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: 1) They are mostly restricted to propositional knowledge bases; 2) Very few of them discuss computational aspects of computing inconsistency measures. In this paper, 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.

VL - 21 UR - http://dx.doi.org/10.1093/logcom/exq053 IS - 6 ER - TY - JOUR T1 - Computational Complexity and Anytime Algorithm for Inconsistency Measurement JF - International Journal of Software and Informatics Y1 - 2010 A1 - Yue Ma A1 - Guilin Qi A1 - Guohui Xiao A1 - Pascal Hitzler A1 - Zuoquan Lin KW - algorithm KW - computational complexity KW - inconsistency measurement KW - Knowledge representation KW - multi-valued logic AB -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

VL - 4 UR - http://www.ijsi.org/ch/reader/view_abstract.aspx?file_no=i41&flag=1 ER - TY - CONF T1 - Distance-based Measures of Inconsistency and Incoherency for Description Logics T2 - Proceedings of the 23rd International Workshop on Description Logics (DL2010) Y1 - 2010 A1 - Yue Ma A1 - Pascal Hitzler ED - Volker Haarslev ED - David Toman ED - Grant Weddell AB -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.

JF - Proceedings of the 23rd International Workshop on Description Logics (DL2010) PB - CEUR-WS.org CY - Waterloo, Canada VL - 573 ER - TY - CONF T1 - An Anytime Algorithm for Computing Inconsistency Measurement T2 - Knowledge Science, Engineering and Management, Third International Conference, KSEM 2009 Y1 - 2009 A1 - Yue Ma A1 - Guilin Qi A1 - Guohui Xiao A1 - Pascal Hitzler A1 - Zuoquan Lin ED - Dimitris Karagiannis ED - Zhi Jin AB -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.

JF - Knowledge Science, Engineering and Management, Third International Conference, KSEM 2009 PB - Springer CY - Vienna, Austria VL - 5914 UR - http://dx.doi.org/10.1007/978-3-642-10488-6_7 ER - TY - CONF T1 - Paraconsistent Reasoning for OWL 2 T2 - Web Reasoning and Rule Systems, Third International Conference, RR 2009 Y1 - 2009 A1 - Yue Ma A1 - Pascal Hitzler ED - Axel Polleres ED - Terrance Swift AB -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.

JF - Web Reasoning and Rule Systems, Third International Conference, RR 2009 PB - Springer CY - Chantilly, VA, USA VL - 5837 UR - http://dx.doi.org/10.1007/978-3-642-05082-4_14 ER -