References [Akkermans et al., 1993] 13 independent and task-specific PSMs. A number of authors have discussed task-independent PSM specifications. In particular [van Heijst and A. Anjewerden, 1996] formulate task-independent PSMs in terms of acceptance criteria . For instance, their task-independent formalization of cover & differentiate states that the 'cover' part of the method is applicable to domains where there is a relation X, which is transitive, anti-symmetric and anti-reflexive. However, this formulation does not say anything about the feasibility of applying the method to a domain. In other words it does not provide a replacement problem solving model (or paradigm) for the task-specific model provided by cover & differentiate. As a matter of fact most of the time it won't make much sense to apply the cover sub-method to a relation with the given properties. In contrast with this approach our task-independent PSMs are described as variations of search methods -i.e. they substitute a task-specific problem solving paradigm with a generic one. The approach taken by [van Heijst and A. Anjewerden, 1996] also postulates a clear separation between task-specific and task-independent descriptions of PSMs. A similar, dualistic view is also taken by McDermott [Mc Dermott, 1988] , who compares rolelimiting methods to weak methods and indicates that "a weak method is more open with respect to control than a role-limiting method can be; a weak method does not put any limits on the nature or complexity of the task-specific control knowledge it uses". We believe this characterization of strong vs weak methods is too coarse-grained. For instance a weak method such as A* makes precise assumptions about the existence of heuristic knowledge, which make it possible to converge to an optimal solution. Moreover, as this paper shows, it is possible to reformulate a strong method such as propose & revise as a specialised, but task-independent search mechanism. So, is such a task-independent propose & revise a weak or a strong method? Basically it is a search algorithm -just like hill-climbing and A* -which makes strong assumptions about the availability of domain-specific knowledge to avoid backtracking when an inconsistent state is found. In a nutshell there are no strong and weak methods, there is a continuum in which one can define search strategies which make stronger and stronger assumptions about the availability of task-specific control knowledge. But there is no sharp dividing line. In this paper we have characterised this method specialization process as one which consists of carrying out the appropriate ontology mappings. This approach clearly separates the specification of a task-independent reasoning strategy from the issue of adapting the strategy to alternative classes of tasks. Another example of this approach is given in who investigated the board game method. This method is a refinement of chronological backtracking for one-player board games. Therefore, the board game method is already a task-specific refinement of a generic search strategy. However, it can be further specialized to become applicable to assignment or parametric design tasks (cf. [Eriksson et al., 1995] ). The use of ontologies for characterising tasks and PSMs is not completely new. For example, [ten Teije, 1997] defines a task ontology for diagnostic problems and [Gennari et al., 1994] have proposed to use ontologies as a way to specify the knowledge requirements of a problem solving method. However, the latter define mainly names for knowledge types and neither approach provides a black-box-style specification of the 12 A drawback of this generalized specification is the weakened notion of the competence of the method. We can guarantee optimality only in the sense that a successor state is a local optimum of the environment of a predecessor state (see Ax 4.2´). In the previous sections we have specified a task ontology for parametric design and weaker and stronger versions of a task-independent propose & revise problem solver. It remains to connect both, i.e. to configure propose & revise for parametric design. This step consists of producing the relevant adapter -see Fig. 6 . 4 The main ontological decision is to interpret a state in terms of a design model. Specifically, the definitions in Fig. 6 identify correct states with valid design models, complete states with complete design models, and partial completeness with the set of parameters which are assigned a value by a design model. Order and equality of partial completeness are defined in terms of set inclusion and set equality of parameter sets. The crucial axiom is Ax 6.3, which ensures that the output of the method corresponds to the goal of the task. The proof of this axiom is rather trivial. The main effort in verifying our ontological specification is to ensure the optimality of the output of propose and revise as assumed by Ax 4.2. Methodologies and tools for verifying such axioms are described in [Fensel & Schönegge, 1997] . 5 In this paper we have defined i) an ontology for the parametric design task, which is independent of any domain and PSM; ii) an ontology for propose & revise, which is independent of any domain and task model; and finally iii) an adapter which integrates task and method specifications. The resulting model constitutes a task-specific variant of propose & revise: propose & revise for parametric design. Thus, we have provided descriptions which enable reuse of task specifications as well as reuse of task-4. The infix-notation in is used to distinguish terms from parametric design (infix PD) and terms from propose & revise (infix P&R).
One early approach by REF tackled reusability by incorporating ontologies for domain, task, and PSM-specific knowledge.
Using ontologies for defining tasks, problem-solving methods and their mappings
Lecture Notes in Computer Science
Lecture Notes in Computer Science
Computer Science