Contracting preference relations for database applications

The binary relation framework has been shown to be applicable to many real-life preference handling scenarios. Here we study preference contraction: the problem of discarding selected preferences. We argue that the property of minimality and the preservation of strict partial orders are crucial for contractions. Contractions can be further constrained by specifying which preferences should be protected. We consider two classes of preference relations: finite and finitely representable. We present algorithms for computing minimal and preference-protecting minimal contractions for finite as well as finitely representable preference relations. We study relationships between preference change in the binary relation framework and belief change in the belief revision theory. We also introduce some preference query optimization techniques which can be used in the presence of contraction. We evaluate the proposed algorithms experimentally and present the results.

Database Querying under Changing Preferences

We present here a formal foundation for an iterative and incremental approach to constructing and evaluating preference queries. Our main focus is on query modification: a query transformation approach which works by revising the preference relation in the query. We provide a detailed analysis of the cases where the order-theoretic properties of the preference relation are preserved by the revision. We consider a number of different revision operators: union, prioritized and Pareto composition. We also formulate algebraic laws that enable incremental evaluation of preference queries. Finally, we consider two variations of the basic framework: finite restrictions of preference relations and weak-order extensions of strict partial order preference relations.

Semantic Optimization Techniques for Preference Queries

Preference queries are relational algebra or SQL queries that contain occurrences of the winnow operator ("find the most preferred tuples in a given relation"). Such queries are parameterized by specific preference relations. Semantic optimization techniques make use of integrity constraints holding in the database. In the context of semantic optimization of preference queries, we identify two fundamental properties: containment of preference relations relative to integrity constraints and satisfaction of order axioms relative to integrity constraints. We show numerous applications of those notions to preference query evaluation and optimization. As integrity constraints, we consider constraint-generating dependencies, a class generalizing functional dependencies. We demonstrate that the problems of containment and satisfaction of order axioms can be captured as specific instances of constraint-generating dependency entailment. This makes it possible to formulate necessary and sufficient conditions for the applicability of our techniques as constraint validity problems. We characterize the computational complexity of such problems.

Monotonic and Nonmonotonic Preference Revision

We study here preference revision, considering both the monotonic case where the original preferences are preserved and the nonmonotonic case where the new preferences may override the original ones. We use a relational framework in which preferences are represented using binary relations (not necessarily finite). We identify several classes of revisions that preserve order axioms, for example the axioms of strict partial or weak orders. We consider applications of our results to preference querying in relational databases.