First-Order Stable Model Semantics with Intensional Functions
This work addresses the limitation of handling nonBoolean fluents in answer set programming, offering a foundational extension that integrates ASP with SMT techniques for broader applications in domains like real-number reasoning.
The paper extends the first-order stable model semantics to include intensional functions, enabling functions to be defined by logic programs similarly to predicates, and uses this extension to define Answer Set Programming Modulo Theories (ASPMT) for effective first-order reasoning with real numbers and reduced grounding issues.
In classical logic, nonBoolean fluents, such as the location of an object, can be naturally described by functions. However, this is not the case in answer set programs, where the values of functions are pre-defined, and nonmonotonicity of the semantics is related to minimizing the extents of predicates but has nothing to do with functions. We extend the first-order stable model semantics by Ferraris, Lee, and Lifschitz to allow intensional functions -- functions that are specified by a logic program just like predicates are specified. We show that many known properties of the stable model semantics are naturally extended to this formalism and compare it with other related approaches to incorporating intensional functions. Furthermore, we use this extension as a basis for defining Answer Set Programming Modulo Theories (ASPMT), analogous to the way that Satisfiability Modulo Theories (SMT) is defined, allowing for SMT-like effective first-order reasoning in the context of ASP. Using SMT solving techniques involving functions, ASPMT can be applied to domains containing real numbers and alleviates the grounding problem. We show that other approaches to integrating ASP and CSP/SMT can be related to special cases of ASPMT in which functions are limited to non-intensional ones.