Researchers in answer set programming and constraint programming have spent significant efforts in the development of hybrid languages and solving algorithms combining the strengths of these traditionally separate fields. These efforts resulted in a new research area: constraint answer set programming. Constraint answer set programming languages and systems proved to be successful at providing declarative, yet efficient solutions to problems involving hybrid reasoning tasks. One of the main contributions of this paper is the first comprehensive account of the constraint answer set language and solver ezcsp, a mainstream representative of this research area that has been used in various successful applications. We also develop an extension of the transition systems proposed by Nieuwenhuis et al. in 2006 to capture Boolean satisfiability solvers. We use this extension to describe the ezcsp algorithm and prove formal claims about it. The design and algorithmic details behind ezcsp clearly demonstrate that the development of the hybrid systems of this kind is challenging. Many questions arise when one faces various design choices in an attempt to maximize system's benefits. One of the key decisions that a developer of a hybrid solver makes is settling on a particular integration schema within its implementation. Thus, another important contribution of this paper is a thorough case study based on ezcsp, focused on the various integration schemas that it provides.

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 boost 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.

Dealing with domains involving substantial quantitative information in Answer Set Programming (ASP) often results in cumbersome and inefficient encodings. Hybrid “CASP” languages combining ASP and Constraint Programming aim to overcome this limitation, but also impose inconvenient constraints – first and foremost that quantitative information must be encoded by means of total functions. This goes against central knowledge representation principles that contribute to the power of ASP, and makes the formalization of certain domains difficult. ASP{f} is being developed with the ultimate goal of providing scientists and practitioners with an alternative to CASP languages that allows for the efficient representation of qualitative and quantitative information in ASP without restricting one's ability to deal with incompleteness or uncertainty. In this paper we present the latest outcome of such research: versions of the language and of the supporting system that allow for practical, industrial-size use and scalability. The applicability of ASP{f} is demonstrated by a case study on an actual industrial application.