An ASP Semantics for Default Reasoning with Constraints

We introduce the logic of Here-and-There with Constraints in order to capture constraint theories in the non-monotonic setting known from Answer Set Programming (ASP). This allows for assigning default values to constraint variables or to leave them undefined. Also, it provides us with a semantic framework integrating ASP and Constraint Processing in a uniform way. We put some emphasis on logic programs dealing with linear constraints on integer variables, where we further introduce a directional assignment operator. We elaborate upon the formal relation and implementation of these programs in terms of Constraint ASP, sketching an existing system.