Inconsistency Measurement based on Variables in Minimal Unsatisfiable Subsets

International audienceMeasuring inconsistency degrees of knowledge bases (KBs) provides important context information for facilitating inconsistency handling. Several semantic and syntax based measures have been proposed separately. In this paper, we propose a new way to define inconsistency measurements by combining semantic and syntax based approaches. It is based on counting the variables of minimal unsatisfiable subsets (MUSes) and minimal correction subsets (MCSes), which leads to two equivalent inconsistency degrees, named IDMUS and IDMCS. We give the theoretical and experimental comparisons between them and two purely semantic-based inconsistency degrees: 4-valued and the Quasi Classical semantics based inconsistency degrees. More- over, the computational complexities related to our new inconsistency measurements are studied. As it turns out that computing the exact inconsistency degrees is intractable in general, we then propose and evaluate an anytime algorithm to make IDMUS and IDMCS usable in knowledge management applications. In particular, as most of syntax based measures tend to be difficult to compute in reality due to the exponential number of MUSes, our new inconsistency measures are practical because the numbers of variables in MUSes are often limited or easily to be approximated. We evaluate our approach on the DC benchmark. Our encourag- ing experimental results show that these new inconsistency measure- ments or their approximations are efficient to handle large knowledge bases and to better distinguish inconsistent knowledge bases

MUS-Based Partitioning for Inconsistency Measures

National audienceMesurer le degré d'incohérence des bases de connaissances permet aux agents une meilleur compréhension de leur environnement. Différentes approches sémantiques et syntaxiques ont été proposées pour quantifier l'incohérence. Dans ce papier, nous proposons d'analyser les limites des approches existantes. Tout d'abord, nous explorons la propriété logique d'additivité en considérant les composantes connexes du graphe représentant les bases de connaissances. Ensuite, nous montrons comment la structure de ce graphe peut être prise en compte pour identifier d'une manière plus fine la responsabilité de chaque formule dans l'incohérence. Finalement, nous étendons notre approche pour fournir une mesure d'incohérence de la base entière en satisfaisant des propriétés définies

Measures of inconsistency and defaults

AbstractWe introduce a method for measuring inconsistency based on the number of formulas needed for deriving a contradiction. The relationships to previously considered methods based on probability measures are discussed. Those methods are extended to conditional probability and default reasoning

Belief Revision, Minimal Change and Relaxation: A General Framework based on Satisfaction Systems, and Applications to Description Logics

Belief revision of knowledge bases represented by a set of sentences in a given logic has been extensively studied but for specific logics, mainly propositional, and also recently Horn and description logics. Here, we propose to generalize this operation from a model-theoretic point of view, by defining revision in an abstract model theory known under the name of satisfaction systems. In this framework, we generalize to any satisfaction systems the characterization of the well known AGM postulates given by Katsuno and Mendelzon for propositional logic in terms of minimal change among interpretations. Moreover, we study how to define revision, satisfying the AGM postulates, from relaxation notions that have been first introduced in description logics to define dissimilarity measures between concepts, and the consequence of which is to relax the set of models of the old belief until it becomes consistent with the new pieces of knowledge. We show how the proposed general framework can be instantiated in different logics such as propositional, first-order, description and Horn logics. In particular for description logics, we introduce several concrete relaxation operators tailored for the description logic \ALC{} and its fragments \EL{} and \ELext{}, discuss their properties and provide some illustrative examples

Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity

[EN] To maintain integrity, constraint violations should be prevented or repaired. However, it may not be feasible to avoid inconsistency, or to repair all violations at once. Based on an abstract concept of violation measures, updates and repairs can be checked for keeping inconsistency bounded, such that integrity violations are guaranteed to never get out of control. This measure-based approach goes beyond conventional methods that are not meant to be applied in the presence of inconsistency. It also generalizes recently introduced concepts of inconsistency-tolerant integrity maintenance.Partially supported by FEDER and the Spanish grants TIN2009-14460-C03 and TIN2010-17139Decker, H. (2013). Measure-Based Inconsistency-Tolerant Maintenance of Database Integrity. Lecture Notes in Computer Science. 7693:149-173. https://doi.org/10.1007/978-3-642-36008-4_7S1491737693Abiteboul, S., Hull, R., Vianu, V.: Foundations of Databases. 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