Fuzzy description logics serve the representation of vague knowledge, typically letting concepts take truth degrees in the unit interval. Expressiveness, logical properties, and complexity vary strongly with the choice of propositional base. The Lukasiewicz propositional base is generally perceived to have preferable logical properties but often entails high complexity or even undecidability. Contrastingly, the less expressive Zadeh propositional base comes with low complexity but entails essentially no change in logical behaviour compared to the classical case. To strike a balance between these poles, we propose non-expansive fuzzy ALC, in which the Zadeh base is extended with Lukasiewicz connectives where one side is restricted to be a rational constant, that is, with constant shift operators. This allows, for instance, modelling dampened inheritance of properties along roles. We present an unlabelled tableau method for non-expansive fuzzy ALC, which allows reasoning over general TBoxes in EXPTIME like in two-valued ALC.

翻译：模糊描述逻辑用于表示模糊知识，通常允许概念在单位区间内取真值度。表达能力、逻辑性质和复杂度随命题基的选择而有显著差异。Łukasiewicz命题基通常被认为具有更优的逻辑性质，但往往导致高复杂度甚至不可判定性。相比之下，表达能力较弱的Zadeh命题基具有低复杂度，但与经典情况相比基本不改变逻辑行为。为在这些极端之间取得平衡，我们提出非扩张模糊ALC，其中Zadeh基通过Łukasiewicz连接词进行扩展，但要求连接词的一侧被限制为有理常数，即采用常数偏移算子。例如，这允许沿角色对属性进行衰减继承建模。我们为非扩张模糊ALC提出了一种无标签表推演方法，使得在一般TBox上的推理能在EXPTIME内完成，与二值ALC的情况相同。