This note sketches the extension of the basic characterisation theorems as
the bisimulation-invariant fragment of first-order logic to modal logic with
graded modalities and matching adaptation of bisimulation. We focus on showing
expressive completeness of graded multi-modal logic for those first-order
properties of pointed Kripke structures that are preserved under counting
bisimulation equivalence among all or among just all finite pointed Kripke
structures.

本文考虑一阶逻辑到带分级的模态逻辑中基本特征定理的拓展，重点在展示分级多模态逻辑对 Kripke 结构中保存在计数等价中的一阶特性的表现完备性。

分级模态逻辑与计数双模拟

Graded modal logic and counting bisimulation

Existential rules, also known as data dependencies in Databases, have been
recently rediscovered as a promising family of languages for Ontology-based
Query Answering. In this paper, we prove that disjunctive embedded dependencies
exactly capture the class of recursively enumerable ontologies in
Ontology-based Conjunctive Query Answering (OCQA). Our expressive completeness
result does not rely on any built-in linear order on the database. To establish
the expressive completeness, we introduce a novel semantic definition for OCQA
ontologies. We also show that neither the class of disjunctive tuple-generating
dependencies nor the class of embedded dependencies is expressively complete
for recursively enumerable OCQA ontologies.

本文证明了分离嵌入式依赖可以精确捕捉基于本体的连词查询应答中的可递归枚举本体类，而关于 “元组生成依赖” 的复杂性类和嵌入式依赖的复杂性类都不能完全表达可递归枚举的 “基于本体的连词查询应答” 本体。