一句话：研究二元关系代数在包含式合取下的算子本原性，证明除有限互依外每个特性都本原。
该文研究二元关系代数中算子的本原性。该代数以并和复合为基础，空集与恒等关系分别为其中性元，并可加入多样性关系、全关系、交、差、投影、余投影、逆及传递闭包等特性。布尔查询通常表示为包含式的有限合取。作者在此片段下考察：若删去某个特性会严格减少可表达的布尔查询，则该特性是本原的。通过刻画各特性之间的有限基本相互依赖，论文证明：在这些互依关系之外，每个考虑的特性都确实是本原的。
The algebra of binary relations provides union and composition as basic operators, with the empty set as neutral element for union and the identity relation as neutral element for composition. The basic algebra can be enriched with additional features. We consider the diversity relation, the full relation, intersection, set difference, projection, coprojection, converse, and transitive closure. It is customary to express boolean queries on binary relational structures as finite conjunctions of containments. We investigate which features are primitive in this setting, in the sense that omitting the feature would allow strictly less boolean queries to be expressible. Our main result is that, modulo a finite list of elementary interdependencies among the features, every feature is indeed primitive.
@inproceedings{SurinxBG17,
title = {The primitivity of operators in the algebra of binary relations under conjunctions of containments},
author = {Dimitri Surinx and Jan Van den Bussche and Dirk Van Gucht},
booktitle = {LICS},
year = {2017},
doi = {10.1109/lics.2017.8005122}
}