Complexity of super-coherence problems in ASP

In the twenty years since the creation of the stable model semantics[4] for logic programs and inclusion of both classical and negation as failure, answer set programming (ASP)[1] has grown from a small fledgeling field within logic programming to a maturing field of its own. In this extended abstract we discuss some future application areas for ASP and theoretic and implementational problems that need to be addressed in order to make them feasible. With the increase in efficiency of the answer set solvers and a better understanding of the formalism, its advantages and disadvantages, more applications areas for ASP are found. While traditional application domains were mainly in the knowledge representation and reasoning area, we now also see more and more applications in areas were competitors like SAT or CSP were considered better alternatives. We believe, these current applications are just the tip of the iceberg. In years to come, we will see more and more successful applications plus further expansion and improvements on existing applications. In recent years we have seen a lot of ASP activity in the fields of the semantic web and web-services with specific workshops dedicated to the topic1. We believe that these fields hold more potential for years to come. For example, ASP could also be used for match-making and service coordination and orchestration. Another application area of ASP is multi-agent systems. In most cases this was always on the more theoretical side of applications. To our knowledge, nobody has used ASP to construct a running multi-agent system where the agents use ASP for reasoning purposes. With our current solvers, we should be able to provide such a system. ASP has also be applied in wide variety of other domains like planning, diagnosis, language-evolution, policy-design, bio-informatics, compiler optimisation, music composition, security, cryptography and game design. Most of these application are in a prototype phase, demonstrating that ASP could be of value in this domain and are slowly making their way to conferences and journals in the domain they are addressing. By doing some domain experts will get to know ASP and its capabilities. In time this will lead to them pointing ASP researchers to similar problems in the same domain. So in the medium term, we believe we can look forward to more ASP applications in bio-informatics, e-health, medicine, e-government and engineering. Normally we refer to ASP as a problem solving paradigm. We model the problem as an ASP program such that the answer sets correspond to the solutions of this problem.

Answer Set Programming (ASP) is a framework in artificial intelligence and knowledge representation for declarative modeling and problem solving. Modern ASP solvers focus on the computation or enumeration of answer sets. However, a variety of probabilistic applications in reasoning or logic programming require counting answer sets. While counting can be done by enumeration, simple enumeration becomes immediately infeasible if the number of solutions is high. On the other hand, approaches to exact counting are of high worst-case complexity. In fact, in propositional model counting, exact counting becomes impractical. In this work, we present a scalable approach to approximate counting for answer set programming. Our approach is based on systematically adding XOR constraints to ASP programs, which divide the search space. We prove that adding random XOR constraints partitions the answer sets of an ASP program. In practice, we use a Gaussian elimination-based approach by lifting ideas from SAT to ASP and integrating it into a state of the art ASP solver, which we call ApproxASP. Finally, our experimental evaluation shows the scalability of our approach over the existing ASP systems.

Recently, Large Language Models (LLMs) have showcased their potential in various natural language processing tasks, including code generation. However, while significant progress has been made in adapting LLMs to generate code for several imperative programming languages and tasks, there remains a notable gap in their application to declarative formalisms, such as Answer Set Programming (ASP). In this paper, we move a step towards exploring the capabilities of LLMs for ASP code generation. First, we perform a systematic evaluation of several state-of-the-art LLMs. Despite their power in terms of number of parameters, training data and computational resources, empirical results demonstrate inadequate performances in generating correct ASP programs. Therefore, we propose LLASP, a fine-tuned lightweight model specifically trained to encode fundamental ASP program patterns. To this aim, we create an ad-hoc dataset covering a wide variety of fundamental problem specifications that can be encoded in ASP. Our experiments demonstrate that the quality of ASP programs generated by LLASP is remarkable. This holds true not only when compared to the non-fine-tuned counterpart but also when compared to the majority of eager LLM candidates, particularly from a semantic perspective. All the code and data used to perform the experiments are publicly available: https://github.com/EricaCoppolillo/LLASP.

Answer Set Programming (ASP) is a widely recognized formalism for Knowledge Representation and Reasoning. Traditional ASP systems, that employ the ground and solve architecture, are subject to the grounding bottleneck (i.e., variable-elimination can exhaust all computational resources). Compilation-based approaches have recently demonstrated how grounding can be effectively bypassed by compiling rules into propagators that simulate them. However, compiling an entire ASP program is not always advantageous. In this paper, we present both a program rewriting technique and an algorithm for the compilation of grounding that allow for unrestricted blending of grounding and compilation. We implement these techniques in a hybrid ASP system that compares favourably with state-of-the-art ASP solvers on established benchmarks.

