G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40-57. Springer-Verlag, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....Definition 1. A grammar G is incorrect w.r.t. an (intended) language L T , if L 6 L(G) Here, L(G) denotes the language generated by G. The grammar G is incomplete w.r.t. L if L 6 L(G) The definition is inspired by a point of view as favoured in the diagnosis of logic programs (cf. [6]) The problem with the definition is that the intended language L is not directly accessible. Also, we need to know how to locate incorrect or incomplete phrases in the grammar, and how to correct and complete them. Finally, incorrectness and incompleteness are intertwined. An incorrect phrase ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. Fritzon, editor, Automated and Algorithmic Debugging, First International Workshop, AADEBUG'93, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 3--5 May 1993.

....correctness of a grammar that is obtained in this way. The kind of restricted correctness we can claim is the following. The generated parser parses all the available code that is also parsed by the compiler. From a different perspective pursued for example in the logic programming community [41, 26], the statement that a parser parses a given test set successfully can be also regarded as a kind of completeness statement. Correctness might be then conceived as the property that the underlying grammar is fully covered by the test set according to a suitable coverage criterion such as rule ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. Fritzon, editor, Automated and Algorithmic Debugging, First International Workshop, AADEBUG'93, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 3--5 May 1993.

....is one interesting and speci c property of logic programs, nite failure, which is not an abstraction of none of the semantics used in the above mentioned techniques and or veri cation frameworks. Diagnosis or veri cation of nite failure is somewhat related to the diagnosis of missing answers in [13], where the actual semantics is the greatest xpoint of the standard ground immediate consequences operator (i.e. the complement of a set of atoms which contains the nite failure set and some atoms whose execution does not terminate) However, if we want to verify properties of nite failures, ....

....nite failure. The corresponding abstract xpoint semantics correctly models nite failure and is and compositional. In this paper we take this semantics (shortly described in Section 2) as the basis for a veri cation method (de ned in Section 3) which extends to nite failure Ferrand s approach [13], which uses two semantics (a least xpoint and a greatest xpoint semantics) and two speci cations. In particular, we apply Ferrand s approach using a least xpoint semantics (T ff P ) and a T ff P # semantics. We obtain a nice interpretation for the veri cation w.r.t. T ff P # ....

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G. Ferrand. The notions of symptom and error in declarative diagnosis of logic programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, Proc. AADEBUG '93, volume 749 of Lecture Notes in Computer Science, pages 40-57. Springer-Verlag, 1993.

....(I) lfp T S u;I Gamma [ H Gamma lfp T e Sj H u;H GammaI ) Theorem 11 The semantics SEM u : S 7 Gamma lfp Psi S u is compositional if the system of units is positively hierarchical. Fitting s semantics : Fitting s semantics can be defined as the lfp of the following operator [12] : Phi u (I) lfp T u;I Gamma [ gfp T u;H GammaI . It is extended by the following operator : Phi S u (I) lfp T S u;I Gamma [ H Gamma gfp T e S j H u;H GammaI ) Theorem 12 The semantics SEM u : S 7 Gamma lfp Phi S u is compositional. 3.3 Validation results If the ....

G'erard Ferrand. The notion of symptom and error in declarative diagnosis of logic programs. In Automated and Algorithmic Debugging, Linkoping, 1993. Springer LNCS.

....insufficiency) a[c] is an incompleteness symptom (resp. insufficiency symptom) of P according to I if a[c] 2 I Gamma lfp(T ffi ;P ) resp. a[c] 2 I Gamma gfp(T ffi ;P ) The interest is that the definitions are formulated in a uniform framework and extend existing definitions of LP [18, 6, 5, 14, 3, 7, 16]. Thus, they are better understood, particularly thanks to proof trees and T ffi ;P . In the particular case of LP: our framework contributes to the comparison between above papers. Lemma 8. 1. If a[c] is a strong insufficiency then a[c] is a weak insufficiency. 2. There exists a strong ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 1993.

