@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 {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 = {<p class="rtejustify">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</p>
},
	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}
}
