System aspmt2smt: Computing ASPMT Theories by SMT Solvers

Abstract. Answer Set Programming Modulo Theories (ASPMT) is an approach to combining answer set programming and satisfiability modulo theories based on the functional stable model semantics. It is shown that the tight fragment of ASPMT programs can be turned into SMT instances, thereby allowing SMT solvers to compute stable models of ASPMT programs. In this paper we present a compiler called ASPSMT2SMT, which implements this translation. The system uses ASP grounder GRINGO and SMT solver Z3. GRINGO partially grounds input programs while leaving some variables to be processed by Z3. We demonstrate that the system can effectively handle real number computations for reasoning about continuous changes.

Introduction to the 28th International Conference on Logic Programming Special Issue

We are proud to introduce this special issue of the Journal of Theory and Practice of Logic Programming (TPLP), dedicated to the full papers accepted for the 28th International Conference on Logic Programming (ICLP). The ICLP meetings started in Marseille in 1982 and since then constitute the main venue for presenting and discussing work in the area of logic programming

First-Order Stable Model Semantics with Intensional Functions

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.Comment: 69 page