The motivation and key concepts behind answer set programming---a promising approach to declarative problem solving.

Answer set programming at a glance

Answer Set Programming (ASP) is a declarative problem solving approach, initially tailored to modeling problems in the area of Knowledge Representation and Reasoning (KRR). More recently, its attractive combination of a rich yet simple modeling language with high-performance solving capacities has sparked interest in many other areas even beyond KRR. This book presents a practical introduction to ASP, aiming at using ASP languages and systems for solving application problems. Starting from the essential formal foundations, it introduces ASP's solving technology, modeling language and methodology, while illustrating the overall solving process by practical examples. Table of Contents: List of Figures / List of Tables / Motivation / Introduction / Basic modeling / Grounding / Characterizations / Solving / Systems / Advanced modeling / Conclusions

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Answer Set Solving in Practice

In this paper, we introduce a family of expressive extensions of Datalog, called Datalog+/-, as a new paradigm for query answering over ontologies. The Datalog+/- family admits existentially quantified variables in rule heads, and has suitable restrictions to ensure highly efficient ontology querying. We show in particular that Datalog+/- generalizes the DL-Lite family of tractable description logics, which are the most common tractable ontology languages in the context of the Semantic Web and databases. We also show how stratified negation can be added to Datalog+/- while keeping ontology querying tractable. Furthermore, the Datalog+/- family is of interest in its own right and can, moreover, be used in various contexts such as data integration and data exchange.

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A general datalog-based framework for tractable query answering over ontologies

A general Datalog-based framework for tractable query answering over ontologies

Answer Set Programming (ASP) is a declarative problem solving paradigm, rooted in Logic Programming and Nonmonotonic Reasoning, which has been gaining increasing attention during the last years This article is a gentle introduction to the subject; it starts with motivation and follows the historical development of the challenge of defining a semantics for logic programs with negation It looks into positive programs over stratified programs to arbitrary programs, and then proceeds to extensions with two kinds of negation (named weak and strong negation), and disjunction in rule heads The second part then considers the ASP paradigm itself, and describes the basic idea It shows some programming techniques and briefly overviews Answer Set solvers The third part is devoted to ASP in the context of the Semantic Web, presenting some formalisms and mentioning some applications in this area The article concludes with issues of current and future ASP research

Answer Set Programming: A Primer

Disjunctive Logic Programming (DLP) under the answer set semantics, often referred to as Answer Set Programming (ASP), is a powerful formalism for knowledge representation and reasoning (KRR). The latest years witness an increasing effort for embedding functions in the context of ASP. Nevertheless, at present no ASP system allows for a reasonably unrestricted use of function terms. Functions are either required not to be recursive or subject to severe syntactic limitations, if allowed at all in ASP systems.

In this work we formally define the new class of finitely-ground programs, allowing for a powerful (possibly recursive) use of function terms in the full ASP language with disjunction and negation. We demonstrate that finitely-ground programs have nice computational properties: (i) both brave and cautious reasoning are decidable, and (ii) answer sets of finitely-ground programs are computable. Moreover, the language is highly expressive, as any computable function can be encoded by a finitely-ground program. Due to the high expressiveness, membership in the class of finitely-ground program is clearly not decidable (we prove that it is semi-decidable). We single out also a subset of finitely-ground programs, called finite-domain programs, which are effectively recognizable, while keeping computability of both reasoning and answer set computation.

We implement all results in DLP, further extending the language in order to support list and set terms, along with a rich library of built-in functions for their manipulation. The resulting ASP system is very powerful: any computable function can be encoded in a rich and fully declarative KRR language, ensuring termination on every finitely-ground program. In addition, termination is "a priori" guaranteed if the user asks for the finite-domain check.

Computable Functions in ASP: Theory and Implementation

Answer Set Programming 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 are compared in the nowadays customary ASP Competition. The Third 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 selected collection of declarative specifications of benchmark problems, taken from a variety of domains as well as real world applications, and instances thereof. The Competition ran on two tracks: the Model & Solve Competition, held on an open problem encoding, on an open language basis, and open to any kind of system based on a declarative specification paradigm; and the System Competition, held on the basis of fixed, public problem encodings, written in a standard ASP language. This paper briefly discuss the format and rationale of the System competition track, and preliminarily reports its results.

The third answer set programming competition: preliminary report of the system competition track

The issue of value invention in logic programming embraces many scenarios, such as logic programming with function symbols, object oriented logic languages, inter-operability with external sources of knowledge, or set unification. This work introduces a framework embedding value invention in a general context. The class of programs having a suitable (but, in general, not decidable) `finite grounding property' is identified, and the class of `value invention restricted' programs is introduced. Value invention restricted programs have the finite grounding property and can be decided in polynomial time. They are a very large polynomially decidable class having this property, when no assumption can be made about the nature of invented values (while this latter is the case in the specific literature about logic programming with function symbols). Relationships with existing formalisms are eventually discussed, and the implementation of a system supporting the class of such programs is described.

External sources of knowledge and value invention in logic programming

We present DLV-Complex, an extension of the DLV system that features the support for a powerful (possibly recursive) use of functions, list and set terms in the full ASP language with disjunction and negation.

Any computable function can be encoded in a rich and fully declarative KRR language, ensuring termination on all programs belonging to the recently introduced class of finitely-ground programs; furthermore, termination can be "a priori" guaranteed on demand by means of a syntactic restriction check that ensures a finite-domain property.

The system, which is already successfully used in many universities and research institutes, comes also equipped with a rich library of built-in functions and predicates for the manipulation of complex terms.

An ASP System with Functions, Lists, and Sets

This paper summarizes our line of research about the introduction of function symbols (functions) in Answer Set Programming (ASP) - a powerful language for knowledge representation and reasoning. The undecid-ability of reasoning on ASP with functions, implied that functions were subject to severe restrictions or disallowed at all, drastically limiting ASP applicability. We overcame most of the technical difficulties preventing this introduction, and we singled out a highly expressive class of programs with functions (FG-programs), allowing the (possibly recursive) use of function terms in the full ASP language with disjunction and negation. Reasoning on FG-programs is decidable, and they can express any computable function (causing membership in this class to be semi-decidable). We singled out also FD-programs, a subset of FG-programs which are effectively recognizable, while keeping the computability of reasoning. We implemented all results into the DLV system, thus obtaining an ASP system allowing to encode any computable function in a rich and fully declarative KRR language, ensuring termination on every FG program. Finally, we singled out the class of DFRP programs, where decidability of reasoning is guaranteed and Prolog-like functions are allowed.

Susanna Cozza

Papers

Computable Functions in ASP: Theory and Implementation

The third answer set programming competition: preliminary report of the system competition track

External sources of knowledge and value invention in logic programming

An ASP System with Functions, Lists, and Sets

Enhancing ASP by functions: decidable classes and implementation techniques