Dealing with incomplete knowledge on CLP(FD) variable domains

Constraint Logic Programming languages on Finite Domains, CLP(FD), provide a declarative framework for Artificial Intelligence problems. However, in many real life cases, domains are not known and must be acquired or computed. In systems that interact with the outer world, domain elements synthesise information on the environment, they are not all known at the beginning of the computation, and must be retrieved through an expensive acquisition process. In this paper, we extend the CLP(FD) language by combining it with a new sort (called Incrementally specified Sets, ISet). In the resulting language, CLP(FD + ISet), FD variables can be defined on partially or fully unknown domains (ISet). Domains can be linked each other through relations, and constraints can be imposed on them. We describe a propagation algorithm (called Known Arc Consistency, KAC) based on known domain elements, and theoretically compare it with arc-consistency. The language can be implemented on top of different CLP systems, thus letting the user exploit different possible semantics for domains (e.g., lists, sets or streams). We state the specifications that the employed system should provide, and we show that two different CLP systems (Conjunto and {log}) can be effectively used. We provide motivating examples and describe promising applications.