Building rules on top of ontologies is the ultimate goal of the logical layer of the Semantic Web. To this aim, an ad-hoc markup language for this layer is currently under discussion. It is intended to follow the tradition of hybrid knowledge representation and reasoning systems, such as -log that integrates the description logic and the function-free Horn clausal language Datalog. In this paper, we consider the problem of automating the acquisition of these rules for the Semantic Web. We propose a general framework for rule induction that adopts the methodological apparatus of Inductive Logic Programming and relies on the expressive and deductive power of -log. The framework is valid whatever the scope of induction (description versus prediction) is. Yet, for illustrative purposes, we also discuss an instantiation of the framework which aims at description and turns out to be useful in Ontology Refinement.

We propose a new method for mining frequent patterns in a language that combines both Semantic Web ontologies and rules. In particular, we consider the setting of using a language that combines description logics (DLs) with DL-safe rules. This setting is important for the practical application of data mining to the Semantic Web. We focus on the relation of the semantics of the representation formalism to the task of frequent pattern discovery, and for the core of our method, we propose an algorithm that exploits the semantics of the combined knowledge base. We have developed a proof-of-concept data mining implementation of this. Using this we have empirically shown that using the combined knowledge base to perform semantic tests can make data mining faster by pruning useless candidate patterns before their evaluation. We have also shown that the quality of the set of patterns produced may be improved: the patterns are more compact, and there are fewer patterns. We conclude that exploiting the semantics of a chosen representation formalism is key to the design and application of (onto-)relational frequent pattern discovery methods.

The paper presents a knowledge representation language $\mathcal{A}log$ which extends ASP with aggregates. The goal is to have a language based on simple syntax and clear intuitive and mathematical semantics. We give some properties of $\mathcal{A}log$, an algorithm for computing its answer sets, and comparison with other approaches.

Logic programming languages, such as Prolog, provide a high-level, declarative approach to programming. Logic Programming offers great potential for implicit parallelism, thus allowing parallel systems to often reduce a program's execution time without programmer intervention. We believe that for complex applications that take several hours, if not days, to return an answer, even limited speedups from parallel execution can directly translate to very significant productivity gains. It has been argued that Prolog's evaluation strategy – SLD resolution – often limits the potential of the logic programming paradigm. The past years have therefore seen widening efforts at increasing Prolog's declarativeness and expressiveness. Tabling has proved to be a viable technique to efficiently overcome SLD's susceptibility to infinite loops and redundant subcomputations. Our research demonstrates that implicit or-parallelism is a natural fit for logic programs with tabling. To substantiate this belief, we have designed and implemented an or-parallel tabling engine – OPTYap – and we used a shared-memory parallel machine to evaluate its performance. To the best of our knowledge, OPTYap is the first implementation of a parallel tabling engine for logic programming systems. OPTYap builds on Yap's efficient sequential Prolog engine. Its execution model is based on the SLG-WAM for tabling, and on the environment copying for or-parallelism. Preliminary results indicate that the mechanisms proposed to parallelize search in the context of SLD resolution can indeed be effectively and naturally generalized to parallelize tabled computations, and that the resulting systems can achieve good performance on shared-memory parallel machines. More importantly, it emphasizes our belief that through applying or-parallelism and tabling to logic programs the range of applications for Logic Programming can be increased.

The problem of scheduling chemotherapy treatments in oncology clinics is a complex problem, given that the solution has to satisfy (as much as possible) several requirements such as the cyclic nature of chemotherapy treatment plans, maintaining a constant number of patients, and the availability of resources, for example, treatment time, nurses, and drugs. At the same time, realizing a satisfying schedule is of upmost importance for obtaining the best health outcomes. In this paper we first consider a specific instance of the problem which is employed in the San Martino Hospital in Genova, Italy, and present a solution to the problem based on Answer Set Programming (ASP). Then, we enrich the problem and the related ASP encoding considering further features often employed in other hospitals, desirable also in S. Martino, and/or considered in related papers. Results of an experimental analysis, conducted on the real data provided by the San Martino Hospital, show that ASP is an effective solving methodology also for this important scheduling problem.

