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.

1 aMa, Yue1 aQi, Guilin1 aHitzler, Pascal uhttp://dx.doi.org/10.1093/logcom/exq05301617nas a2200229 4500008004100000245008100041210006900122300001100191490000600202520090100208653001401109653002901123653003001152653002901182653002301211100001201234700001501246700001701261700002001278700001701298856007201315 2010 eng d00aComputational Complexity and Anytime Algorithm for Inconsistency Measurement0 aComputational Complexity and Anytime Algorithm for Inconsistency a3–210 v43 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 measurement10aKnowledge representation10amulti-valued logic1 aMa, Yue1 aQi, Guilin1 aXiao, Guohui1 aHitzler, Pascal1 aLin, Zuoquan uhttp://www.ijsi.org/ch/reader/view_abstract.aspx?file_no=i41&flag=101613nas a2200181 4500008004100000245008400041210006900125260003400194300001200228490000800240520097700248100001201225700002001237700002101257700001701278700001901295856011701314 2010 eng d00aDistance-based Measures of Inconsistency and Incoherency for Description Logics0 aDistancebased Measures of Inconsistency and Incoherency for Desc aWaterloo, CanadabCEUR-WS.org a475-4850 v5733 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, Pascal1 aHaarslev, Volker1 aToman, David1 aWeddell, Grant uhttps://daselab.cs.ksu.edu/publications/distance-based-measures-inconsistency-and-incoherency-description-logics01441nas a2200205 4500008004100000245006500041210006200106260003000168300001200198490000900210520084600219100001201065700001501077700001701092700002001109700001701129700002601146700001301172856005001185 2009 eng d00aAn Anytime Algorithm for Computing Inconsistency Measurement0 aAnytime Algorithm for Computing Inconsistency Measurement aVienna, AustriabSpringer a29–400 v59143 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 aHitzler, Pascal1 aLin, Zuoquan1 aKaragiannis, Dimitris1 aJin, Zhi uhttp://dx.doi.org/10.1007/978-3-642-10488-6_701311nas a2200169 4500008004100000245003900041210003900080260003300119300001400152490000900166520084400175100001201019700002001031700001901051700002001070856005101090 2009 eng d00aParaconsistent Reasoning for OWL 20 aParaconsistent Reasoning for OWL 2 aChantilly, VA, USAbSpringer a197–2110 v58373 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, Pascal1 aPolleres, Axel1 aSwift, Terrance uhttp://dx.doi.org/10.1007/978-3-642-05082-4_14