Michael P. Wellman

From knowledge bases to decision models

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.

Modular utility representation for decision-theoretic planning

Specification of objectives constitutes a central issue in knowledge representation for planning. Decision-theoretic approaches require that representations of objectives possess a firm semantics in terms of utility functions, yet provide the flexible compositionality needed for practical preference modeling for planning systems. Modularity, or separability in specification, is the key representational feature enabling this flexibility. In the context of utility specification, modularity corresponds exactly to well-known independence concepts from multiattribute utility theory, and leads directly to approaches for composing separate preference specifications. Ultimately, we seek to use this utility-theoretic account to justify and improve existing mechanisms for specification of preference information, and to develop new representations exhibiting tractable specification and flexible composition of preference criteria.

A logic of relative desire

Although many have proposed formal characterizations of belief structures as bases for rational action, the problem of characterizing rational desires has attracted little attention. AI relies heavily on goal conditions interpreted (apparently) as absolute expressions of desirability, but these cannot express varying degrees of goal satisfaction or preferences among alternative goals. Our previous work provided a relative interpretation of goals as qualitative statements about preferability, all else equal. We extend that treatment to the comparison of arbitrary propositions, and develop a propositional logic of relative desire suitable for formalizing properties of planning and problem-solving methods.

WHITHER QUALITATIVE REASONING?: A RESPONSE TO SACKS AND DOYLE

Ideally, all reasoning would be qualitative. That is, reasoners would refer to exactly those qualities that concern them, making all relevant distinctions and ignoring the rest. Of course, in any knowledge representation effort we strive to design languages expressing the useful distinctions. But when the subject of reasoning involves quantities, there is a great temptation to apply more precision than is needed or wanted for any given task. In particular, numeric precision typically renders the reasoning problem vivid, and thus amenable to a large body of analytic techniques. Indeed, most automated analysis methods developed by engineers require full numeric precision in the specification of mathematical models. A1 researchers in qualitative reasoning are right to resist the temptation of precision. While numeric models may facilitate efficient analysis and produce stronger conclusions, unmotivated distinctions impose an excess burden of specification and degrade the generality of results. Designers of systems that reason about quantities must face this central trade-off and may resolve it in different ways, depending on their objectives. Mathematicians, who are inclined to place a great premium on generality, have-as Sacks and Doyle point out-devoted significant effort to the exploration of qualitative properties of relations among quantities. Engineers, who tend to require strong results and straightforward algorithmic solutions, have typically taken the numeric route. But economy of specification and generality of results are nonetheless significant objectives in engineering problem solving, and to whatever extent we can further these goals without excessively compromising computational tractability and power, we should do so. Therein lies the potential contribution of qualitative reasoning. But we should not deny that there is a compromise involved, at least regarding strength of conclusions.’ There is no avoiding the fact that weaker constraints on a mathematical model lead to weaker entailments. In fact, the limitations are often quite clear. For instance, the incompleteness in qualitative analyses of what Sacks and Doyle call “type 2 SPQR equations” was first noted by Kuipers (1985). Possessing a clear characterization of the limits of a given technique helps us understand where it fits in a comprehensive problemsolving architecture. For example, in decision-theoretic reasoning, qualitative ambiguity is the hallmark of a “trade-off situation” (Wellman 19901, and signals the need for complementary analysis techniques. An important virtue of qualitative representations is that their boundaries often correspond to intuitive problem classes, and thus their scope may often be succinctly characterized. Too often, however, the tendency in research is to deemphasize limitations in favor of more positive capabilities of a proposed new idea. Sacks and Doyle have thus provided

Rational Self-Government and Universal Default Logics

ABSTRACT Many partial and conflicting theories of nonlogical assumptions and default reasoning have been proposed. The theory of rational self-government suggests that there is no universal logic which subsumes these. We first show how default reasoning may be viewed as rational selection of assumptions according to preferences embodied in the different partial theories. We then adapt Arrows social choice theorem to prove that every universal theory of default reasoning will violate at least one reasonable principle of rational reasoning.