Francesco Scarcello

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.

A comparison of structural CSP decomposition methods

Abstract We compare tractable classes of constraint satisfaction problems (CSPs). We first give a uniform presentation of the major structural CSP decomposition methods. We then introduce a new class of tractable CSPs based on the concept of hypertree decomposition recently developed in Database Theory, and analyze the cost of solving CSPs having bounded hypertree-width. We provide a framework for comparing parametric decomposition-based methods according to tractability criteria and compare the most relevant methods. We show that the method of hypertree decomposition dominates the others in the case of general CSPs (i.e., CSPs of unbounded arity). We also make comparisons for the restricted case of binary CSPs. Finally, we consider the application of decomposition methods to the dual graph of a hypergraph. In fact, this technique is often used to exploit binary decomposition methods for nonbinary CSPs. However, even in this case, the hypertree-decomposition method turns out to be the most general method.

The complexity of acyclic conjunctive queries

This paper deals with the evaluation of acyclic Booleanconjunctive queries in relational databases. By well-known resultsof Yannakakis[1981], this problem is solvable in polynomial time;its precise complexity, however, has not been pinpointed so far. Weshow that the problem of evaluating acyclic Boolean conjunctivequeries is complete for LOGCFL, the class of decision problems thatare logspace-reducible to a context-free language. Since LOGCFL iscontained in AC1 and NC2, the evaluation problem of acyclic Booleanconjunctive queries is highly parallelizable. We present a paralleldatabase algorithm solving this problem with alogarithmic number ofparallel join operations. The algorithm is generalized to computingthe output of relevant classes of non-Boolean queries. We also showthat the acyclic versions of the following well-known database andAI problems are all LOGCFL-complete: The Query Output Tuple problemfor conjunctive queries, Conjunctive Query Containment, ClauseSubsumption, and Constraint Satisfaction. The LOGCFL-completenessresult is extended to the class of queries of bounded tree widthand to other relevant query classes which are more general than theacyclic queries.

A Deductive System for Non-Monotonic Reasoning

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.

Disjunctive Stable Models

Disjunctive logic programs have become a powerful tool in knowledge representation and commonsense reasoning. This paper focuses on stable model semantics, currently the most widely acknowledged semantics for disjunctive logic programs. After presenting a new notion of unfounded sets for disjunctive logic programs, we provide two declarative characterizations of stable models in terms of unfounded sets. One shows that the set of stable models coincides with the family of unfounded-free models (i.e., a model is stable iff it contains no unfounded atoms). The other proves that stable models can be defined equivalently by a property of their false literals, as a model is stable iff the set of its false literals coincides with its greatest unfounded set. We then generalize the well-founded WPoperator to disjunctive logic programs, give a fixpoint semantics for disjunctive stable models and present an algorithm for computing the stable models of function-free programs. The algorithms soundness and completeness are proved and some complexity issues are discussed.

Hypertree decompositions and tractable queries

1 A preliminary version of this paper appeared in the ‘‘Proceedings of the Eighteenth ACM Symposium on Principles of Database Systems (PODS’99),’’ pp. 21–32, Philadelphia, May 1999. Research supported by FWF (Austrian Science Funds) under the Project Z29-INF. Part of the work of Francesco Scarcello has been carried out while visiting the Technische Universitat Wien. Part of the work of Nicola Leone has been carried out while he was with the Technische Universitat Wien. Georg Gottlob

Pure Nash equilibria: hard and easy games

In this paper we investigate complexity issues related to pure Nash equilibria of strategic games. We show that, even in very restrictive settings, determining whether a game has a pure Nash Equilibrium is NP-hard, while deciding whether a game has a strong Nash equilibrium is ΣP2-complete. We then study practically relevant restrictions that lower the complexity. In particular, we are interested in quantitative and qualitative restrictions of the way each players move depends on moves of other players. We say that a game has small neighborhood if the utility function for each player depends only on (the actions of) a logarithmically small number of other players, The dependency structure of a game 𝒢 can he expressed by a graph G(𝒢) or by a hypergraph H(𝒢). Among other results, we show that if 𝒢 has small neighborhood and if H(𝒢) has bounded hypertree width (or if G(𝒢) has bounded treewidth), then finding pure Nash and Pareto equilibria is feasible in polynomial time. If the game is graphical, then these problems are LOGCFL-complete and thus in the class NC2 of highly parallelizable problems.

Hypertree Decompositions: A Survey

This paper surveys recent results related to the concept of hypertree decomposition and the associated notion of hypertree width. A hypertree decomposition of a hypergraph (similar to a tree decomposition of a graph) is a suitable clustering of its hyperedges yielding a tree or a forest. Important NP hard problems become tractable if restricted to instances whose associated hypergraphs are of bounded hypertree width. We also review a number of complexity results on problems whose structure is described by acyclic or nearly acyclic hypergraphs.

Fixed-parameter complexity in AI and nonmonotonic reasoning

Many relevant intractable problems become tractable if some problem parameter is fixed. However, various problems exhibit very different computational properties, depending on how the runtime required for solving them is related to the fixed parameter chosen. The theory of parameterized complexity deals with such issues, and provides general techniques for identifying fixed-parameter tractable and fixed-parameter intractable problems. We study the parameterized complexity of various problems in AI and nonmonotonic reasoning. We show that a number of relevant parameterized problems in these areas are fixed-parameter tractable. Among these problems are constraint satisfaction problems with bounded treewidth and fixed domain, restricted forms of conjunctive database queries, restricted satisfiability problems, propositional logic programming under the stable model semantics where the parameter is the dimension of a feedback vertex set of the programs dependency graph, and circumscriptive inference from a positive k-CNF restricted to models of bounded size. We also show that circumscriptive inference from a general propositional theory, when the attention is restricted to models of bounded size, is fixed-parameter intractable and is actually complete for a novel fixed-parameter complexity class.

Hypertree decompositions: structure, algorithms, and applications

We review the concepts of hypertree decomposition and hypertree width from a graph theoretical perspective and report on a number of recent results related to these concepts. We also show – as a new result – that computing hypertree decompositions is fixed-parameter intractable.