....definitions of LP. Thus, they are better understood, particularly thanks to proof trees and T ffi ;P . Particular case of LP is obtained when we change constraints by substitutions and the cover by the single cover less general . The uniform framework contributes to the comparison between [9, 8, 6, 19, 10, 5]. Lemma 4.2 1. If a[c] is a strong insufficiency then a[c] is a weak insufficiency. 2. There exists a strong insufficiency iff there exists a weak insufficiency. 3. If a[c] is an insufficiency symptom then a[c] is an incompleteness symptom. 4. There exists a strong insufficiency if there exists ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 1993.

....the validity of a constrained atom in I. That is to say, the interaction with the intended semantics is only based on constrained atoms. Therefore, the intended semantics can be formalized by a set of constrained atoms. We propose to use the notion of oracle O to formalize the intended semantics [17, 7, 15, 8]. O accepts or rejects constrained atoms in accordance with the intended semantics. Remark 36 An oracle O is such that O rejects c b 1 ; Delta Delta Delta ; b n iff there exists i 2 f1; Delta Delta Delta ; ng such that O rejects c b i iff there exists i 2 f1; Delta Delta Delta ; ....

G. Ferrand, The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs, AADEBUG'93, LNCS 749, pp 40-57, Springer-Verlag, 1993.

....But, only the intended declarative semantics of the program is required. Declarative error diagnosis in Logic Programming (LP) was introduced by E. Y. Shapiro [27] under the name of algorithmic debugging. Many techniques inspired by the Shapiro s method have been developed for logic programs [12, 11, 21, 8, 13, 7, 9, 22, 24, 3]. But, declarative diagnosis of constraint logic programs is relatively unexplored. We focus in this paper on the theoretical aspects of the declarative insufficiency diagnosis of constraint logic programs. That is, how to declaratively point a small piece of erroneous code when an answer is ....

G'erard Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 1993.

....turn out to be the same for the class of programs we are interested in (see Section 3) Ferrand s choice is motivated by the fact that gfp (T P ) is related to finite failures. The approach of using two different semantics for reasoning about incorrectness and incompleteness has been pursued in [9], leading to an elegant uniform (yet non effective) characterization of correctness and completeness. It is straightforward to realize that an atom may sometimes be an (incorrectness or incompleteness) symptom, just because of another symptom. The diagnosis determines the basic symptoms, and, ....

....that we know to be correct (G 2 I ) have to be computed answers. Note also that definition 5.1 is derived from Definition 3.1 by taking I Gamma and I as specifications to be used for correctness and completeness respectively. Positive and negative specifications have been used in [9] with the aim of separately modeling the behavior w.r.t. incorrectness and incompleteness. I and I Gamma are not partial specifications, rather they are specifications of the (complete) intended lfp (T P ) and of the (complete) intended gfp (T P ) The derived definitions and results are ....

G. Ferrand. The notions of symptom and error in declarative diagnosis of logic programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, Proc. AADEBUG '93, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, Berlin, 1993.

....As it is written in the introduction, constraint solving combines domain reduction and labeling. A perspective is to really take into account labeling in our model. 12 We plan to use explanations in order to diagnose errors in a CSP (according to an expected semantics) in the style of [15, 7]. Another perspective is to take advantage of the glass box model [5] and more generally the S box model [9] and to distinguish di erent levels of rules (x in r, built in constraints, S box, Acknowledgements Discussions with Patrice Boizumault and Narendra Jussien are gracefully ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40-57. Springer-Verlag, 1993.

.... would be incoherent to use only low level debugging tools whereas theses languages benefit from a declarative semantics (as opposed to operational semantics) Declarative Debugging (DD) was introduced in Logic Programming (LP) by Shapiro (and called Algorithmic Program Debugging [24] see also [8, 14, 6, 7, 21, 5, 18, 19]) Declarative means that the user has no need to consider the computational behaviour of the logic programming system, he needs only a declarative knowledge of the expected properties of the program. The previous reflections on symptoms and errors can be applied to Constraint Logic Programming ....

