Foundations of Similarity and Utility

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In this paper we discuss a rigorous foundation of similarity reasoning based on the concept of utility. If utility is formulated in mathematical terms it can serve as a formal specification for a similarity system. However, utility can also be formulated in informal ways. We consider subjective versions, competing ones and those that change dynamically over time. These are illustrated by examples from risk analysis, speech recognition, and urban planning. From the examples we derive a number of challenges.