Simona Perri

The DLV system for knowledge representation and reasoning

Disjunctive Logic Programming (DLP) is an advanced formalism for knowledge representation and reasoning, which is very expressive in a precise mathematical sense: it allows one to express every property of finite structures that is decidable in the complexity class ΣP2 (NPNP). Thus, under widely believed assumptions, DLP is strictly more expressive than normal (disjunction-free) logic programming, whose expressiveness is limited to properties decidable in NP. Importantly, apart from enlarging the class of applications which can be encoded in the language, disjunction often allows for representing problems of lower complexity in a simpler and more natural fashion.This article presents the DLV system, which is widely considered the state-of-the-art implementation of disjunctive logic programming, and addresses several aspects. As for problem solving, we provide a formal definition of its kernel language, function-free disjunctive logic programs (also known as disjunctive datalog), extended by weak constraints, which are a powerful tool to express optimization problems. We then illustrate the usage of DLV as a tool for knowledge representation and reasoning, describing a new declarative programming methodology which allows one to encode complex problems (up to ΔP3-complete problems) in a declarative fashion. On the foundational side, we provide a detailed analysis of the computational complexity of the language of DLV, and by deriving new complexity results we chart a complete picture of the complexity of this language and important fragments thereof.Furthermore, we illustrate the general architecture of the DLV system, which has been influenced by these results. As for applications, we overview application front-ends which have been developed on top of DLV to solve specific knowledge representation tasks, and we briefly describe the main international projects investigating the potential of the system for industrial exploitation. Finally, we report about thorough experimentation and benchmarking, which has been carried out to assess the efficiency of the system. The experimental results confirm the solidity of DLV and highlight its potential for emerging application areas like knowledge management and information integration.

The DLV System

The development of the DLV system has started as a research projectfinanced by FWF (the Austrian Science Funds) in 1996,and has evolved into an international collaboration over the years. Currently, the University of Calabria and TU Wien participate in the project, supported by a scientific-technological collaboration between Italy and Austria. At the time of writing, the latest version of the system has been released on April 12, 2002.

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

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 disjunctive datalog system DLV

DLV is one of the most successful and widely used answer set programming (ASP) systems. It supports a powerful language extending Disjunctive Datalog with many expressive constructs, including aggregates, strong and weak constraints, functions, lists, and sets. The system provides database connectivity offering a simple way for powerful reasoning on top of relational databases. In this paper, we provide an ample overview of the DLV system. We illustrate its input language and give indications on how to use it for representing knowledge. We also provide a panorama on the system architecture and the main optimizations it incorporates. We then focus on DLVDB, an extension of the basic system which allows for tight coupling with traditional database systems. Finally, we report on a number industrial applications which rely on DLV.

Improving ASP Instantiators by Join-Ordering Methods

Most Answer Set Programming (ASP) systems, including DLV and Smodels, are endowed with an instantiation module. The instantiator generates a new program which is equivalent to the input program, but does not contain any variables (i.e., it is ground). Normal (i.e., disjunction-free) stratified programs are completely solved by the instantiator, which generates the output model directly. The instantiation process may be computationally expensive in some cases, and the instantiator is crucial for the efficiency of the entire ASP system. In this paper, we propose to employ join-ordering techniques to improve the instantiation process. We design a new join-ordering method, and adapt a classical database method to this context. We implement these techniques in the ASP system DLV, and we carry out an experimentation activity on a collection of benchmark problems taken from different domains. The results of experiments are very positive, the new techniques improve sensibly the efficiency of the DLV system, whose instantiation module confirms to be a main strong point of DLV w.r.t. the other ASP systems.

