The implication problem for measure-based constraints

We study the implication problem of measure-based constraints. These constraints are formulated in a framework for measures generalizing that for mathematical measures. Measures arise naturally in a wide variety of domains. We show that measure constraints, for particular measures, correspond to constraints that occur in relational databases, data mining applications, cooperative game theory, and in the Dempster–Shafer and possibility theories of reasoning about uncertainty. We prove that the implication problem for measure constraints is in general decidable. We introduce inference systems for particular classes of measure constraints and show that some of these are complete, yielding tractability for the corresponding implication problem. r 2007 Elsevier B.V. All rights reserved.