A Framework for Reasoning with Expressive Continuous Fuzzy Description Logics

Abstract

Abstract. In the current paper we study the reasoning problem for fuzzy SI (f-SI) under arbitrary continuous fuzzy operators. Our work can be seen as an extension of previous works that studied reasoning algorithms for f-SI, but focused on specific fuzzy operators, e.g. fKD-SI and of reasoning algorithms for less expressive fuzzy DLs, like fL-ALC and fP-ALC (fuzzy ALC under the Lukasiewicz and product fuzzy operators, respectively). We show how transitivity can be handled for all the range of continuous fuzzy DLs and discuss about blocking and correctness in this setting. Based on these analysis, we present a unifying framework for reasoning over the class of continuous fuzzy DLs. Finally use the results to prove decidability of several fuzzy SI DLs.