This paper provides a historical summary of the motivations which have led several research communities to contemplate qualitative techniques. Qualitative reasoning satisfies various problem solving needs in high level decision tasks, embodied in a set of tools which allow deep knowledge to be put in compatible form with software requirements while still remaining realistic. An overview of these mathematical formalisms is presented; qualitative simulation is introduced as one of the most significant outcomes. Finally, some current research issues concerning temporal aspects of qualitative reasoning are discussed.

Some weaknesses of current decision support technologies are discussed. Numerical methods have strong theoretical foundations but are representationally weak, and only deal with a small part of the decision process. Knowledge-based systems offer greater flexibility, but have not been accompanied by a clear decision theory. Theoretical development of symbolic decision procedures is advocated, an approach to the design of decision support systems based on first-order logic is presented, and work on this approach is reviewed. A central proposal is an extended form of inference called argumentation; reasoning qualitatively for and against decision options from generalized domain theories. Argumentation captures a natural and familiar form of reasoning, and contributes to the robustness, flexibility and intelligibility of problem solving, while having a clear theoretical basis. Argumentation was developed initially for medical applications though it may have much wider applicability.

In recent years there has been a growing interest among AI researchers in probabilistic and decision modelling, spurred by significant advances in representation and computation with network modelling formalisms. In applying these techniques to decision support tasks, fixed network models have proven to be inadequately expressive when a broad range of situations must be handled. Hence many researchers have sought to combine the strengths of flexible knowledge representation languages with the normative status and well-understood computational properties of decision-modelling formalisms and algorithms. One approach is to encode general knowledge in an expressive language, then dynamically construct a decision model for each particular situation or problem instance. We have developed several systems adopting this approach, which illustrate a variety of interesting techniques and design issues.

The representation of physical systems using qualitative formalisms is examined in this review, with an emphasis on recent developments in the area. The push to develop reasoning systems incorporating deep knowledge originally focused on naive physical representations, but has now shifted to more formal ones based on qualitative mathematics. The qualitative differential constraint formalism used in systems like QSIM is examined, and current efforts to link this to competing representations like Qualitative Process Theory are noted. Inference and representation are intertwined, and the decision to represent notions like causality explicitly, or infer it from other properties, has shifted as the field has developed. The evolution of causal and functional representations is thus examined. Finally, a growing body of work that allows reasoning systems to utilize multiple representations of a system is identified. Dimensions along which multiple model hierarchies could be constructed are examined, including mode of behaviour, granularity, ontology, and representational depth.