In this paper we introduce a formalism for solving Hierarchical Task Network (HTN) Planning using Answer Set Programming (ASP). We consider the formulation of HTN planning as described in the SHOP planning system and define a systematic translation method from SHOP’s representation of the planning problem into logic programs with negation. We show that our translation is sound and complete: answer sets of the logic program obtained by our translation correspond exactly to the solutions of the planning problem. We compare our method to (1) similar approaches based on non-HTN planning and (2) SHOP, a dedicated planning system. We show that our approach outperforms non-HTN methods and that its performance is better with ASP systems that allow for nonground programs than with ASP systems that require ground programs.

Answer Set Programming (ASP) is a constraint-based programming paradigm proposed recently by AI researchers. In this paradigm one solves a problem by encoding constraints as logic program rules in such a way that the solutions to the original problem correspond to the so-called answer sets of the logic program. This new programming paradigm has found applications in problems ranging from combinatorial search problems, such as the graph coloring and Hamiltonian circuit problems, to product configuration and data encryption problems. In this dissertation, we make the following two contributions to the new programming paradigm ASP. First, we propose and implement a new ASP system using traditional SAT (propositional satisfiability) solvers. This is done by a translation from logic programs to sets of clauses in propositional logic. Our experimental results show that for many benchmark domains, our system performs better than existing specialized ASP systems. Secondly, we study the phase transition phenomenon in randomly generated logic programs, and identify a region in a class of randomly generated logic programs where the logic programs are hard for all existing ASP systems.

回答集编程(answer set programming,ASP)是一种回答集语义下的逻辑编程范例,可应用于非单调推理,叙述式问题求解等领域.本文为ASP提出并实现了一种破圈启发方法与一种基部限制式前向搜索过程,所得到的系统称为LPS.实验结果显示,相对于其他经典的ASP系统,LPS能够有效地解决处于相变难区域中的逻辑程序,通常这些程序被认为是计算困难的.除此以外,通过使用被称为动态变元过滤(dynamic variable filtering,DVF)的技术,LPS可以在计算过程中极大地缩小搜索树的尺寸.

The recent application of Machine Learning techniques to the Answer Set Programming (ASP) field proved to be effective. In particular, the multi-engine ASP solver ME-ASP is efficient: it is able to solve more instances than any other ASP system that participated to the 3rd ASP Competition on the System Track benchmarks. In the ME-ASP approach, classification methods inductively learn off-line algorithm selection policies starting from both a set of features of instances in a training set, and the solvers performance on such instances. In this paper we present an improvement to the multi-engine framework of ME-ASP , in which we add the capability of updating the learned policies when the original approach fails to give good predictions. An experimental analysis, conducted on training and test sets of ground instances obtained from the ones submitted to the System Track of the 3rd ASP Competition, shows that the policy adaptation improves the performance of ME-ASP when applied to test sets containing domains of instances that were not considered for training.

In recent years, answer set programming (ASP) has been extended to deal with multivalued predicates. The resulting formalismsallow for the modeling of continuous problems as elegantly as ASP allows for the modeling of discrete problems, by combining thestable model semantics underlying ASP with fuzzy logics. However, contrary to the case of classical ASP where manyefficient solvers have been constructed, to date there is no efficient fuzzy ASP solver. A well-knowntechnique for classical ASP consists of translating an ASP programPto a propositional theory whose models exactlycorrespond to the answer sets ofP. In this paper, we show how this idea can be extended to fuzzy ASP, paving the wayto implement efficient fuzzy ASP solvers that can take advantage of existing fuzzy logic reasoners.

Most recently, Answer Set Programming (ASP) has been attracting interest as a new paradigm for problem solving. An important aspect, for which several approaches have been presented, is the handling of preferences between rules. In this paper, we consider the problem of implementing preference handling approaches by means of meta-interpreters in Answer Set Programming. In particular, we consider the preferred answer set approaches by Brewka and Eiter, by Delgrande, Schaub and Tompits, and by Wang, Zhou and Lin. We present suitable meta-interpreters for these semantics using DLV, which is an efficient engine for ASP. Moreover, we also present a meta-interpreter for the weakly preferred answer set approach by Brewka and Eiter, which uses the weak constraint feature of DLV as a tool for expressing and solving an underlying optimization problem. We also consider advanced meta-interpreters, which make use of graph-based characterizations and often allow for more efficient computations. Our approach shows the suitability of ASP in general and of DLV in particular for fast prototyping. This can be fruitfully exploited for experimenting with new languages and knowledge-representation formalisms.

