Conditional Constraint Satisfaction: Logical Foundations and Complexity

Georg Gottlob, Gianluigi Greco, Toni Mancini

Conditional Constraint Satisfaction Problems (CCSPs) are generalizations of classical CSPs that support conditional activation of variables and constraints. Despite the interest emerged for CCSPs in the context of modelling the intrinsic dynamism of diagnosis, structural design, and product configuration applications, a complete characterization of their computational properties and of their expressiveness is still missing. In fact, the aim of the paper is precisely to face these open research issues. First, CCSPs are formally characterized in terms of a suitable fragment of first-order logic. Second, the complexity of some basic reasoning tasks for CCSPs is studied, by establishing completeness results for the first and the second level of the polynomial hierarchy. Finally, motivated by the hardness results, an island of tractability for CCSPs is identified, by extending structural decomposition methods originally proposed for CSPs.