state based approach. This technique is different from previous work on abstraction [7] in that we transform encapsulated event subsets into abstract events, instead of transforming individual operators into abstract operators. We explore spatial locality where each encapsulated event subset has local conditions that only appear in the causal rules associated with the events in the ....

Craig A. Knoblock. Learning abstraction hierarchies in problem solving. In Proceedings AAAI-90, pages 923--928. AAAI, 1990.

....to analyze our planners performances in various domains, but first we observe several limitations. First, while it may be possible to determine if a set of subgoals is independent, little work has been done on the problem of determining that a set of subgoals is serializable and finding the order [3, 4, 15]. The obvious method for verifying the serializability of a set of subgoals is harder than simply solving the problem without subgoals. Second, the knowledge that a set of subgoals is serializable just indicates that there exists an order such that they can be solved monotonically, but provides no ....

....possible to construct some sort of domain theory compiler which identified good and bad orderings, then the benefits would be considerable. In fact, much of the work on abstraction in planning can be viewed as doing exactly this. Perhaps it might be possible to generalize the techniques in ALPINE [15, 16] or the subgoal interaction analysis of STATIC [9] in this direction. A major weakness in our work is its dependence on the STRIPS representation. We plan to use UCPOP [27] to explore whether partial order representations are useful given more expressive domains, such as ADL [26] which include ....

C. Knoblock. Learning Abstraction Hierarchies for Problem Solving. In Proceedings of AAAI-90, pages 923--928, August 1990.

....: return PLAN (P Phi ae) P is the current partial plan and the operator Phi symbolises the insertion of a resolver in the partial plan. Abstraction I X T E T is a hierarchical planner, in the way that its control is based on an Ordered Monotonicity Property similar to the one described in [10]. Ordered Monotonicity Property for I X T E T (OMP) For all possible current plans, each refinement of those plans only creates new flaws belonging to the current or next abstraction levels. This property orders the planner s search space. The flaws appearing in the partial plan will be ....

C.A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings AAAI-90, pages 923--928, 1990.

.... (Friedman Weld 1996) ucparse and ucreduce illustrate two alternative approaches for exploiting hierarchical task network information in the planning process (Barrett Weld 1994b) In the future, we expect to adopt additional speedup learning and optimization techniques, e.g. Minton 1990; Knoblock 1990; Etzioni 1993c; 1993b; Peot Smith 1993; Smith Peot 1993; Kambhampati Chen 1993; Joslin Pollack 1994; Veloso 1994; Ihrig Kambhampati 1994; Schubert Gerevini 1995; Joslin Pollack 1995; Smith Peot 1996) In order to create an expressive interface, the softbot planner must handle a ....

Knoblock, C. 1990. Learning abstraction hierarchies for problem solving. In Proc. 8th Nat. Conf. on A.I., 923--928.

....[Carbonell, 1983; Hall, 1987; Veloso, 1994] These learning algorithms, however, are themselves representation dependent: they easily learn useful information with some problem descriptions, but become helpless with others. For example, the alpine algorithm for learning abstraction hierarchies [Knoblock, 1990] usually fails to generate a hierarchy when the domain contains unnecessary additional operators or the operator descriptions are too general [Knoblock, 1991a; Fink and Yang, 1992] however, if the user selects a suitable domain description, alpine becomes very effective in reducing complexity of ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

....systems are going to reason effectively in complex domains, they too must be able to create automatically appropriate abstractions. This idea was the driving force of several early works (e.g. Sacerdoti, 1974; Plaisted, 1981 ] and has recently received renewed attention (e.g. Ellman, 1992; Knoblock, 1990; Bacchus and Yang, 1992; Ellman, 1993 ] The need for abstraction is rooted in the fact that a declarative representation is designed for a variety of queries and consequently, it is likely to be too detailed for any given query. Essentially, the idea proposed in these works is that instead of ....