....17] to what extent it depends on the standard computation rule and how it can be generalized to CLP) The paper is only devoted to the theoretical basis of the approach. 2 Abstract Notions of Symptoms and Errors for Inductive Definitions Symptom and errors can be defined in an abstract scheme ([7, 19]) They have been first defined for definite programs by Shapiro ( 24] using essentially an inductive framework: on the one hand least fixpoint, i.e. induction, for the relation between incorrectness symptom ( wrong answer ) and incorrectness (a kind of error) on the other hand greatest ....

[Article contains additional citation context not shown here]

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 1993.

....the expected semantics can be given by the programmer during the diagnosis session or it can be specified by other means but, in any case, from a conceptual viewpoint, this information is given by an oracle. 2 Abstract Symptoms and Errors Symptom and errors can be defined in an abstract scheme ([18, 32]) They have been first defined for definite programs by Shapiro ( 39] using essentially an inductive framework: on the one hand least fixpoint, i.e. induction, for the relation between incorrectness symptom ( wrong answer ) and incorrectness (a kind of error) on the other hand greatest ....

....which are effectively computed by SLD resolution or finite failure. In this framework with lfp(T ) on the one hand and gfp(T ) on the other hand, we can consider positive and negative information together. This framework can be generalized to logic programs with negation (normal programs) [18, 4]) Fitting semantics ( 19] gives a logical view for this framework. Again each symptom is linked to some error but now any interaction is possible through negations between symptom and error, so wrong (resp. missing) answers are not necessary linked to incorrectness (resp. insufficiency) In ....

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. Springer-Verlag, 1993.

....allows us to remain in a purely set theoretical framework. However, in practice, sets of literals are likely to be represented by logical assertions and sets of ground rules by programs. A proof method of partial correctness has been given in [8] for the wellfounded semantics, and indirectly in [7] for Fitting s semantics. The dual approach completeness , has been studied by Malfon [17] in a framework which unifies the well founded, Fitting and Kunen s semantics. But these results do only concern what is called programming in the small and for larger programs, these non compositional ....

....is any set of atoms. We say that : ffl P is partially correct wrt S iff lfp T P S. ffl P is complete wrt C iff C lfp T P . If we replace lfp by gfp (greatest fixed point) we get another notion : ffl P is sufficient wrt C iff C gfp T P . Sufficiency has a close relationship with debugging [7]. In this paper, we will call these properties atomic properties since they only deal with sets of atoms. 2.2 Normal programs In this paper, we use the following notations. ffl HB denotes the Herbrand base. ffl For a 2 HB, Gammaa = a, Gamma:a = a and jaj = j:aj = a. ffl If A HB is a set ....

[Article contains additional citation context not shown here]

G'erard Ferrand. The notion of symptom and error in declarative diagnosis of logic programs. In Automated and Algorithmic Debugging, Linkoping, 1993. Springer LNCS.

.... it would be incoherent to use only low level debugging tools whereas theses languages benefit from a declarative semantics (as opposed to operational semantics) Declarative Debugging was introduced in Logic Programming (LP) by Shapiro (and called Algorithmic Program Debugging [18] see also [11, 5, 6, 17, 4, 15, 16]) Declarative means that the user has no need to consider the computational behaviour of the logic programming system, he needs only a declarative knowledge of the expected properties of the program. The previous reflections on symptoms and errors can be applied to Constraint Logic Programming ....

....in a top down computation) Because of compositionality, it is sufficient to consider positive symptoms c G where G is just an atom and negative symptoms G c 1 Delta Delta Delta c n where G is just the conjunction of a constraint and an atom. In former works on declarative debugging ([18, 6, 11]) the duality positive negative was not introduced in the same way. From an abstract viewpoint the former notions of incorrectness symptom and insufficiency symptom can be defined in an inductive framework, to be more precise induction (least fixpoint) for incorrectness and co induction ....

[Article contains additional citation context not shown here]

G. Ferrand. The Notions of Symptom and Error in Declarative Diagnosis of Logic Programs. In P. A. Fritzson, editor, Automated and Algorithmic Debugging, volume 749 of Lecture Notes in Computer Science, pages 40--57. SpringerVerlag, 1993.

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