On relation between constraint answer set programming and satisfiability modulo theories

Abstract

Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. It is often informally related to the field of satisfiability modulo theories. Yet, the exact formal link is obscured as the terminology and concepts used in these two research areas differ. In this paper, we connect these two research areas by uncovering the precise formal relation between them. We believe that this work will booster the cross-fertilization of the theoretical foundations and the existing solving methods in both areas. As a step in this direction we provide a translation from constraint answer set programs with integer linear constraints to satisfiability modulo linear integer arithmetic that paves the way to utilizing modern satisfiability modulo theories solvers for computing answer sets of constraint answer set programs. Under consideration in Theory and Practice of Logic Programming (TPLP).

Aggregate Semantics for Propositional Answer Set Programs

“…Similar to aggregate expressions, monotonicity properties of external atoms affect reasoning about them, and dedicated solving techniques take advantage of so-called assignment-monotonicity (Eiter et al 2018). Extensions of ASP systems by theory propagators (Cuteri et al 2020;Janhunen et al 2017;Lierler and Susman 2017) likewise interpret specific atoms as custom aggregate expressions and incorporate respective procedures for propagating their truth values. In this broad sense, the notion of an aggregate includes any method of evaluating atoms as a compound, where some frequently used aggregation functions, in particular, the SUM aggregation function, are accommodated off-the-shelf in the modeling language of ASP.…”

SMT-based Constraint Answer Set Solver EZSMT+

“…Lierler and Susman generalized these concepts to programs including such commonly used ASP features as choice rules and denials [16]. Lierler and Susman also develop a mapping from a logic program to an SMT logic called smt(il) such that the models of a constructed smt(il) theory are in one-to-one correspondence with answer sets of the program [16]. The developed mappings generalize the ones presented by Niemela [19].…”

“…To process non-tight programs, we utilize the extension of theory originally developed by Niemela [19], where the author characterizes solutions of non-tight "normal" programs in terms of level rankings. Lierler and Susman generalized these concepts to programs including such commonly used ASP features as choice rules and denials [16]. Lierler and Susman also develop a mapping from a logic program to an SMT logic called smt(il) such that the models of a constructed smt(il) theory are in one-to-one correspondence with answer sets of the program [16].…”

“…Originally, systems that process CASP programs rely on combining algorithms/solvers employed in ASP and constraint processing [11,1]. Lee and Meng; Susman and Lierler; Lierler and Susman [14,22,16] proposed an alternative approach that utilizes satisfiability modulo theory (SMT) solvers [4] in design of CASP systems.…”

A Logic-Based Framework Leveraging Neural Networks for Studying the Evolution of Neurological Disorders

“…Some works have been carried out to integrate data-driven solutions into declarative systems with the aim of increasing performance; for instance, such solutions are used for inductively choosing configurations, algorithms selection, and proper coupling of subsystems Maratea et al 2014;Fuscà et al 2017). In some proposals, see for instance SMT (Cok et al 2015;Mellarkod et al 2016; Barrett and Tinelli 2018;Barrett et al 2013) or CASP (Baselice et al 2005;Mellarkod et al 2008;Balduccini and Lierler 2017;Lierler and Susman 2017;Shen and Lierler 2018;Arias et al 2018), the logic solver can select statements that should be checked by external theory/numerical solvers, so that the next steps carried out by the logic solver depend on the answers produced by the external ones. Some works mix statistical analysis and ASP (Gelfond 2010;Nickles and Mileo 2014;Beck et al 2015): here, the aim is to extend logic programs with probabilistic reasoning, either by a direct integration or by embedding external predicates.…”