Invited Talks

Constraint Answer Set Programming (CASP) integrates the high-level modeling capabilities of Answer Set Programming (ASP) with the efficient numerical computation of Constraint Programming (CP). By partitioning the problem space, CASP leverages the complementary strengths of its underlying solvers: the ASP component facilitates rich relational modeling and non-monotonic reasoning, specifically the handling of defaults and exceptions, while the CP component manages variables over expansive numeric domains via specialized propagators

However, this synthesis introduces significant semantic challenges regarding the interaction between stable model semantics and classical constraint theory. Central to ASP is the ability to differentiate between founded and unfounded atoms, a departure from the classical treatment of variables in SAT where truth is typically a matter of assignment rather than derivation. As CASP systems have evolved, diverse interpretations of foundedness have emerged regarding how these logical requirements should extend to constraints and numeric variables.

This talk examines the semantic foundations of several CASP systems to illustrate these nuances. In particular, we present /flingo/, a CASP system designed to preserve the declarative richness of ASP within constraint satisfaction problems. By supporting default values, undefined variables, non-deterministic assignments, and aggregates directly within numeric constraints, /flingo/ restores the expressive power often lost in traditional CASP translations. We explore how this approach allows for a more natural integration of numeric attributes without sacrificing the foundational principles of ASP.