We introduce a new flexible paradigm of grounding and solving in Answer Set Programming (ASP), which we refer to as multi-shot ASP solving, and present its implementation in the ASP system clingo. Multi-shot ASP solving features grounding and solving processes that deal with continuously changing logic programs. In doing so, they remain operative and accommodate changes in a seamless way. For instance, such processes allow for advanced forms of search, as in optimization or theory solving, or interaction with an environment, as in robotics or query-answering. Common to them is that the problem specification evolves during the reasoning process, either because data or constraints are added, deleted, or replaced. This evolutionary aspect adds another dimension to ASP since it brings about state changing operations. We address this issue by providing an operational semantics that characterizes grounding and solving processes in multi-shot ASP solving. This characterization provides a semantic account of grounder and solver states along with the operations manipulating them. The operative nature of multi-shot solving avoids redundancies in relaunching grounder and solver programs and benefits from the solver's learning capacities. clingo accomplishes this by complementing ASP's declarative input language with control capacities. On the declarative side, a new directive allows for structuring logic programs into named and parameterizable subprograms. The grounding and integration of these subprograms into the solving process is completely modular and fully controllable from the procedural side. To this end, clingo offers a new application programming interface that is conveniently accessible via scripting languages.

The Potsdam answer set solving collection, or Potassco for short, bundles various tools implementing and/or applying answer set programming. The article at hand succeeds an earlier description of the Potassco project published in Gebser et al. (AI Commun 24(2):107–124, 2011). Hence, we concentrate in what follows on the major features of the most recent, fifth generation of the ASP system clingo and highlight some recent resulting application systems.

Answer Set Programming (ASP) is an approach to declarative problem solving, combining a rich yet simple modeling language with high performance solving capacities. We here develop an ASP-based approach to curriculum-based course timetabling (CB-CTT), one of the most widely studied course timetabling problems. The resulting teaspoon system reads a CB-CTT instance of a standard input format and converts it into a set of ASP facts. In turn, these facts are combined with a first-order encoding for CB-CTT solving, which can subsequently be solved by any off-the-shelf ASP systems. We establish the competitiveness of our approach by empirically contrasting it to the best known bounds obtained so far via dedicated implementations. Furthermore, we extend the teaspoon system to multi-objective course timetabling and consider minimal perturbation problems .

We present the third generation of the constraint answer set system clingcon, combining Answer Set Programming (ASP) with finite domain constraint processing (CP). While its predecessors rely on a black-box approach to hybrid solving by integrating the CP solver gecode, the new clingcon system pursues a lazy approach using dedicated constraint propagators to extend propagation in the underlying ASP solver clasp. No extension is needed for parsing and grounding clingcon's hybrid modeling language since both can be accommodated by the new generic theory handling capabilities of the ASP grounder gringo. As a whole, clingcon 3 is thus an extension of the ASP system clingo 5, which itself relies on the grounder gringo and the solver clasp. The new approach of clingcon offers a seamless integration of CP propagation into ASP solving that benefits from the whole spectrum of clasp's reasoning modes, including for instance multi-shot solving and advanced optimization techniques. This is accomplished by a lazy approach that unfolds the representation of constraints and adds it to that of the logic program only when needed. Although the unfolding is usually dictated by the constraint propagators during solving, it can already be partially (or even totally) done during preprocessing. Moreover, clingcon's constraint preprocessing and propagation incorporate several well established CP techniques that greatly improve its performance. We demonstrate this via an extensive empirical evaluation contrasting, first, the various techniques in the context of CSP solving and, second, the new clingcon system with other hybrid ASP systems. Under consideration in Theory and Practice of Logic Programming (TPLP)

Conflict learning plays a key role in modern Boolean constraint solving. Advanced in satisfiability testing, it has meanwhile become a base technology in many neighboring fields, among them answer set programming (ASP). However, learned constraints are only valid for a currently solved problem instance and do not carry over to similar instances. We address this issue in ASP and introduce a framework featuring an integrated feedback loop that allows for reusing conflict constraints. The idea is to extract (propositional) conflict constraints, generalize and validate them, and reuse them as integrity constraints. Although we explore our approach in the context of dynamic applications based on transition systems, it is driven by the ultimate objective of overcoming the issue that learned knowledge is bound to specific problem instances. We implemented this workflow in two systems, namely, a variant of the ASP solver clasp that extracts integrity constraints along with a downstream system for generalizing and validating them.

