A fuzzy spatial description logic for the semantic web

Spatial information is a critical feature in a large number of application domains. Spatial information, however, is often not crisp but with the nature of imprecision and fuzziness. As the increasing requirements of spatial applications, there emerges many challenges regarding to the representation and reasoning of spatial knowledge. Description logic (DL) is a logical basis for representing knowledge and realizing reasoning tasks in the Semantic Web. Therefore, how to extend DL to achieve the goal of representing and reasoning fuzzy spatial knowledge needs to be settled. In this work, we study a fuzzy spatial extension of the well known fuzzy ALC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {ALC}$$\end{document} DL to reason fuzzy spatial knowledge. First, we construct a fuzzy spatial concrete domain S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document} which is comprised of fuzzy spatial regions and fuzzy RCC relationships. More importantly, we give the admissibility proof of fuzzy spatial concrete domain S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document}. Then we extend fuzzy ALC\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {ALC}$$\end{document} with an admissible fuzzy spatial concrete domain S\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mathcal {S}$$\end{document} and present a fuzzy spatial description logic f-ALC(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {ALC}}({\mathcal S})$$\end{document}. Finally, we address a decision procedure for f-ALC(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {ALC}}({\mathcal S})$$\end{document} ABox consistency problem. Also, we show that the decision procedure is correct and the consistency problem for f-ALC(S)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathcal {ALC}}({\mathcal S})$$\end{document} is decidable in PSPACE-complete.