Utility Functions for Ceteris Paribus Preferences

Computational Intelligence (Impact Factor: 0.67). 04/2004; 20(2):158 - 217. DOI: 10.1111/j.0824-7935.2004.00235.x
Source: DBLP


Ceteris paribus (all-else equal) preference statements concisely represent preferences over outcomes or goals in a way natural to human thinking. Although deduction in a logic of such statements can compare the desirability of specific conditions or goals, many decision-making methods require numerical measures of degrees of desirability. To permit ceteris paribus specifications of preferences while providing quantitative comparisons, we present an algorithm that compiles a set of qualitative ceteris paribus preferences into an ordinal utility function. Our algorithm is complete for a finite universe of binary features. Constructing the utility function can, in the worst case, take time exponential in the number of features, but common independence conditions reduce the computational burden. We present heuristics using utility independence and constraint-based search to obtain efficient utility functions.

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Available from: Jon Doyle,
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    • "Observe that specifying a utility function U as in (2) can be expensive due to the fact that |X | = O(2 n ). Hence, previous works on OUR searched for special conditions under which U can be represented compactly (e.g., see [1] [3] [5] [11] [17] [18]). The general scheme followed by these works (which we refer to as independence-based methodology) is as follows. "
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    ABSTRACT: Tackling the problem of ordinal preference revelation and reasoning, we propose a novel methodology for generating an ordinal utility function from a set of qualitative preference statements. To the best of our knowledge, our proposal constitutes the first nonparametric solution for this problem that is both efficient and semantically sound. Our initial experiments provide strong evidence for practical effectiveness of our approach.
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    • "A weak order satisfies p ≥ q T if and only if α β holds for all outcomes α and β such that α extends p, and β extends q, and α and β agree on T : α(T ) = β(T ). As shown in [16], such statements can be used to represent CP-nets [2] [3], TCP-nets [6] [7], feature vector rules [12] and cp-theories [15] [17]. It can also represent a preference of one outcome, α, over another, β: as a statement α ≥ β ∅, which we abbreviate to just α ≥ β; this can be useful, for instance, for application to recommender systems [14] "
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    ABSTRACT: A basic task in preference reasoning is inferring a pref-erence between a pair of outcomes (alternatives) from an input set of preference statements. This preference inference task for compara-tive preferences has been shown to be computationally very hard for the standard kind of inference. Recently, a new kind of preference inference has been developed, which is polynomial for relatively ex-pressive preference languages, and has the additional property of be-ing much less conservative; this can be a major advantage, since it will tend to make the number of undominated outcomes smaller. It derives from a semantics where models are weak orders that are gen-erated by objects called cp-trees, which represent a kind of condi-tional lexicographic order. We show that there are simple conditions, based on the notion of importance, that determine whether a weak order can be generated by a cp-tree of the given form. This enables a simple characterisation of the less conservative preference inference. We go on to study the importance properties satisfied by a simple kind of cp-tree, leading to another characterisation of the correspond-ing preference inference.
    Frontiers in Artificial Intelligence and Applications 01/2012; 242. DOI:10.3233/978-1-61499-098-7-852
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    • "Generic approaches to preference handling can be found in the area of artificial intelligence (Boutilier, Brafman, Domshlak, Hoos, & Poole, 2004; Doyle, 2004; McGeachie & Doyle, 2004; Domshlak & Joachims, 2007). Reasoning frameworks infer additional knowledge from basic preference statements within a well-defined logic. "
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    ABSTRACT: Whereas today's information systems are well-equipped for efficient query handling, their strict mathematical foundations hamper their use for everyday tasks. In daily life, people expect information to be offered in a personalized and focused way. But currently, personalization in digital systems still only takes explicit knowledge into account and does not yet process conceptual information often naturally implied by users. We discuss how to bridge the gap between users and today's systems, building on results from cognitive psychology.
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