@article {61, title = {Paraconsistent OWL and Related Logics}, journal = {Semantic Web}, volume = {4}, year = {2013}, pages = {395{\textendash}427}, abstract = {The Web Ontology Language OWL is currently the most prominent formalism for representing ontologies in Semantic Web applications. OWL is based on description logics, and automated reasoners are used to infer knowledge implicitly present in OWL ontologies. However, because typical description logics obey the classical principle of explosion, reasoning over inconsistent ontologies is impossible in OWL. This is so despite the fact that inconsistencies are bound to occur in many realistic cases, e.g., when multiple ontologies are merged or when ontologies are created by machine learning or data mining tools. In this paper, we present four-valued paraconsistent description logics which can reason over inconsistencies. We focus on logics corresponding to OWL DL and its profiles. We present the logic SROIQ4, showing that it is both sound relative to classical SROIQ and that its embedding into SROIQ is consequence preserving. We also examine paraconsistent varieties of EL++, DL-Lite, and Horn-DLs. The general framework described here has the distinct advantage of allowing classical reasoners to draw sound but nontrivial conclusions from even inconsistent knowledge bases. Truth-value gaps and gluts can also be selectively eliminated from models (by inserting additional axioms into knowledge bases). If gaps but not gluts are eliminated, additional classical conclusions can be drawn without affecting paraconsistency.}, keywords = {Automated Deduction, Complexity, Description Logic, OWL, Paraconsistency, Semantic Web, Web Ontology Language}, doi = {10.3233/SW-2012-0066}, url = {http://dx.doi.org/10.3233/SW-2012-0066}, author = {Frederick Maier and Yue Ma and Pascal Hitzler} } @article {73, title = {Computing Inconsistency Measure based on Paraconsistent Semantics}, journal = {Journal of Logic and Computation}, volume = {21}, year = {2011}, pages = {1257{\textendash}1281}, abstract = {

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.

}, doi = {10.1093/logcom/exq053}, url = {http://dx.doi.org/10.1093/logcom/exq053}, author = {Yue Ma and Guilin Qi and Pascal Hitzler} } @article {83, title = {Computational Complexity and Anytime Algorithm for Inconsistency Measurement}, journal = {International Journal of Software and Informatics}, volume = {4}, year = {2010}, pages = {3{\textendash}21}, abstract = {

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

}, keywords = {algorithm, computational complexity, inconsistency measurement, Knowledge representation, multi-valued logic}, url = {http://www.ijsi.org/ch/reader/view_abstract.aspx?file_no=i41\&flag=1}, author = {Yue Ma and Guilin Qi and Guohui Xiao and Pascal Hitzler and Zuoquan Lin} } @conference {407, title = {Distance-based Measures of Inconsistency and Incoherency for Description Logics}, booktitle = {Proceedings of the 23rd International Workshop on Description Logics (DL2010)}, volume = {573}, year = {2010}, pages = {475-485}, publisher = {CEUR-WS.org}, organization = {CEUR-WS.org}, address = {Waterloo, Canada}, abstract = {

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.

}, author = {Yue Ma and Pascal Hitzler}, editor = {Volker Haarslev and David Toman and Grant Weddell} } @conference {116, title = {An Anytime Algorithm for Computing Inconsistency Measurement}, booktitle = {Knowledge Science, Engineering and Management, Third International Conference, KSEM 2009}, volume = {5914}, year = {2009}, pages = {29{\textendash}40}, publisher = {Springer}, organization = {Springer}, address = {Vienna, Austria}, abstract = {

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.

}, doi = {10.1007/978-3-642-10488-6_7}, url = {http://dx.doi.org/10.1007/978-3-642-10488-6_7}, author = {Yue Ma and Guilin Qi and Guohui Xiao and Pascal Hitzler and Zuoquan Lin}, editor = {Dimitris Karagiannis and Zhi Jin} } @conference {118, title = {Paraconsistent Reasoning for OWL 2}, booktitle = {Web Reasoning and Rule Systems, Third International Conference, RR 2009}, volume = {5837}, year = {2009}, pages = {197{\textendash}211}, publisher = {Springer}, organization = {Springer}, address = {Chantilly, VA, USA}, abstract = {

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.

}, doi = {10.1007/978-3-642-05082-4_14}, url = {http://dx.doi.org/10.1007/978-3-642-05082-4_14}, author = {Yue Ma and Pascal Hitzler}, editor = {Axel Polleres and Terrance Swift} }