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The Nature of Problem Solving

In Newell's approach the knowledge level rationalises behaviour in terms of the reasons that an agent has to believe that certain actions will lead to achieving certain goals. In this sense knowledge is a means to an end, a resource for behaviour [28]. The goal of problem solving is to select one of the possible actions. More recently a different view is being explored, namely the view of problem solving as modelling. The idea is that problem solving is the construction of a situation specific model [12] or case model [47][35].

From a knowledge level perspective the agent's perception of the world is through knowledge alone. A goal therefore must correspond to a desired state of ones knowledge about the world. Consequently this knowledge must refer to the specific systems that the goal is about. This model - let us call it the case model - at every moment during problem solving summarises the agent's understanding of the problem, and allows it to eventually conclude that the goal has been reached.

The actions are the means that the agent has for interacting with the world [28]. Again, since at the knowledge level the agent's perception is through knowledge an action must be viewed as a way of obtaining knowledge about the reality. Actions of perception naturally fit in this scheme but also genuine acts of interaction do [41]. For example when a spray-painting robot paints some part then it will probably assume that the part has paint on it afterwards. In the problem solving as modelling view, then, the actions are not the goal of problem solving but are themselves a means to an end. That end is the construction of a model of part of the world that allows the agent to conclude eventually that its goals have been achieved.

The view of problem solving as modelling can be linked to the Knowledge Level approach outlined so far. Modelling a system in the world is to make assumptions about that world (Sect. ). For example assuming a causal model of a car's functioning implies an assumption that this causal view leads to a sufficient approximation of what the car's functioning is all about. Thus, making a domain model is not just packaging statements about the domain, but it entails augmenting these statements with a series of assumptions about how the information about the systems is connected. To decide to model a system in a certain way means to assume that these assumptions hold as well as all the conclusions that follow from them.

Similarly a task model embodies assumptions about the meaning of goals. For example, if one models a diagnostic task as a process of generate and test over components of a system, then one implicitly assumes that the fault one is looking for can be localised in a component, and for instance not in the external working conditions of the system or in the connections between the components. Thus, modelling a task corresponding to a goal is to make more precise what one assumes that goal to mean.

The role of the problem solving method is to tie domain and task models together in an argument on what accomplishing the task means in terms of the available models. I have called this the competence theory of the method [39]. For example, a heuristic classification problem solver assumes that the solution to its problem is within the differential. This is no more than an assumption, but it is what the problem solver believes that it can say about the problem. It defines its competence. In addition the competence theory also allows one to make more precise what rationality means. For example, a heuristic classification problem solver will use its knowledge and actions to reduce the size of the differential. I called this a (method specific) specialized principle of rationality. It contains the basis for all "why" questions about the system's behavior: actions are taken to get the model into the state dictated by the principle of rationality. This model is the case model and it is obtained from the partial instantiation of the competence theory through actions. Specific control regimes (e.g., data-driven or hypothesis-driven heuristic classification) correspond to different ways of operationalising the specialized principle of rationality [42]

The configuration of models, tasks and methods entails a set of assumptions that together can be interpreted as a model of the problem. The goal of problem solving is to instantiate this model by grounding it in reality by making derivations from the case-specific knowledge obtained by the agent's actions and the assumptions embodied in the domain and task models. The form of the case model is determined by the selection of problem solving method.

In this view problem solving is no longer an input-output process (as in KADS-I [46]), neither a means to select actions (as in Newell's knowledge level theory [28]), nor is it a model transformation process (as in Components of Expertise [35]). Rather it is a process of organising knowledge (obtained through actions) by making assumptions (i.e., constructing a model) that allow one to conclude (in effect, only assume) that the task is accomplished. Successful problem solving is a matter of making the right assumptions and exploring their consequences. Problem solving is thus viewed as the `creation' of a suitable case model and the interaction with the world is only a resource for this, almost a side-effect in the process of maintaining an internal organisation and identity [42]. We are now in a peculiar position by claiming that knowledge is a resource for action and action is a resource for knowledge. This circular view on knowledge and behavior is reminiscent of Maturana's view of autonomous systems [25]. We use it here as a view from the observer's perspective without making claims, as Maturana does, about implications for a biological theory of cognition. However, I will argue that it does have some implications for the design of future generation AI architectures.

walter@arti