New Directions in Preference Research

I will survey several recently proposed applications and extensions of a logical approach to preference specification and querying. In that approach, preferences are defined as binary relations that are finitely representable using first-order formulas. Preference querying is done using the winnow operator that picks the "best" tuples in a given relation. First, I will discuss the operation of discarding preferences: preference contraction. Minimality and preservation of strict partial orders (SPOs) seem to be crucial in this context. I will show how to construct minimal SPO-preserving contractions, both for finite and finitely-representable preference relations. Second, I will describe a logical framework for set preferences. Candidate sets are represented using profiles consisting of scalar features. This reduces set preferences to tuple preferences over set profiles. I will also discuss a heuristic algorithm for the computation of the ``best'' sets. This is joint work with my Ph.D. students: Denis Mindolin and Xi Zhang.