%0 Journal Article
%D 2011
%T Computing Inconsistency Measure based on Paraconsistent Semantics
%A Yue Ma
%A Guilin Qi
%A Pascal Hitzler
%X Measuring inconsistency in knowledge bases has been recognized as an important problem in several research areas. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. However, existing methods suffer from two limitations: (i) they are mostly restricted to propositional knowledge bases; (ii) very few of them discuss computational aspects of computing inconsistency measures. In this article, we try to solve these two limitations by exploring algorithms for computing an inconsistency measure of first-order knowledge bases. After introducing a four-valued semantics for first-order logic, we define an inconsistency measure of a first-order knowledge base, which is a sequence of inconsistency degrees. We then propose a precise algorithm to compute our inconsistency measure. We show that this algorithm reduces the computation of the inconsistency measure to classical satisfiability checking. This is done by introducing a new semantics, named S[n]-4 semantics, which can be calculated by invoking a classical SAT solver. Moreover, we show that this auxiliary semantics also gives a direct way to compute upper and lower bounds of inconsistency degrees. That is, it can be easily revised to compute approximating inconsistency measures. The approximating inconsistency measures converge to the precise values if enough resources are available. Finally, by some nice properties of the S[n]-4 semantics, we show that some upper and lower bounds can be computed in P-time, which says that the problem of computing these approximating inconsistency measures is tractable.
%G eng
%0 Journal Article
%J International Journal of Software and Informatics
%D 2010
%T Computational Complexity and Anytime Algorithm for Inconsistency Measurement
%A Yue Ma
%A Guilin Qi
%A Guohui Xiao
%A Pascal Hitzler
%A Zuoquan Lin
%K algorithm
%K computational complexity
%K inconsistency measurement
%K multi-valued logic
%X Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first give a complete analysis of the computational complexity of computing inconsistency degrees. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximations of the inconsistency degree from above and below. We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm.
%B International Journal of Software and Informatics
%P 3-21
%G eng
%0 Conference Proceedings
%D 2010
%T Distance-based Measures of Inconsistency and Incoherency for Description Logics
%A Yue Ma
%A Pascal Hitzler
%X Inconsistency and incoherency are two sorts of erroneous information in a DL ontology which have been widely discussed in ontology-based applications. For example, they have been used to detect modeling errors during ontology construction. To provide more informative metrics which can tell the differences between inconsistent ontologies and between incoherent terminologies, there has been some work on measuring inconsistency of an ontology and on measuring incoherency of a terminology. However, most of them merely focus either on measuring inconsistency or on measuring incoherency and no clear ideas of how to extend them to allow for the other. In this paper, we propose a novel approach to measure DL ontologies, named distance-based measures. It has the merits that both inconsistency and incoherency can be measured in a unified framework. Moreover, only classical DL interpretations are used such that there is no restriction on the DL languages used.
%I 23rd International Workshop on Description Logics (DL2010)
%C Waterloo, Canada
%G eng
%0 Conference Paper
%B Third International Conference, KSEM 2009
%D 2009
%T An Anytime Algorithm for Computing Inconsistency Measurement
%A Yue Ma
%A Guilin Qi
%A Guohui Xiao
%A Zuoquan Lin
%A Pascal Hitzler
%X Measuring inconsistency degrees of inconsistent knowledge bases is an important problem as it provides context information for facilitating inconsistency handling. Many methods have been proposed to solve this problem and a main class of them is based on some kind of paraconsistent semantics. In this paper, we consider the computational aspects of inconsistency degrees of propositional knowledge bases under 4-valued semantics. We first analyze its computational complexity. As it turns out that computing the exact inconsistency degree is intractable, we then propose an anytime algorithm that provides tractable approximation of the inconsistency degree from above and below.We show that our algorithm satisfies some desirable properties and give experimental results of our implementation of the algorithm.
%B Third International Conference, KSEM 2009
%G eng
%0 Conference Paper
%B Third International Conference, RR
%D 2009
%T Paraconsistent Reasoning for OWL 2
%A Yue Ma
%A Pascal Hitzler
%X A four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as under the classical semantics. However, this approach has so far only been studied for the basid description logic ALC. In this paper, we further study how to extend the four-valued semantics to the more expressive description logic SROIQ which underlies the forthcoming revision of the Web Ontology Language, OWL 2, and also investigate how it fares when adapated to tractable description logics including EL++, DL-Lite, and Horn-DLs. We define the four-valued semantics along the same lines as for ALC and show that we can retain most of the desired properties.
