Reprinted from Working Notes of the AAAI Spring Symposium on Decision-Theoretic Planning, March, 1994, Steve Hanks, Stuart Russell, and Michael Wellman, editors. Representing Preferences as Ceteris Paribus Comparatives Jon Doyle Laboratory for Computer Science Massachusetts Institute of Technology 545 Technology Square Cambridge, MA 02139 doyle@lcs.mit.edu Michael P. Wellman Artificial Intelligence Laboratory University of Michigan 1101 Beal Avenue Ann Arbor, MI 48109-2110 wellman@engin.umich.edu Abstract Decision-theoretic preferences specify the rela- tive desirability of all possible outcomes of al- ternative plans. In order to express general patterns of preference holding in a domain, we require a language that can refer directly to preferences over classes of outcomes as well as individuals. We present the basic concepts of a theory of meaning for such generic compar- atives to facilitate their incremental capture and exploitation in automated reasoning sys- tems. Our semantics lifts comparisons of indi- viduals to comparisons of classes “other things being equal” by means of contextual equiva- lences, equivalence relations among individuals that vary with the context of application. We discuss implications of the theory for represent- ing preference information. 1 Introduction Decision-theoretic treatments of preferences represent the objectives of a decision maker by an ordering over the possible outcomes of available plans. In taking a decision-theoretic approach to planning, we view this ordering relation as an ideal, but cannot hope to com- pletely and directly encode it in the planning system, as the domain of outcomes is combinatorially large or infinite, and the relevant preference criteria vary across problem instances. Therefore, in designing preference languages for decision-theoretic planning, we seek con- structs for describing general patterns of preference that hold over classes of outcomes and situations. The re- sult is a logic of preference affording flexible specification of objectives for planning, underpinned by a decision- theoretic semantics. 1.1 Preferences as comparatives The theory presented here grows out of an effort to un- derstand the relations between decision-theoretic pref- erences and problem-solving goals (Wellman and Doyle, 1991; Doyle et al., 1991; Wellman and Doyle, 1992). In this work, we have found that the underlying notion of preference as a specification of relative desire sup- ports the general statements about preferences we wish to express as well as our effort to relate the preference logic to decision theory. As our formal framework de- veloped, however, we realized that the techniques useful for conveying preference information have no special ties to preference relations, so our treatment here presents the theory in somewhat greater generality. Neverthe- less, specification of preferences and goals remain prime applications of our general approach to comparatives, and we use notation drawn from the domain of prefer- ences to discuss abstract comparative relations among individuals. 1.2 Specifying comparatives and superlatives Finding ways of formalizing knowledge that make spec- ifications convenient for human informants and efficient for automated reasoning constitutes a central issue in knowledge representation. Human convenience usually means that the formalizations should stay close to com- mon means of human expression. Formalizations that offer human conveniences sometimes also make for ef- ficient reasoning, in that human communication places great value on compact specifications that directly entail the most important conclusions. Comparatives and superlatives offer excellent exam- ples of the tendency of humans to exploit succinct ex- pressions of knowledge. Knowledge in many fields in- volves knowledge of comparative relationships, such as relative probability and desirability, relative height and weight, comparative attractiveness and dangerousness. Comparisons of individuals (Abby is taller than Bob, Carl is more handsome than Dan, Ella’s graduating is likelier than Fred’s, Guy’s the best baritone) along these dimensions pose only routine problems; formalizers typi- cally assume linear scales with which to measure degrees to which individuals exhibit these properties. These di- mensional orderings induce preorderings (reflexive and transitive relations) on the appropriate sets of individu- als, so that one assesses comparative statements applied to individuals by checking the agreement of the state- ments with the appropriate preorder, and assesses su- perlative statements applied to individuals by checking that the individuals hold maximal rank in the appropri- ate preorder. But few people restrict their use of comparatives and superlatives to statements about individuals, as use of these constructs in reference to classes of individuals