Semantic inconsistency measures using 3-valued logics

AI systems often need to deal with inconsistencies. One way of getting information about inconsistencies is by measuring the amount of information in the knowledgebase. In the past 20 years numerous inconsistency measures have been proposed. Many of these measures are syntactic measures, that is, they are based in some way on the minimal inconsistent subsets of the knowledgebase. Very little attention has been given to semantic inconsistency measures, that is, ones that are based on the models of the knowledgebase where the notion of a model is generalized to allow an atom to be assigned a truth value that denotes contradiction. In fact, only one nontrivial semantic inconsistency measure, the contension measure, has been in wide use. The purpose of this paper is to define a class of semantic inconsistency measures based on 3-valued logics. First, we show which 3-valued logics are useful for this purpose. Then we show that the class of semantic inconsistency measures can be developed using a graphical framework similar to the way that syntactic inconsistency measures have been studied. We give several examples of semantic inconsistency measures and show how they apply to three useful 3-valued logics. We also investigate the properties of these inconsistency measures and show their computation for several knowledgebases

Analysing inconsistent information using distance-based measures

There have been a number of proposals for measuring inconsistency in a knowledgebase (i.e. a set of logical formulae). These include measures that consider the minimally inconsistent subsets of the knowledgebase, and measures that consider the paraconsistent models (3 or 4 valued models) of the knowledgebase. In this paper, we present a new approach that considers the amount by which each formula has to be weakened in order for the knowledgebase to be consistent. This approach is based on ideas of knowledge merging by Konienczny and Pino-Perez. We show that this approach gives us measures that are different from existing measures, that have desirable properties, and that can take the significance of inconsistencies into account. The latter is useful when we want to differentiate between inconsistencies that have minor significance from inconsistencies that have major significance. We also show how our measures are potentially useful in applications such as evaluating violations of integrity constraints in databases and for deciding how to act on inconsistency

Finding problems in knowledge bases using modal logics

In this paper I propose that it is suitable to consider some statements that an expert makes during knowledge elicitation as being statements in a modal logic. This approach gives us several advantages in finding inconsistencies between a knowledge base and an expert's intuition in her field. I illustrate this approach by using the modal logic VC, a logic of counterfactual conditionals. In an appendix, I give brief details of theorem proving in VC

Paraconsistency in hybrid logic

As in standard knowledge bases, hybrid knowledge bases (i.e. sets of information specified by hybrid formulas) may contain inconsistencies arising from different sources, namely from the many mechanisms used to collect relevant information. Being a fact, rather than a queer anomaly, inconsistency also needs to be addressed in the context of hybrid logic applications. This article introduces a paraconsistent version of hybrid logic which is able to accommodate inconsistencies at local points without implying global failure. A main feature of the resulting logic, crucial to our approach, is the fact that every hybrid formula has an equivalent formula in negation normal form. The article also provides a measure to quantify the inconsistency of a hybrid knowledge base, useful as a possible basis for comparing knowledge bases. Finally, the concepts of extrinsic and intrinsic inconsistency of a theory are discussed

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

Paraconsistência em lógica híbrida

Mestrado em Matemática e AplicaçõesThe use of hybrid logics allows the description of relational structures, at the same time that allows establishing accessibility relations between states and, furthermore, nominating and making mention to what happens at speci c states. However, the information we collect is subject to inconsistencies, namely, the search for di erent information sources can lead us to pick up contradictions. Nowadays, by having so many means of dissemination available, that happens frequently. The aim of this work is to develop tools capable of dealing with contradictory information that can be described as hybrid logics' formulas. To build models, to compare inconsistency in di erent databases, and to see the applicability of this method in day-to-day life are the basis for the development of this dissertation.O uso de lógicas híbridas permite a descrição de estruturas relacionais, ao mesmo tempo que permite estabelecer relações de acessibilidade entre estados, e, para além disso, nomear e fazer referência ao que acontece em estados específicos. No entanto, a informação que recolhemos está sujeita a inconsistências, isto é, a procura de diferentes fontes de informação pode levar a recolha de contradições. O que nos dias de hoje, com tantos meios de divulgação disponíveis, acontece frequentemente. O objetivo deste trabalho e desenvolver ferramentas capazes de lidar com informação contraditória que possa ser descrita através de fórmulas de lógicas híbridas. Construir modelos e comparar a inconsistência de diferentes bases de dados e ver a aplicabilidade deste método no dia-a-dia são a base para o desenvolvimento desta dissertação

Towards a Unified Framework for Syntactic Inconsistency Measures

A number of proposals have been made to define inconsistency measures. Each has its rationale. But to date, it is not clear how to delineate the space of options for measures, nor is it clear how we can classify measures systematically. In this paper, we introduce a general framework for comparing syntactic inconsistency measures. It uses the construction of an inconsistency graph for each knowledgebase. We then introduce abstractions of the inconsistency graph and use the hierarchy of the abstractions to classify a range of inconsistency measures