....conclusions. Creating an abstract KB can also be viewed as an instance of knowledge compilation [ Selman and Kautz, 1991 ] The key difference in our work is that we compile the KB w.r.t. a given set of queries, and therefore we can determine exactly when the compiled KB is applicable. Knoblock [ Knoblock, 1990 ] also considers automatic generation of abstractions that are suited for a specific query (i.e. planning goal) by removing preconditions of actions. His ALPINE system generates TI abstractions, but provides the planner with a condition that enables it to prune the search needed to refine an ....

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Knoblock, Craig A. 1990. Learning abstraction hierarchies for problem solving. In Proceedings of AAAI-90.

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Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National ConferenceonArtificial Intelligence, pages 923--928, Boston, MA, 1990.

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Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National ConferenceonArtificial Intelligence, pages 923--928, Boston, MA, 1990.

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Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

....across levels since it requires that it is an inherent property of a problem space. While this constraint may be more restrictive than necessary, it provides a very effective heuristic for generating useful abstraction hierarchies. This constraint is captured by the ordered monotonicity property [31]. The ordered monotonicity property requires that every refinement of an abstract plan leaves the literals that comprise the abstract space unchanged. This property has two important features. First, it is computationally tractable to find abstraction hierarchies with this property from only the ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, Boston, MA, 1990, 923--928.

....but it was a human expert who determined the importance of literals. ABSTRIPS planner [Sacerdoti, 1974] was the first attempt to automate the formation of abstraction spaces, but this system needed a human expert to find some outline of a hierarchy, and thus only partially automated the process. Knoblock in 1990 implemented the abstraction learner ALPINE that completely automates the formation of abstraction hierarchies [Knoblock, 1991a] ALPINE produces useful abstraction hierarchies in a number of problem domains. To formalize his method, Knoblock introduced the notion of ordered abstraction ....

....of optimizing plans, but also for abstract problem solving. Several important concepts describing the algorithms 29 3.1. BACKWARD JUSTIFICATION 30 for generating abstraction hierarchies are defined via justified plans. For example, the theoretical concepts underlying Knoblock s planner ALPINE [Knoblock, 1990] are based on the notions of justified plans. Other results that depend on this notion are presented in [Yang and Tenenberg, 1990] Knoblock et al. 1991] and [Bacchus and Yang, 1991] In spite of the importance of the concept of justified plans, relatively few efforts have been made to explore ....

[Article contains additional citation context not shown here]

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

....in the picture, the problem is to find a sequence of operators to move the three disks from the first peg to the third peg. Abstraction in PRODIGY prodigy s abstraction module, alpine, takes an initial problem space specification and automatically generates a hierarchy of abstraction spaces [ Knoblock, 1990, Knoblock, 1991 ] Each abstraction space in the hierarchy is formed by dropping conditions from the original problem space. An abstraction space is defined by a set of abstract operators and states. In the Tower of Hanoi, for example, an abstract problem space can be formed by dropping all of ....

....uses for learned macro operators in the abstrips system. More recent work has explored the use of simplified or in 2 Minor syntactic variations on the problem space specification, required to integrate the two modules, degrade alpine s performance slightly relative to the results reported in [Knoblock, 1990]. complete explanations to address the intractable theory problem in ebl [ Chien, 1989, Tadepalli, 1989, Bhatnagar and Mostow, 1990 ] The most closely related work is by Unruh and Rosenbloom [ 1989 ] who developed an automatic abstraction mechanism in soar. While their method for generating ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....of abstraction spaces is formed by removing successive classes of literals, such that each abstraction space is an approximation of the original problem space. The hierarchy is ordered such that the highest level is the most abstract. The final hierarchy has the ordered monotonicity property [Knoblock, 1990a] which requires that the literals are partitioned in such a way that the achievement of a literal introduced at one level cannot change the truth value of a literal in a more abstract level. The algorithm for producing a hierarchy of abstraction spaces is shown in Table 2. The algorithm forms a ....