Answer Set Programming (ASP) is a prominent knowledge representation language with roots in logic programming and non-monotonic reasoning. Biennial ASP competitions are organized in order to furnish challenging benchmark collections and assess the advancement of the state of the art in ASP solving. In this paper, we report on the design and results of the Seventh ASP Competition, jointly organized by the University of Calabria (Italy), the University of Genova (Italy), and the University of Potsdam (Germany), in affiliation with the 14th International Conference on Logic Programming and Non-Monotonic Reasoning (LPNMR 2017).

Constraint Handling Rules (CHR) is a high-level programming language based on multiheaded multiset rewrite rules. Originally designed for writing user-defined constraint solvers, it is now recognized as an elegant general purpose language. Constraint Handling Rules related research has surged during the decade following the previous survey by Frühwirth (J. Logic Programming, Special Issue on Constraint Logic Programming, 1998, vol. 37, nos. 1–3, pp. 95–138). Covering more than 180 publications, this new survey provides an overview of recent results in a wide range of research areas, from semantics and analysis to systems, extensions, and applications.

We extend the 0-approximation of sensing actions and incomplete information in Son and Baral (2001) to action theories with static causal laws and prove its soundness with respect to the possible world semantics. We also show that the conditional planning problem with respect to this approximation is NP-complete. We then present an answer set programming based conditional planner, called ASCP, that is capable of generating both conformant plans and conditional plans in the presence of sensing actions, incomplete information about the initial state, and static causal laws. We prove the correctness of our implementation and argue that our planner is sound and complete with respect to the proposed approximation. Finally, we present experimental results comparing ASCP to other planners.

Unsatisfiable core analysis can boost the computation of optimum stable models for logic programs with weak constraints. However, current solvers employing unsatisfiable core analysis either run to completion, or provide no suboptimal stable models but the one resulting from the preliminary disjoint cores analysis. This drawback is circumvented here by introducing a progression based shrinking of the analyzed unsatisfiable cores. In fact, suboptimal stable models are possibly found while shrinking unsatisfiable cores, hence resulting into an anytime algorithm. Moreover, as confirmed empirically, unsatisfiable core analysis also benefits from the shrinking process in terms of solved instances.

The non-classical, nonmonotonic inference relation associated with the answer set semantics for logic programs gives rise to a relationship of strong equivalence between logical programs that can be verified in 3-valued Gödel logic, G3, the strongest non-classical intermediate propositional logic (Lifschitz et al., 2001). In this paper we will show that KC (the logic obtained by adding axiom $\neg A\vee\neg\neg A$ to intuitionistic logic), is the weakest intermediate logic for which strongly equivalent logic programs, in a language allowing negations, are logically equivalent.

We present a method for the automated verification of temporal properties of infinite state systems. Our verification method is based on the specialization of constraint logic programs (CLP) and works in two phases: (1) in the first phase, a CLP specification of an infinite state system is specialized with respect to the initial state of the system and the temporal property to be verified, and (2) in the second phase, the specialized program is evaluated by using a bottom-up strategy. The effectiveness of the method strongly depends on the generalization strategy which is applied during the program specialization phase. We consider several generalization strategies obtained by combining techniques already known in the field of program analysis and program transformation, and we also introduce some new strategies. Then, through many verification experiments, we evaluate the effectiveness of the generalization strategies we have considered. Finally, we compare the implementation of our specialization-based verification method to other constraint-based model checking tools. The experimental results show that our method is competitive with the methods used by those other tools.

Answer Set Programming (ASP) is a popular logic programming paradigm that has been applied for solving a variety of complex problems. Among the most challenging real-world applications of ASP are two industrial problems defined by Siemens: the Partner Units Problem (PUP) and the Combined Configuration Problem (CCP). The hardest instances of PUP and CCP are out of reach for state-of-the-art ASP solvers. Experiments show that the performance of ASP solvers could be significantly improved by embedding domain-specific heuristics, but a proper effective integration of such criteria in off-the-shelf ASP implementations is not obvious. In this paper the combination of ASP and domain-specific heuristics is studied with the goal of effectively solving real-world problem instances of PUP and CCP. As a byproduct of this activity, the ASP solver wasp was extended with an interface that eases embedding new external heuristics in the solver. The evaluation shows that our domain-heuristic-driven ASP solver finds solutions for all the real-world instances of PUP and CCP ever provided by Siemens.