Answer Set Programming (ASP) is a model, ground, and solve paradigm. The integration of application- or theory-specific reasoning into ASP systems thus impacts on many if not all elements of its workflow, viz. input language, grounding, intermediate language, solving, and output format. We address this challenge with the fifth generation of the ASP system clingo and its grounding and solving components by equipping them with well-defined generic interfaces facilitating the manifold integration efforts. On the grounder's side, we introduce a generic way of specifying language extensions and propose an intermediate format accommodating their ground representation. At the solver end, this is accompanied by high-level interfaces easing the integration of theory propagators dealing with these extensions.

Answer Set Programming (ASP) has recently been employed to specify and run dynamic programming (DP) algorithms on tree decompositions, a central approach in the field of parameterized complexity, which aims at solving hard problems efficiently for instances of certain structure. This ASP-based method followed the standard DP approach where tables are computed in a bottom-up fashion, yielding good results for several counting or enumeration problems. However, for optimization problems this approach lacks the possibility to report solutions before the optimum is found, and for search problems it often computes a lot of unnecessary rows. In this paper, we present a novel ASP-based system allowing for "lazy" DP, which utilizes recent multi-shot ASP technology. Preliminary experimental results show that this approach not only yields better performance for search problems, but also outperforms some state-of-the-art ASP encodings for optimization problems in terms of anytime computation, i.e., measuring the quality of the best solution after a certain timeout.

Answer set programming is a declarative problem‐solving paradigm that rests upon a work flow involving modeling, grounding, and solving. While the former is described by Gebser and Schaub (2016), we focus here on key issues in grounding, or how to systematically replace object variables by ground terms in an effective way, and solving, or how to compute the answer sets, of a propositional logic program obtained by grounding.

We describe the novel functionalities comprised in clasp’s series 3. This includes parallel solving of disjunctive logic programs, parallel optimization with orthogonal strategies, declarative support for specifying domain heuristics, a portfolio of prefabricated expert configurations, and an application programming interface for library integration. This is complemented by experiments evaluating clasp 3’s optimization capacities as well as the impact of domain heuristics.

Answer set programming (ASP) is a declarative programming paradigm for solving search problems arising in knowledge-intensive domains. One viable way to implement the computation of answer sets corresponding to problem solutions is to recast a logic program as a Boolean satisfiability (SAT) problem and to use existing SAT solver technology for the actual search. Such mappings can be obtained by augmenting Clark's completion with constraints guaranteeing the strong justifiability of answer sets. To this end, we consider an extension of SAT by graphs subject to an acyclicity constraint, called SAT modulo acyclicity. We devise a linear embedding of logic programs and study the performance of answer set computation with SAT modulo acyclicity solvers.

We present the new ASP system clingo 4. Unlike its predecessors, being mere monolithic combinations of the grounder gringo with the solver clasp, the new clingo 4 series offers high-level constructs for realizing complex reasoning processes. Among others, such processes feature advanced forms of search, as in optimization or theory solving, or even interact with an environment, as in robotics or query-answering. Common to them is that the problem specification evolves during the reasoning process, either because data or constraints are added, deleted, or replaced. In fact, clingo 4 carries out such complex reasoning within a single integrated ASP grounding and solving process. This avoids redundancies in relaunching grounder and solver programs and benefits from the solver’s learning capacities. clingo 4 accomplishes this by complementing ASP’s declarative input language by control capacities expressed via the embedded scripting languages Lua and Python. On the declarative side, clingo 4 offers a new directive that allows for structuring logic programs into named and parameterizable subprograms. The grounding and integration of these subprograms into the solving process is completely modular and fully controllable from the procedural side, viz. the scripting languages. By strictly separating logic and control programs, clingo 4 also abolishes the need for dedicated systems for incremental and reactive reasoning, like iclingo and oclingo, respectively, and its flexibility goes well beyond the advanced yet still rigid solving processes of the latter.

We investigate the composition of representative benchmark sets for evaluating and improving the performance of robust Boolean constraint solvers in the context of satisfiability testing and answer set programming. Starting from an analysis of current practice, we isolate a set of desiderata for guiding the development of a parametrized benchmark selection algorithm. Our algorithm samples a benchmark set from a larger base set or distribution comprising a large variety of instances. This is done fully automatically, in a way that carefully calibrates instance hardness and instance similarity. We demonstrate the usefulness of this approach by means of empirical results showing that optimizing solvers on the benchmark sets produced by our method leads to better configurations than obtained based on the much larger, original sets.

Modeling in ASP is still an art; it requires craft, experience, and knowledge. Although the resulting ASP encodings are usually quite succinct and easy to understand, crafting an ASP encoding that also leads to the best possible system performance is not yet as obvious as it might seem. This is why ASP modeling is an active and interesting area of current research. To illustrate this, let us begin by conducting an initial case study dealing with the n-queens problem introduced in Section 3.2.