This paper surveys various complexity results on different forms of logic programming. The main focus is on decidable forms of logic programming, in particular, propositional logic programming and datalog, but we also mention general logic programming with function symbols. Next to classical results on plain logic programming (pure Horn clause programs), more recent results on various important extensions of logic programming are surveyed. These include logic programming with different forms of negation, disjunctive logic programming, logic programming with equality, and constraint logic programming. The complexity of the unification problem is also addressed.

In this paper, we review recent work aimed at the application of declarative logic programming to knowledge representation in artificial intelligence. We consider exten- sions of the language of definite logic programs by classical (strong) negation, disjunc- tion, and some modal operators and show how each of the added features extends the representational power of the language.

Abduction is an important form of nonmonotonic reasoning allowing one to find explanations for certain symptoms or manifestations. When the application domain is described by a logical theory, we speak about logic-based abduction. Candidates for abductive explanations are usually subjected to minimality criteria such as subsetminimality, minimal cardinality, minimal weight, or minimality under prioritization of individual hypotheses. This paper presents a comprehensive complexity analysis of relevant decision and search problems related to abduction on propositional theories. Our results indicate that abduction is harder than deduction. In particular, we show that with the most basic forms of abduction the relevant decision problems are complete for complexity classes at the second level of the polynomial hierarchy, while the use of prioritization raises the complexity to the third level in certain cases.

The high computational complexity of advanced reasoning tasks such as reasoning about knowledge and planning calls for efficient and reliable algorithms for reasoning problems harder than NP. In this paper we propose Evaluate, an algorithm for evaluating Quantified Boolean Formulae, a language that extends propositional logic in a way such that many advanced forms of propositional reasoning, e.g., circumscription, can be easily formulated as evaluation of a QBF. Algorithms for evaluation of QBFs are suitable for the experimental analysis on a wide range of complexity classes, a property not easily found in other formalisms. Evaluate is based on a generalization of the Davis-Putnam procedure for SAT, and is guaranteed to work in polynomial space. Before presenting the algorithm, we discuss several abstract properties of QBFs that we singled out to make it more efficient. We also discuss various options that were investigated about heuristics and data structures, and report the main res...

In databases with integrity constraints, data may not satisfy the constraints. In this paper, we address the problem of obtaining consistent answers in such a setting, when key and inclusion dependencies are expressed on the database schema. We establish decidability and complexity results for query answering under different assumptions on data (soundness and/or completeness). In particular, after showing that the problem is in general undecidable, we identify the maximal class of inclusion dependencies under which query answering is decidable in the presence of key dependencies. Although obtained in a single database context, such results are directly applicable to data integration, where multiple information sources may provide data that are inconsistent with respect to the global view of the sources. 1.

this paper we survey recent results in knowledge compilation of propositional knowledge bases. We first define and limit the scope of such a technique, then we survey exact and approximate knowledge compilation methods. We include a discussion of compilation for non-monotonic knowledge bases. Keywords: Knowledge Representation, Efficiency of Reasoning

This paper surveys the main results appeared in the literature on the computational complexity of non-monotonic inference tasks. We not only give results about the tractability/intractability of the individual problems but we also analyze sources of complexity and explain intuitively the nature of easy/hard cases. We focus mainly on non-monotonic formalisms, like default logic, autoepistemic logic, circumscription, closed-world reasoning and abduction, whose relations with logic programming are clear and well studied. Complexity as well as recursion-theoretic results are surveyed. Work partially supported by the ESPRIT Basic Research Action COMPULOG and the Progetto Finalizzato Informatica of the CNR (Italian Research Council). The first author is supported by a CNR scholarship 1 Introduction Non-monotonic logics and negation as failure in logic programming have been defined with the goal of providing formal tools for the representation of default information. One of the ideas und...

Closed-world inference is the process of determining that a logical sentence is false based on its absence from a knowledge base, or the inability to derive it. This process is essential for planning with incomplete information. We describe a novel method for closed-world inference and update over the first-order theories of action used by planning algorithms such as NONLIN, TWEAK, and UCPOP. We show the method to be sound and efficient, but incomplete. In our experiments, closed-world inference consistently averaged about 2 milliseconds, while updates averaged approximately 1.2 milliseconds. We incorporated the method into the XII planner, which supports our Internet Softbot (software robot). The method cut the number of actions executed by the Softbot bya factor of one hundred, and resulted in a corresponding speedup to XII. 1

Abstract. We introduce the notion of combinatorial vote, where a group of agents (or voters) is supposed to express preferences and come to a common decision concerning a set of non-independent variables to assign. We study two key issues pertaining to combinatorial vote, namely preference representation and the automated choice of an optimal decision. For each of these issues, we briefly review the state of the art, we try to define the main problems to be solved and identify their computational complexity.

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