The so called “cogen approach” to program specialisation, writing a compiler generator instead of a specialiser, has been used with considerable success in partial evaluation of both functional and imperative languages. This paper demonstrates that the cogen approach is also applicable to the specialisation of logic programs (called partial deduction) and leads to effective specialisers. Moreover, using good binding-time annotations, the speed-ups of the specialised programs are comparable to the speed-ups obtained with online specialisers. The paper first develops a generic approach to offline partial deduction and then a specific offline partial deduction method, leading to the offline system LIX for pure logic programs. While this is a usable specialiser by itself, it is used to develop the cogen system LOGEN. Given a program, a specification of what inputs will be static, and an annotation specifying which calls should be unfolded, LOGEN generates a specialised specialiser for the program at hand. Running this specialiser with particular values for the static inputs results in the specialised program. While this requires two steps instead of one, the efficiency of the specialisation process is improved in situations where the same program is specialised multiple times. The paper also presents and evaluates an automatic binding-time analysis that is able to derive the annotations. While the derived annotations are still suboptimal compared to hand-crafted ones, they enable non-expert users to use the LOGEN system in a fully automated way. Finally, LOGEN is extended so as to directly support a large part of Prolog's declarative and non-declarative features and so as to be able to perform so called mixline specialisations.

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 of why an 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 is not an answer set or why no solution exists at all.

We present some applications of intermediate logics in the field of Answer Set Programming (ASP). A brief, but comprehensive introduction to the answer set semantics, intuitionistic and other intermediate logics is given. Some equivalence notions and their applications are discussed. Some results on intermediate logics are shown, and applied later to prove properties of answer sets. A characterization of answer sets for logic programs with nested expressions is provided in terms of intuitionistic provability, generalizing a recent result given by Pearce. It is known that the answer set semantics for logic programs with nested expressions may select non-minimal models. Minimal models can be very important in some applications, therefore we studied them; in particular we obtain a characterization, in terms of intuitionistic logic, of answer sets which are also minimal models. We show that the logic G3 characterizes the notion of strong equivalence between programs under the semantic induced by these models. Finally we discuss possible applications and consequences of our results. They clearly state interesting links between ASP and intermediate logics, which might bring research in these two areas together.

In this paper, a Gaifman–Shapiro-style module architecture is tailoredto the case of smodels programs under the stable model semantics. Thecomposition of smodels program modules is suitably limited by moduleconditions which ensure the compatibility of the module system with stablemodels. Hence the semantics of an entire smodels program dependsdirectly on stable models assigned to its modules. This result is formalized asa module theorem which truly strengthens V. Lifschitz and H.Turner's splitting-set theorem (June 1994, Splitting a logic program. InLogic Programming: Proceedings of the Eleventh InternationalConference on Logic Programming, Santa Margherita Ligure, Italy, P.V. Hentenryck, Ed. MIT Press, 23–37) for the class of smodelsprograms. To streamline generalizations in the future, the module theorem isfirst proved for normal programs and then extended to cover smodelsprograms using a translation from the latter class of programs to the formerclass. Moreover, the respective notion of module-level equivalence, namelymodular equivalence, is shown to be a proper congruencerelation: it is preserved under substitutions of modules that are modularlyequivalent. Principles for program decomposition are also addressed. Thestrongly connected components of the respective dependency graph can beexploited in order to extract a module structure when there is no explicita priori knowledge about the modules of a program. Thepaper includes a practical demonstration of tools that have been developed forautomated (de)composition of smodels programs.

