Transformation Rules for Locally Stratified Constraint Logic Programs

We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally stratified and, thus, it has a unique perfect model. We give sufficient conditions which ensure that the proposed set of transformation rules preserves the perfect model of the programs. Our rules extend in some respects the rules for logic programs and constraint logic programs already considered in the literature and, in particular, they include a rule for unfolding a clause with respect to a negative literal.Comment: To appear in: M. Bruynooghe, K.-K. Lau (Eds.) Program Development in Computational Logic, Lecture Notes in Computer Science, Springe

Pac-learning Recursive Logic Programs: Negative Results

In a companion paper it was shown that the class of constant-depth determinate k-ary recursive clauses is efficiently learnable. In this paper we present negative results showing that any natural generalization of this class is hard to learn in Valiant's model of pac-learnability. In particular, we show that the following program classes are cryptographically hard to learn: programs with an unbounded number of constant-depth linear recursive clauses; programs with one constant-depth determinate clause containing an unbounded number of recursive calls; and programs with one linear recursive clause of constant locality. These results immediately imply the non-learnability of any more general class of programs. We also show that learning a constant-depth determinate program with either two linear recursive clauses or one linear recursive clause and one non-recursive clause is as hard as learning boolean DNF. Together with positive results from the companion paper, these negative results establish a boundary of efficient learnability for recursive function-free clauses.Comment: See http://www.jair.org/ for any accompanying file

A Program-Level Approach to Revising Logic Programs under the Answer Set Semantics

An approach to the revision of logic programs under the answer set semantics is presented. For programs P and Q, the goal is to determine the answer sets that correspond to the revision of P by Q, denoted P * Q. A fundamental principle of classical (AGM) revision, and the one that guides the approach here, is the success postulate. In AGM revision, this stipulates that A is in K * A. By analogy with the success postulate, for programs P and Q, this means that the answer sets of Q will in some sense be contained in those of P * Q. The essential idea is that for P * Q, a three-valued answer set for Q, consisting of positive and negative literals, is first determined. The positive literals constitute a regular answer set, while the negated literals make up a minimal set of naf literals required to produce the answer set from Q. These literals are propagated to the program P, along with those rules of Q that are not decided by these literals. The approach differs from work in update logic programs in two main respects. First, we ensure that the revising logic program has higher priority, and so we satisfy the success postulate; second, for the preference implicit in a revision P * Q, the program Q as a whole takes precedence over P, unlike update logic programs, since answer sets of Q are propagated to P. We show that a core group of the AGM postulates are satisfied, as are the postulates that have been proposed for update logic programs

Symmetries in logic programs

We investigate the structures and above all, the applications of a class of symmetric groups induced by logic programs. After establishing the relationships between minimal models of logic programs and their simplified forms, and models of their completions, we show that in general when deriving negative information, we can apply the CWA, the GCWA, and the completion procedure directly from some simplified forms of the original logic programs. The least models and the results of SLD-resolution stay invariant for definite logic programs and their simplified forms. The results of SLDNF-resolution, the standard or perfect models stay invariant for hierarchical, stratified logic programs and some of their simplified forms, respectively. We introduce a new proposal to derive negative information termed OCWA, as well as the new concepts of quasi-definite, quasi-hierarchical and quasi-stratified logic programs. We also propose semantics for them

Inconsistency and Incompleteness in Relational Databases and Logic Programs

The aim of this thesis is to study the role played by negation in databases and to develop data models that can handle inconsistent and incomplete information. We develop models that also allow incompleteness through disjunctive information under both the CWA and the OWA in relational databases. In the area of logic programming, extended logic programs allow explicit representation of negative information. As a result, a number of extended logic programs have an inconsistent semantics. We present a translation of extended logic programs to normal logic programs that is more tolerant to inconsistencies. Extended logic programs have also been used widely in order to compute the repairs of an inconsistent database. We present some preliminary ideas on how source information can be incorporated into the repair program in order to produce a subset of the set of all repairs based on a preference for certain sources over others

Logic-Based Decision Support for Strategic Environmental Assessment

Strategic Environmental Assessment is a procedure aimed at introducing systematic assessment of the environmental effects of plans and programs. This procedure is based on the so-called coaxial matrices that define dependencies between plan activities (infrastructures, plants, resource extractions, buildings, etc.) and positive and negative environmental impacts, and dependencies between these impacts and environmental receptors. Up to now, this procedure is manually implemented by environmental experts for checking the environmental effects of a given plan or program, but it is never applied during the plan/program construction. A decision support system, based on a clear logic semantics, would be an invaluable tool not only in assessing a single, already defined plan, but also during the planning process in order to produce an optimized, environmentally assessed plan and to study possible alternative scenarios. We propose two logic-based approaches to the problem, one based on Constraint Logic Programming and one on Probabilistic Logic Programming that could be, in the future, conveniently merged to exploit the advantages of both. We test the proposed approaches on a real energy plan and we discuss their limitations and advantages.Comment: 17 pages, 1 figure, 26th Int'l. Conference on Logic Programming (ICLP'10