%B Third International Conference, RR
%I Web Reasoning and Rule Systems, Third International Conference, RR 2009
%C Chantilly, VA, USA
%P 197-211
%8 10/2009
%G eng
%0 Conference Paper
%D 2008
%T Paraconsistent Reasoning for Expressive and Tractable Description Logics
%A Yue Ma
%A Zuoquan Lin
%A Pascal Hitzler
%X Four-valued description logic has been proposed to reason with description logic based inconsistent knowledge bases, mainly ALC. This approach has a distinct advantage that it can be implemented by invoking classical reasoners to keep the same complexity as classical semantics. In this paper, we further study how to extend the four-valued semantics to more expressive description logics, such as SHIQ, and to more tractable description logics including EL++, DL-Lite, and Horn-DLs. The most effort we spend defining the four-valued semantics of expressive four-valued description logics is on keeping the reduction from four-valued semantics to classical semantics as in the case of ALC; While for tractable description logics, we mainly focus on how to maintain their tractability when adopting four-valued semantics.
%I 21st International Workshop on Description Logics, DL2008
%G eng
%0 Conference Paper
%B Proceedings of Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty
%D 2007
%T An Algorithm for Computing Inconsistency Measurement by Paraconsistent Semantics
%A Yue Ma
%A Guilin Qi
%A Zuoquan Lin
%A Pascal Hitzler
%X Measuring inconsistency in knowledge bases has been recognized as an important problem in many research areas. Most of approaches proposed for measuring inconsistency are based on paraconsistent semantics. However, very few of them provide an algorithm for implementation. In this paper, we first give a four-valued semantics for first-order logic and then propose an approach for measuring the degree of inconsistency based on this four-valued semantics. After that, we propose an algorithm to compute the inconsistency degree by introducing a new semantics for first order logic, which is called S[n]-4 semantics.
%B Proceedings of Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty
%C Hammamet,Tunisia
%P 91-102
%G eng
%0 Conference Paper
%B 4th European Semantic Web Conference, ESWC2007
%D 2007
%T Algorithms for Paraconsistent Reasoning with OWL
%A Yue Ma
%A Zuoquan Lin
%A Pascal Hitzler
%B 4th European Semantic Web Conference, ESWC2007
%C Innsbruck, Austria
%G eng
%0 Conference Paper
%B Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty
%D 2007
%T Measuring Inconsistency for Description Logics Based on Paraconsistent Semantics
%A Yue Ma
%A Guilin Qi
%A Zuoquan Lin
%A Pascal Hitzler
%X In this paper, we present an approach for measuring inconsistency in a knowledge base.We first define the degree of inconsistency using a four-valued semantics for the description logic ALC. Then an ordering over knowledge bases is given by considering their inconsistency degrees. Our measure of inconsistency can provide important information for inconsistency handling.
%B Ninth European Conference on Symbolic and Quanlitative Approaches to Reasoning with Uncertainty
%C Hammamet, Tunisia
%G eng
%0 Conference Paper
%D 2007
%T Measuring Inconsistency for Description Logics Based on Paraconsistent Semantics
%A Yue Ma
%A Guilin Qi
%A Pascal Hitzler
%A Zuoquan Lin
%X In this paper, we present an approach for measuring inconsistency in a knowledge base.We first define the degree of inconsistency using a four-valued semantics for the description logic ALC. Then an ordering over knowledge bases is given by considering their inconsistency degrees. Our measure of inconsistency can provide important information for inconsistency handling.
%I the 2007 International Workshop on Description Logics (DL-2007)
%G eng
%0 Conference Paper
%D 2007
%T Paraconsistent Resolution for Four-valued Description Logics
%A Yue Ma
%A Zuoquan Lin
%A Pascal Hitzler
%X In this paper, we propose an approach to translating any *ALC* ontology (possible inconsistent) into a logically consistent set of disjunctive datalog rules. We achieve this in two steps: First we give a simple way to make any *ALC* based ontology 4-valued satisfiable, and then we study a sound and complete paraconsistent ordered-resolution decision procedure for our 4-valued *ALC*. Our approach can be viewed as a paraconsistent version of KAON2 algorithm.
%I the 2007 International Workshop on Description Logics (DL-2007)
%G eng