Parameterized Complexity and Fixed-Parameter Tractability of Description Logic Reasoning

Abstract

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 $\mathcal{ALCI}$ is ExpTime-complete, which means that $\mathcal{ALCI}$ 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 $\mathcal{ALCI}$ 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.