Enhancing DLV instantiator by backjumping techniques

Disjunctive logic programming (DLP) is a powerful formalism for knowledge representation and reasoning. The high expressiveness of DLP language, together with the recent availability of some efficient DLP system, has favoured the application of DLP in emerging areas like Knowledge Management and Information Integration. These applications have often to deal with huge input data, and have evidenced the need to improve the efficiency of DLP instantiators. Program instantiation is the first phase of a DLP computation; in this phase, variables are replaced by constants to generate a ground program which is then evaluated by propositional algorithms in the second phase of the computation. The instantiation process may be computationally expensive, and in fact its efficiency has been recognized to be a key issue for solving real-world problems by using disjunctive logic programming. Given a program P, a good instantiation for P is a ground program P′ having precisely the same answer sets as P and such that: (1) P′ can be computed efficiently from P, and (2) P′ does not contain “useless” rules, (P′ is as small as possible) and can thus be evaluated efficiently. In this paper, we present a structure-based backjumping algorithm for the instantiation of disjunctive logic programs, that meets the above requirements. In particular, given a rule r to be grounded, our algorithm exploits both the semantical and the structural information about r for computing efficiently the ground instances of r, avoiding the generation of “useless” rules. That is, from each general rule r, we compute only a relevant subset of its ground instances, avoiding the generation of “useless” instances, while fully preserving the semantic of the program. We have implemented this algorithm in DLV—the state-of-the-art implementation of DLP—and we have carried out an experimentation activity on an ample collection of benchmark problems. The experimental results are very positive: the new technique improves sensibly the efficiency of the DLV system on many program classes.

System Description: DLV

DLV is an efficient Answer Set Programming (ASP) system implementing the consistent answer set semantics [5] with various language enhancements like support for logic programming with inheritance and queries, integer arithmetics, and various other built-in predicates.

Experimenting with parallelism for the instantiation of ASP programs

In the last few years, microprocessor technologies have been moving towards multi-core architectures, in order to improve performance as well as reduce power consumption. This makes real Symmetric MultiProcessing (SMP) available even on non-dedicated machines, and paves the way to the development of better performing software. Notably, the recent application of Answer Set Programming (ASP) in different emerging areas, such as knowledge management or information extraction/integration, shows that performance is a crucial issue also for ASP systems. Among the tasks performed by such systems, the instantiation process, which consists of generating a variable-free program equivalent to the input one, is one of the most expensive from a computational viewpoint, especially in the case of huge input data. In this paper a new strategy exploiting parallelism for the instantiation of ASP programs is proposed. An implementation of this strategy and its integration with the grounding module of the DLV system is discussed. The results of an experimental analysis are also presented, which confirm that the strategy is effective in making ASP instantiation more efficient.

Unfounded sets and well-founded semantics of answer set programs with aggregates

Logic programs with aggregates (LPA) are one of the major linguistic extensions to Logic Programming (LP). In this work, we propose a generalization of the notions of unfounded set and well-founded semantics for programs with monotone and antimonotone aggregates (LPm,aA programs). In particular, we present a new notion of unfounded set for LPm,aA programs, which is a sound generalization of the original definition for standard (aggregate-free) LP. On this basis, we define a well-founded operator for LPm,aA programs, the fixpoint of which is called well-founded model (or well-founded semantics) for LPm,aA programs. The most important properties of unfounded sets and the well-founded semantics for standard LP are retained by this generalization, notably existence and uniqueness of the well-founded model, together with a strong relationship to the answer set semantics for LPm,aA programs. We show that one of the D-well-founded semantics, defined by Pelov, Denecker, and Bruynooghe for a broader class of aggregates using approximating operators, coincides with the well-founded model as defined in this work on LPm,aA programs. We also discuss some complexity issues, most importantly we give a formal proof of tractable computation of the well-founded model for LPm,aA programs. Moreover, we prove that for general LPA programs, which may contain aggregates that are neither monotone nor antimonotone, deciding satisfaction of aggregate expressions with respect to partial interpretations is coNP-complete. As a consequence, a well-founded semantics for general LPA programs that allows for tractable computation is unlikely to exist, which justifies the restriction on LPm,aA programs. Finally, we present a prototype system extending DLV, which supports the well-founded semantics for LPm,aA programs, at the time of writing the only implemented system that does so. Experiments with this prototype show significant computational advantages of aggregate constructs over equivalent aggregate-free encodings.

Grounding and Solving in Answer Set Programming

Answer set programming is a declarative problem solving paradigm that rests upon a workflow 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 a effective way, and solving, or how to compute the answer sets of a propositional logic program obtained by grounding.