In complex reasoning tasks, as expressible by Answer Set Programming (ASP), problems often permit for multiple solutions. In dynamic environments, where knowledge is continuously changing, the question arises how a given model can be incrementally adjusted relative to new and outdated information. This paper introduces Ticker, a prototypical engine for well-defined logical reasoning over streaming data. Ticker builds on a practical fragment of the recent rule-based language LARS, which extends ASP for streams by providing flexible expiration control and temporal modalities. We discuss Ticker's reasoning strategies: first, the repeated one-shot solving mode calls Clingo on an ASP encoding. We show how this translation can be incrementally updated when new data is streaming in or time passes by. Based on this, we build on Doyle's classic justification-based truth-maintenance system to update models of non-stratified programs. Finally, we empirically compare the obtained evaluation mechanisms.

Answer Set Programming (ASP) is a well-established paradigm of declarative programming in close relationship with other declarative formalisms such as SAT Modulo Theories, Constraint Handling Rules, FO(.), PDDL and many others. Since its first informal editions, ASP systems have been compared in the now well-established ASP Competition. The Third (Open) ASP Competition, as the sequel to the ASP Competitions Series held at the University of Potsdam in Germany (2006–2007) and at the University of Leuven in Belgium in 2009, took place at the University of Calabria (Italy) in the first half of 2011. Participants competed on a pre-selected collection of benchmark problems, taken from a variety of domains as well as real world applications. The Competition ran on two tracks: the Model and Solve (M&S) Track, based on an open problem encoding, and open language, and open to any kind of system based on a declarative specification paradigm; and the System Track, run on the basis of fixed, public problem encodings, written in a standard ASP language. This paper discusses the format of the competition and the rationale behind it, then reports the results for both tracks. Comparison with the second ASP competition and state-of-the-art solutions for some of the benchmark domains is eventually discussed.

Oz is a multiparadigm language that supports logic programming as one of its major paradigms. A multiparadigm language is designed to support different programming paradigms (logic, functional, constraint, object-oriented, sequential, concurrent, etc.) with equal ease. This paper has two goals: to give a tutorial of logic programming in Oz; and to show how logic programming fits naturally into the wider context of multiparadigm programming. Our experience shows that there are two classes of problems, which we call algorithmic and search problems, for which logic programming can help formulate practical solutions. Algorithmic problems have known efficient algorithms. Search problems do not have known efficient algorithms but can be solved with search. The Oz support for logic programming targets these two problem classes specifically, using the concepts needed for each. This is in contrast to the Prolog approach, which targets both classes with one set of concepts, which results in less than optimal support for each class. We give examples that can be run interactively on the Mozart system, which implements Oz. To explain the essential difference between algorithmic and search programs, we define the Oz execution model. This model subsumes both concurrent logic programming (committed-choice-style) and search-based logic programming (Prolog-style). Furthermore, as consequences of its multiparadigm nature, the model supports new abilities such as first-class top levels, deep guards, active objects, and sophisticated control of the search process. Instead of Horn clause syntax, Oz has a simple, fully compositional, higher-order syntax that accommodates the abilities of the language. We give a brief history of Oz that traces the development of its main ideas and we summarize the lessons learned from this work. Finally, we give many entry points into the Oz literature.

Distribution semantics is one of the most prominent approaches for the combination of logic programming and probability theory. Many languages follow this semantics, such as Independent Choice Logic, PRISM, pD, Logic Programs with Annotated Disjunctions (LPADs), and ProbLog. When a program contains functions symbols, the distribution semantics is well–defined only if the set of explanations for a query is finite and so is each explanation. Well–definedness is usually either explicitly imposed or is achieved by severely limiting the class of allowed programs. In this paper, we identify a larger class of programs for which the semantics is well–defined together with an efficient procedure for computing the probability of queries. Since Logic Programs with Annotated Disjunctions offer the most general syntax, we present our results for them, but our results are applicable to all languages under the distribution semantics. We present the algorithm “Probabilistic Inference with Tabling and Answer subsumption” (PITA) that computes the probability of queries by transforming a probabilistic program into a normal program and then applying SLG resolution with answer subsumption. PITA has been implemented in XSB and tested on six domains: two with function symbols and four without. The execution times are compared with those of ProbLog, cplint, and CVE. PITA was almost always able to solve larger problems in a shorter time, on domains with and without function symbols.