@article {60,
	title = {Complexities of Horn Description Logics},
	journal = {ACM Trans. Comput. Log.},
	volume = {14},
	year = {2013},
	pages = {2},
	abstract = {Description Logics (DLs) have become a prominent paradigm for representing knowledge bases in a variety of application areas. Central to leveraging them for corresponding systems is the provision of a favourable balance between expressivity of the knowledge representation formalism on the one hand, and runtime performance of reasoning algorithms on the other. Due to this, Horn description logics (Horn DLs) have attracted attention since their (worst-case) data complexities are in general lower than their overall (i.e. combined) complexities, which makes them attractive for reasoning with large sets of instance data (ABoxes). However, the natural question whether Horn DLs also provide advantages for schema (TBox) reasoning has hardly been addressed so far. In this paper, we therefore provide a thorough and comprehensive analysis of the combined complexities of Horn DLs. While the combined complexity for many Horn DLs studied herein turns out to be the same as for their non-Horn counterparts, we identify subboolean DLs where Hornness simplifies reasoning. We also provide convenient normal forms for Horn DLs.},
	keywords = {computational complexity, description logics, Horn logic},
	doi = {10.1145/2422085.2422087},
	url = {http://doi.acm.org/10.1145/2422085.2422087},
	author = {Markus Kr{\"o}tzsch and Sebastian Rudolph 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}
}
