循环描述逻辑TBOX中的完备格

Complete Lattice in Cyclic Description Logic TBOX

描述逻辑中含有循环定义的TBox通常使用固定点模型来刻画循环定义的语义,对于固定点模型,不仅需要研究其存在性,还需要研究模型之间的关系,如是否存在最大、最小固定点模型。TBox中所有模型扩展集合上的偏序关系可以诱导出格结构,而且是完备格,现有的研究得出的一些结论主要是针对此完备格。考虑在特定固定点下,概念解释域上的偏序关系同样可以诱导出格。对这种格进行研究得出了一些有益的结论,这些结论为深入研究循环描述逻辑语义提供了新的思路。

Description Logic TBOX with cyclic definitions is generally used fixpoint model to character its semantics ,we need study the existence of fixpoint model and also relations between models such as GFP or LFP model is existed .All partial order relations on existents set of models in TBOX can induce Lattice structure which is complete .Some conclusions have been drawn from this complete lattice so far .It is considered partial order relations on interpretation domain of concept can also induce lattice structure .we study this lattice and draw some conclusions ,which provide a new way of thinking for studying the semantics of cyclic description logic deeply .