knowledge bases worst-case complexity base goal knowledge base reasoning exponential time chapters formalism worst-case complexity results 2022-05-10T10:52 axioms same size constructors logic An important goal of research in description logics (DLs) and related logic-based KR formalisms is to identify the worst-case complexity of reasoning. Such results, however, measure the complexity of a logic as a whole. For example, reasoning in the basic DL \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{ALCI}$\end{document} is ExpTime-complete, which means that \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{ALCI}$\end{document} constructors can be used in a way so that exponential time is strictly required for solving a reasoning problem. It is, however, well known that, given two \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{ALCI}$\end{document} knowledge bases of roughly the same size, reasoning with one knowledge base may be much more difficult than with the other, depending on the interaction of the axioms in the KBs. Thus, existing worst-case complexity results provide only a very coarse measure of reasoning complexity, and they do not tell us much about the “hardness” of each individual knowledge base. reasoning problems basis coarse measure https://scigraph.springernature.com/explorer/license/ description logics 2012-01-01 research important goal KR formalisms logic reasoning time basic description logic measures 2012 kb chapter description logic reasoning Parameterized Complexity and Fixed-Parameter Tractability of Description Logic Reasoning complexity results 13-14 Such results individual's knowledge base parameterized complexity parameter tractability way whole false example hardness size results complexity tractability https://doi.org/10.1007/978-3-642-28717-6_3 problem en interaction Nikolaj Bjørner 978-3-642-28716-9 Logic for Programming, Artificial Intelligence, and Reasoning 978-3-642-28717-6 Computation Theory and Mathematics Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK Department of Computer Science, University of Oxford, Wolfson Building, Parks Road, OX1 3QD, Oxford, UK doi 10.1007/978-3-642-28717-6_3 Voronkov Andrei Springer Nature - SN SciGraph project Boris Motik dimensions_id pub.1019752486 Information and Computing Sciences Springer Nature