Gérard Ferrand

Error diagnosis in logic programming, an adaptation of E.Y. Shapiro's method

Abstract We study Shapiros method of bug diagnosis in the theoretical framework of Horn clause logic programming. Within the framework of Clarks semantics (Herbrands universe with variables, which is more general than the most usual semantics without variables) we extend the scope of fixpoint and declarative semantics of logic programming.

Declarative Diagnosis in the CLP Scheme

When a result is computed but it is considered as incorrect because it is not expected, we consider that we have a symptom (of error). The symptom may be a wrong answer or a missing answer. The role of diagnosis is to locate an error, that is a limited program fragment responsible for the symptom. The notions of symptom and error have a meaning only w.r.t. some notion of expected semantics. We consider only declarative semantics. The user does not need to understand the operational behaviour of the CLP system. Symptom and error are connected via some kind of tree and the diagnosis amounts to search for a kind of minimal symptom in this tree. Several search strategies are possible. The principles of an implementation are described, with a diagnosis session.

The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs

The aim of this paper is to explain, in a tutorial style, the notions of symptom and error, and the relation between symptom and error, in declarative diagnosis of logic programs. The emphasis is on the declarative nature of these notions (they do not depend on a particular computational behaviour). Our framework is not a logical formalism but an inductive formalism.

PROOF METHOD OF PARTIAL CORRECTNESS AND WEAK COMPLETENESS FOR NORMAL LOGIC PROGRAMS

Abstract We present a proof method for partial correctness and weak completeness for any normal programs, which coincides with the already known proof methods for partial correctness and completeness for definite programs. The purpose of such a validation method is to compare the actual semantics of a program with some expected properties, sometimes called specifications. We consider that the actual semantics of a normal program is the three-valued well-founded semantics . Thus the actual semantics of a program is defined by two sets of ground atoms: the set of the true atoms and the set of the false atoms. The expected properties may be formulated also by two sets of ground atoms; partial correctness and weak completeness are formulated by set inclusions. Soundness and completeness of our proof method comes from an inductive characterization of the well-founded model. The method may be used also to prove that some given set of atoms characterizes exactly the set of true atoms, if the semantics is in fact bivalued and the specification is total.

Theoretical Foundations of Value Withdrawal Explanations for Domain Reduction

Solvers on finite domains use local consistency notions to remove values from the domains. This paper defines value withdrawal explanations. Domain reduction is formalized with chaotic iterations of monotonic operators. To each operator is associated its dual which will be described by a set of rules. For classical consistency notions, there exists a natural such system of rules. They express value removals as consequences of other value removals. The linking of these rules inductively defines proof trees. Such a proof tree clearly explains the removal of a value (the root of the tree). Explanations can be considered as the essence of domain reduction.

A Logic Program Characterization of Domain Reduction Approximations in Finite Domain CSPs

We provide here a declarative and model-theoretic characterization of the approximations computed by consistency during the resolution of finite domain constraint satisfaction problems.