02036nas a2200121 4500008004100000245007000041210006900111520165400180100001201834700001501846700002001861856003301881 2011 eng d00aComputing Inconsistency Measure based on Paraconsistent Semantics0 aComputing Inconsistency Measure based on Paraconsistent Semantic3 aMeasuring 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.1 aMa, Yue1 aQi, Guilin1 aHitzler, Pascal uhttp://knoesis.org/node/159801491nas a2200205 4500008004100000245008100041210006900122300000900191520087500200653001401075653002901089653003001118653002301148100001201171700001501183700001701198700002001215700001701235856003301252 2010 eng d00aComputational Complexity and Anytime Algorithm for Inconsistency Measurement0 aComputational Complexity and Anytime Algorithm for Inconsistency a3-213 aMeasuring 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. 10aalgorithm10acomputational complexity10ainconsistency measurement10amulti-valued logic1 aMa, Yue1 aQi, Guilin1 aXiao, Guohui1 aHitzler, Pascal1 aLin, Zuoquan uhttp://knoesis.org/node/161801430nas a2200121 4500008004100000245008400041210006900125260008100194520096800275100001201243700002001255856003301275 2010 eng d00aDistance-based Measures of Inconsistency and Incoherency for Description Logics0 aDistancebased Measures of Inconsistency and Incoherency for Desc aWaterloo, Canadab23rd International Workshop on Description Logics (DL2010)3 aInconsistency 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.1 aMa, Yue1 aHitzler, Pascal uhttp://knoesis.org/node/184601245nas a2200145 4500008004100000245006500041210006200106520081700168100001200985700001500997700001701012700001701029700002001046856003301066 2009 eng d00aAn Anytime Algorithm for Computing Inconsistency Measurement0 aAnytime Algorithm for Computing Inconsistency Measurement3 aMeasuring 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.1 aMa, Yue1 aQi, Guilin1 aXiao, Guohui1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/124601251nas a2200133 4500008004100000245003900041210003900080260010500119300001200224520081600236100001201052700002001064856003301084 2009 eng d00aParaconsistent Reasoning for OWL 20 aParaconsistent Reasoning for OWL 2 aChantilly, VA, USAbWeb Reasoning and Rule Systems, Third International Conference, RR 2009c10/2009 a197-2113 aA 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.1 aMa, Yue1 aHitzler, Pascal uhttp://knoesis.org/node/125001290nas a2200133 4500008004100000245007700041210006900118260006200187520082500249100001201074700001701086700002001103856003301123 2008 eng d00aParaconsistent Reasoning for Expressive and Tractable Description Logics0 aParaconsistent Reasoning for Expressive and Tractable Descriptio b21st International Workshop on Description Logics, DL20083 aFour-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.1 aMa, Yue1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/184901102nas a2200157 4500008004100000245008500041210006900126260002100195300001100216520062000227100001200847700001500859700001700874700002000891856003300911 2007 eng d00aAn Algorithm for Computing Inconsistency Measurement by Paraconsistent Semantics0 aAlgorithm for Computing Inconsistency Measurement by Paraconsist aHammamet,Tunisia a91-1023 aMeasuring 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.1 aMa, Yue1 aQi, Guilin1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/121500374nas a2200121 4500008004100000245005300041210005300094260002300147100001200170700001700182700002000199856003300219 2007 eng d00aAlgorithms for Paraconsistent Reasoning with OWL0 aAlgorithms for Paraconsistent Reasoning with OWL aInnsbruck, Austria1 aMa, Yue1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/122100837nas a2200145 4500008004100000245008500041210006900126260002200195520037700217100001200594700001500606700001700621700002000638856003300658 2007 eng d00aMeasuring Inconsistency for Description Logics Based on Paraconsistent Semantics0 aMeasuring Inconsistency for Description Logics Based on Paracons aHammamet, Tunisia3 aIn 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.1 aMa, Yue1 aQi, Guilin1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/121600883nas a2200145 4500008004100000245008500041210006900126260006800195520037700263100001200640700001500652700002000667700001700687856003300704 2007 eng d00aMeasuring Inconsistency for Description Logics Based on Paraconsistent Semantics0 aMeasuring Inconsistency for Description Logics Based on Paracons bthe 2007 International Workshop on Description Logics (DL-2007)3 aIn 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.1 aMa, Yue1 aQi, Guilin1 aHitzler, Pascal1 aLin, Zuoquan uhttp://knoesis.org/node/183500934nas a2200133 4500008004100000245006500041210006400106260006800170520048000238100001200718700001700730700002000747856003300767 2007 eng d00aParaconsistent Resolution for Four-valued Description Logics0 aParaconsistent Resolution for Fourvalued Description Logics bthe 2007 International Workshop on Description Logics (DL-2007)3 aIn 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.1 aMa, Yue1 aLin, Zuoquan1 aHitzler, Pascal uhttp://knoesis.org/node/1837