Valuation-based systems: a framework for managing uncertainty in expert systems
Fuzzy logic for the management of uncertainty
Fundamenta Informaticae - Special issue: logics for artificial intelligence
Handbook of logic in artificial intelligence and logic programming (vol. 3)
Semiring-based constraint satisfaction and optimization
Journal of the ACM (JACM)
Bucket elimination: a unifying framework for reasoning
Artificial Intelligence
Semiring-based constraint logic programming: syntax and semantics
ACM Transactions on Programming Languages and Systems (TOPLAS)
Soft constraint propagation and solving in CHRs
Proceedings of the 2002 ACM symposium on Applied computing
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Nonserial Dynamic Programming
Mini-buckets: A general scheme for bounded inference
Journal of the ACM (JACM)
Soft Concurrent Constraint Programming
ESOP '02 Proceedings of the 11th European Symposium on Programming Languages and Systems
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Semirings for Soft Constraint Solving and Programming (LECTURE NOTES IN COMPUTER SCIENCE)
Extending CP-nets with stronger conditional preference statements
AAAI'04 Proceedings of the 19th national conference on Artifical intelligence
Journal of Artificial Intelligence Research
Valued constraint satisfaction problems: hard and easy problems
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Decision diagrams for the computation of semiring valuations
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Reasoning with conditional ceteris paribus preference statements
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Extending uncertainty formalisms to linear constraints and other complex formalisms
International Journal of Approximate Reasoning
Ordering based decision making - A survey
Information Fusion
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Representing and reasoning with an agent's preferences is important in many applications of constraints formalisms. Such preferences are often only partially ordered. One class of soft constraints formalisms, semiring-based CSPs, allows a partially ordered set of preference degrees, but this set must form a distributive lattice; whilst this is convenient computationally, it considerably restricts the representational power. This paper constructs a logic of soft constraints where it is only assumed that the set of preference degrees is a partially ordered set, with a maximum element 1 and a minimum element 0. When the partially ordered set is a distributive lattice, this reduces to the idempotent semiring-based CSP approach, and the lattice operations can be used to define a sound and complete proof theory. A generalised possibilistic logic, based on partially ordered values of possibility, is also constructed, and shown to be formally very strongly related to the logic of soft constraints. It is shown how the machinery that exists for the distributive lattice case can be used to perform sound and complete deduction, using a compact embedding of the partially ordered set in a distributive lattice.