Logic Programming with Preferences and Constraints

This paper discusses a logic programming (LP) paradigm and accompanying semantic foundations for specifying constraints and preferences. While the use of constraints in LP languages is well-known, we show that preferences are also natural and are useful in logical speciication of optimization and relaxation problems which arise in many applications involving constraints, e.g., engineering design, scheduling, decision support, etc. In optimization, we are interested in nding the optimal (i.e., best) solutions to a set of constraints with respect to an objective function. In many applications, optimal solutions may be diicult or impossible to obtain, and hence we are interested in nding suboptimal solutions, by either relaxing the constraints or relaxing the objective function. The contribution of this paper lies in providing a framework for performing optimization and relaxation in a logically principled manner. Essentially, in this framework we can: (a) designate certain predicates as optimization predicates, and state the criteria for determining their optimal solutions; and (b) designate which optimization predicates are to be relaxed and state the criteria for relaxation. These criteria are understood using the concept of preference and hence we call this framework preference logic programming (PLP). The model-theoretic semantics of this paradigm is based on simple concepts from modal logic: Essentially, each world in the possible-worlds semantics for a preference logic program is a model for the constraints of the program, and an ordering over these worlds is determined by the objective function. Optimization can then be expressed as truth in strongly optimal worlds, while relaxation becomes truth in suitably-deened suboptimal worlds. We also present an operational semantics for optimization and relaxation using the concept of Pruned-Tree SLD derivation, as well as correctness results. Our conclusion is that the concept of preference provides a unifying framework for formulating optimization as well as relaxation problems.