In this paper, we address the issue of how Gelfond and Lifschitz's answer set semantics for extended logic programs can be suitably modified to handle prioritized programs. In such programs an ordering on the program rules is used to express preferences. We show how this ordering can be used to define preferred answer sets and thus to increase the set of consequences of a program. We define a strong and a weak notion of preferred answer sets. The first takes preferences more seriously, while the second guarantees the existence of a preferred answer set for programs possessing at least one answer set. Adding priorities

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Model checking is an automatic verification technique for finite state concurrent systems. In this approach to verification, temporal logic specifications are checked by an exhaustive search of the state space of the concurrent system. Since the size of the state space grows exponentially with the number of processes, model checking techniques based on explicit state enumeration can only handle relatively small examples. This phenomenon is commonly called the "State Explosion Problem". Over the past ten years considerable progress has been made on this problem by (1) representing the state space symbolically using BDDs and by (2) using abstraction to reduce the size of the state space that must be searched. As a result model checking has been used successfully to find extremely subtle errors in hardware controllers and communication protocols. In spite of these successes, however, additional research is needed to handle large designs of industrial complexity. This aim of this paper is to give a succinct survey of symbolic model checking and to introduce the reader to recent advances in abstraction. 1

In this paper we show that Datalog is well-suited as a temporal verification language. Datalog is a well-known database query language relying on the logic programming paradigm. We introduce Datalog LITE, a fragment of Datalog with negation, and present a linear time model checking algorithm for Datalog LITE. We show that Datalog LITE subsumes temporal languages such as CTL and the alternation-free -calculus, and in fact give easy syntactic characterizations of these temporal languages. We prove that Datalog LITE has the same expressive power as the alternation-free portion of guarded fixed point logic.

We survey recent results about the relation between Datalog and temporal verification logics. Datalog is a well-known database query language relying on the logic programming paradigm. We introduce Datalog LITE, a fragment of Datalog with well-founded negation, which has an easy stratified semantics and a linear time model checking algorithm. Datalog LITE subsumes temporal languages such as CTL and the alternation-free -calculus. We give easy syntactic characterizations of these temporal languages by fragments of Datalog LITE, and show that Datalog LITE has the same expressive power as the alternation-free portion of guarded fixed point logic.

Generalized quantifiers are an important concept in modeltheoretic logic which has applications in different fields such as linguistics, philosophical logic and computer science. In this paper, we consider a novel application in the field of logic programming, which has been presented recently. The enhancement of logic programs by generalized quantifiers is a convenient tool for interfacing extra-logical functions and provides a natural framework for the definition of modular logic programs.

Hierarchical graph definitions allow a modular description of structures using modules for the specification of repeated substructures. Beside this modularity, hierarchical graph definitions allow to specify structures of exponential size using polynomial size descriptions. In many cases, this succinctness increases the computational complexity of decision problems when input structures are defined hierarchically. In this paper, the model-checking problem for first-order logic (FO), monadic second-order logic (MSO), and second-order logic (SO) on hierarchically defined input structures is investigated. It is shown that in general these model-checking problems are exponentially harder than their non-hierarchical counterparts, where the input structures are given explicitly. As a consequence, several new complete problems for the levels of the polynomial time hierarchy and the exponential time hierarchy are obtained. Based on classical results of Gaifman and Courcelle, two restrictions on the structure of hierarchical graph definitions that lead to more efficient model-checking algorithms are presented.

We study the complexity of data disjunctions in disjunctive deductive databases (DDDBs), i.e., minimal clauses R(c 1 ) \Delta \Delta \Delta R(c k ), k 2, derived from the database in which all atoms involve the same predicate R. We consider deciding existence and uniqueness of a data disjunction, as well as actually computing one, both for propositional (data) and nonground (program) complexity of the database. Our results extend and complement previous results on the complexity of disjunctive databases, and provide tools for the analysis of the complexity of function computation using upgrading techniques, which we develop for this purpose.