In answer-set programming (ASP), the solutions of a problem are encoded in dedicated models, called answer sets, of a logical theory. These answer sets are computed from the program that represents the theory by means of an ASP solver and returned to the user as sets of ground first-order literals. As this type of representation is often cumbersome for the user to interpret, tools like ASPVIZ and IDPDraw were developed that allow for visualising answer sets. The tool Kara, introduced in this paper, follows these approaches, using ASP itself as a language for defining visualisations of interpretations. Unlike existing tools that position graphic primitives according to static coordinates only, Kara allows for more high-level specifications, supporting graph structures, grids, and relative positioning of graphical elements. Moreover, generalising the functionality of previous tools, Kara provides modifiable visualisations such that interpretations can be manipulated by graphically editing their visualisations. This is realised by resorting to abductive reasoning techniques using ASP itself. Kara is part of SeaLion, an integrated development environment (IDE) for ASP.

The goal of the Nurse Scheduling Problem is to find an assignment of nurses to shifts according to specific requirements. Frequently, a computed schedule may become not usable because of sudden absences of some nurses. In this cases, Nurse Rescheduling amounts to the computation of a new schedule, which has to satisfy the original requirements and the new absences. Additionally, a good solution to the Nurse Rescheduling Problem must be as similar as possible to the original schedule, which practically means that the number of changes has to be minimized. This paper focuses on the requirements specified by an Italian hospital, and recently addressed by an approach based on Answer Set Programming (ASP). Even if promising results have been obtained with ASP, the original encoding presents some intrinsic weaknesses, which are identified and eventually circumvented in this paper. The new encoding is designed by taking into account both intrinsic properties of Nurse Scheduling and internal details of ASP solvers, such as cardinality and weight constraint propagators. The performance gain of clingo and wasp is empirically verified on instances from ASP literature. As an additional contribution, the performance of clingo and wasp is compared to other declarative frameworks, namely SAT and ILP; the best performance is obtained by clingo running the new ASP encoding. The advanced ASP encodings are then extended to solve Nurse Rescheduling, and an empirical evaluation is conducted with clingo and wasp.

We present a prototypical system, plasp, implementing Planning by compilation to Answer Set Programming (ASP). Our approach is inspired by Planning as Satisfiability, yet it aims at keeping the actual compilation simple in favor of modeling planning techniques by meta-programming in ASP. This has several advantages. First, ASP modelings are easily modifiable and can be studied in a transparent setting. Second, we can take advantage of available ASP grounders to obtain propositional representations. Third, we can harness ASP solvers providing incremental solving mechanisms. Finally, the ASP community gains access to a wide range of planning problems, and the planning community benefits from the knowledge representation and reasoning capacities of ASP.KeywordsPlanning ProblemOperator SplittingConcurrent ActionPropositional RepresentationAutomate PlanningThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Answer Set Programming (ASP) is a declarative programming paradigm targeted to solving search problems. The basic idea of ASP is similar to, for example, SAT-based planning or constraint satisfaction problems but ASP provides a more powerful knowledge representation language for effective problem encoding. A number of successful ASP systems have already been developed and applied in a large range of areas. The talk explains the theoretical underpinnings of ASP, introduces the answer set programming paradigm, outlines computational techniques used in current ASP solvers, and discusses some interesting applications of the approach.

Artificial intelligence (AI) approaches to problem-solving and decision-making are becoming more and more complex, leading to a decrease in the understandability of solutions. The European Union’s new General Data Protection Regulation tries to tackle this problem by stipulating a “right to explanation” for decisions made by AI systems. One of the AI paradigms that may be affected by this new regulation is answer set programming (ASP). Thanks to the emergence of efficient solvers, ASP has recently been used for problem-solving in a variety of domains, including medicine, cryptography, and biology. To ensure the successful application of ASP as a problem-solving paradigm in the future, explanations of ASP solutions are crucial. In this survey, we give an overview of approaches that provide an answer to the question ofwhyan answer set is a solution to a given problem, notably off-line justifications, causal graphs, argumentative explanations, and why-not provenance, and highlight their similarities and differences. Moreover, we review methods explaining why a set of literals isnotan answer set or why no solution exists at all.