....solving reduces the search space in this domain from O(b l ) to O(l) 4.3 Empirical Results This section compares problem solving in the Tower of Hanoi both with and without using the abstractions described in this paper. The abstractions are generated by the alpine abstraction learner [Knoblock, 1990a, Knoblock, 1991] and then used in a hierarchical version of prodigy [Minton et al. 1989, Carbonell et al. 1991] a means ends analysis problem solver. To evaluate the abstractions empirically, prodigy was run both with and without the abstractions using breadth first search, depth first search, ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....changed, what these systems change is the problem solving strategy. The reformulation then solve approach changes the problem statement instead of the problem solving strategy. In our approach, we even try to reformulate the problem (query) to fit the problem solver (query execution unit) ALPINE [Knoblock 90] the abstraction learner of Prodigy, is another example of learning for reformulation to improve performance of problem solving. ALPINE learns to construct the abstraction levels of the problem search space. When given a problem, ALPINE reformulates the problem into subproblems of abstraction ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....the conditions under which hierarchical problem solving will be effective in practice. The experiments were run on the Tower of Hanoi both with and without using the abstraction hierarchy described in the preceding sections. The abstractions were automatically generated by the alpine system [ Knoblock, 1990 ] and then used in a hierarchical version of the prodigy problem solver [ Minton et al. 1989 ] To evaluate empirically the use of hierarchical problem solving in the Tower of Hanoi, prodigy was run both with and without the abstractions using a depthfirst iterative deepening search, a ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....that the preconditions that are determined to be details will be independent. In those cases where the independence assumption fails to hold, abstrips can degrade the performance of the planner. The paper also compares the abstrips approach to generating abstractions to the one used in alpine [ Knoblock, 1990 ] and describes how alpine avoids the problem that arises in abstrips. 1 Introduction One approach to reducing search in planning is to exploit abstractions of a problem space to plan hierarchically. A problem is first solved in an abstract space and then refined at successively more detailed ....

....reconstruction of the algorithm for generating abstractions and an analysis of how and when this approach will work. The third section presents an example problem that illustrates a shortcoming of the abstrips approach. The fourth section compares the approaches used in abstrips and alpine [ Knoblock, 1990, Knoblock, 1991 ] for generating abstractions and shows how alpine avoids the problem that arises in abstrips. The fifth section presents experimental results that compare abstrips abstractions to alpine s in the prodigy problem solver. The sixth section compares the criteria used for ....

[Article contains additional citation context not shown here]

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, Boston, MA, 1990.

....At the third point on the spectrum lie the ordered hierarchies. Recall that these hierarchies impose an order on a partitioned hierarchy such that every refinement of an abstract plan will leave the literals in a more abstract space unchanged. This property is used in the alpine system [ Knoblock, 1990a ] which automatically generates abstraction hierarchies that have this property. Conclusion and Future Directions This paper presents a formalism for studying abstraction in planning. It explores the properties of abstraction hierarchies that are generated by gradually restricting the ....

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

No context found.

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Thomas Dietterich and William Swartout, editors, Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI-90), Menlo Park, California, 1990. AAAI Press.

No context found.

Knoblock, C. A. 1990. Learning abstraction hierarchies for problem solving. In Dietterich, T., and Swartout, W., eds., Proceedings of the Eighth National Conference on Artificial Intelligence (AAAI-90). Menlo Park, California: AAAI Press.

No context found.

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, pages 923--928, 1990.

No context found.

C. A. Knoblock. Learning abstraction hierarchies for problem solving. In Thomas Dietterich and William Swartout, editors, Proceedings of the 8th National Conference on Artificial Intelligence, Menlo Park, California, 1990. AAAI Press.

No context found.

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Proceedings of the Eighth National Conference on Artificial Intelligence, Los Altos, CA, 1990. Morgan Kaufmann.

No context found.

Craig A. Knoblock. Learning abstraction hierarchies for problem solving. In Thomas Dietterich and William Swartout, editors, Proceedings of the Eighth National Conference on Arti cial Intelligence (AAAI-90), Menlo Park, California, 1990. AAAI Press.

No context found.

Knoblock, C.A. Learning Abstraction Hierarchies for Problem Solving, Proc. of the 8th AAAI Conf., Menlo Park, CA, 1990, 923-928. 34

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