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 for knowledge representation and reasoning

Extending and implementing the stable model semantics

Logic programming with the stable model semantics is put forward as a novel constraint programming paradigm. This paradigm is interesting because it bring advantages of logic programming based knowledge representation techniques to constraint programming and because implementation methods for the stable model semantics for ground (variabledfree) programs have advanced significantly in recent years. For a program with variables these methods need a grounding procedure for generating a variabledfree program. As a practical approach to handling the grounding problem a subclass of logic programs, domain restricted programs, is proposed. This subclass enables efficient grounding procedures and serves as a basis for integrating builtdin predicates and functions often needed in applications. It is shown that the novel paradigm embeds classical logical satisfiability and standard (finite domain) constraint satisfaction problems but seems to provide a more expressive framework from a knowledge representation point of view. The first steps towards a programming methodology for the new paradigm are taken by presenting solutions to standard constraint satisfaction problems, combinatorial graph problems and planning problems. An efficient implementation of the paradigm based on domain restricted programs has been developed. This is an extension of a previous implementation of the stable model semantics, the Smodels system, and is publicly available. It contains, e.g., builtdin integer arithmetic integrated to stable model computation. The implementation is described briefly and some test results illustrating the current level of performance are reported.

Logic programs with stable model semantics as a constraint programming paradigm

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

Answer set programming at a glance

In this paper we reexamine the place and role of stable model semantics in logic programming and contrast it with a least Herbrand model approach to Horn programs We demonstrate that inherent features of stable model semantics naturally lead to a logic programming system that offers an interesting alternative to more traditional logic programming styles of Horn logic programming, stratified logic programming and logic programming with well-founded semantics The proposed approach is based on the interpretation of program clauses as constraints In this setting, a program does not describe a single intended model, but a family of its stable models These stable models encode solutions to the constraint satisfaction problem described by the program Our approach imposes restrictions on the syntax of logic programs In particular, function symbols are eliminated from the language We argue that the resulting logic programming system is well-attuned to problems in the class NP, has a well-defined domain of applications, and an emerging methodology of programming We point out that what makes the whole approach viable is recent progress in implementations of algorithms to compute stable models of propositional logic programs

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Stable Models and an Alternative Logic Programming Paradigm

The addition of aggregates has been one of the most relevant enhancements to the language of answer set programming (ASP). They strengthen the modeling power of ASP, in terms of concise problem representations. While many important problems can be encoded using nonrecursive aggregates, some relevant examples lend themselves for the use of recursive aggregates. Previous semantic definitions typically agree in the nonrecursive case, but the picture is less clear for recursion. Some proposals explicitly avoid recursive aggregates, most others differ, and many of them do not satisfy desirable criteria, such as minimality or coincidence with answer sets in the aggregate-free case.

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Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity

dlv is a knowledge representation system, based on disjunctive logic programming, which ooers front-ends to several advanced KR formalisms. The system has been developed since one year at the Technical University of Vienna in an ongoing project funded by the Austrian Science Funds. After a report on the current state of the art in the implementation of dlv and of its application front-ends, the paper compares dlv with other knowledge representation systems. Both a qualitative and a quantitative comparison are carried out. The rst compares the representational power of the systems (intended as the ability to represent problems in a natural and simple fashion). The latter compares the performances of the systems. The dlv system turns out to be very powerful from the knowledge representation side and, on the other hand, quite good also in computational power.

The KR system dlv: progress report, comparisons and benchmarks

Disjunctive Deductive Databases (DDDBs) — function-free disjunctive logic programs with negation in rule bodies allowed — have been recently recognized as a powerful tool for knowledge representation and commonsense reasoning. Much research has been spent on issues like semantics and complexity of DDDBs, but the important area of implementing DDDBs has been less addressed so far. However, a thorough investigation thereof is a basic requirement for building systems which render previous foundational work on DDDBs useful for practice.

A Deductive System for Non-Monotonic Reasoning

The need for representing indefinite information led to disjunctive deductive databases, which also fertilized work on disjunctive logic programming. Base on this paradigm, the DLV system has been designed and implemented as a tool for declarative knowledge representation. In this paper, we focus on the usage of DLV for solving problems in a declarative manner and report on experiments that we have run on a suite of benchmark problems. We discuss how problems can be solved in a natural way using a "Guess&Check"-paradigm where solutions are guessed and verified by parts of the program. Furthermore, we describe various front-ends that can be used for solving problems in specific applications. The experiments show that due to the ongoing implementation efforts, which include fine -tuning of the underlying algorithms, successive and significant performance improvements have been achieved during the last two years. The results indicate that DLV is capable of solving some complex problems quite efficiently.

Gerald Pfeifer

Papers

The DLV system for knowledge representation and reasoning

Recursive Aggregates in Disjunctive Logic Programs: Semantics and Complexity

The KR system dlv: progress report, comparisons and benchmarks

A Deductive System for Non-Monotonic Reasoning

Declarative problem-solving using the DLV system