二元关系性质的一个代数
An Algebra of Properties of Binary Relations
摘要：
我们考虑所有16个一元运算，给定一个齐次二元关系R，通过xRy和yRx的布尔组合定义一个新的。操作可以由逐点定义的逻辑连接器组合和连接。我们考虑关系的通常属性，并允许通过预先放置一个操作来解除它们。我们研究了提升属性之间的外延等式（例如，一个关系是连通的当且仅当它的补集是不对称的），并给出了一个表来决定这个等式。在反例生成器和归结定理证明器的支持下，我们研究了提升性质之间的所有3-原子蕴涵，并给出了它们的一个合理而完整的公理集（例如：“如果R的补是左欧几里德的且R是右串行的，则R的对称核是左串行的”）.
英文摘要：
We consider all 16 unary operations that, given a homogeneous binary relation R, define a new one by a boolean combination of xRy and yRx. Operations can be composed, and connected by pointwise-defined logical junctors. We consider the usual properties of relations, and allow them to be lifted by prepending an operation. We investigate extensional equality between lifted properties (e.g. a relation is connex iff its complement is asymmetric), and give a table to decide this equality. Supported by a counter-example generator and a resolution theorem prover, we investigate all 3-atom implications between lifted properties, and give a sound and complete axiom set for them (containing e.g. "if R's complement is left Euclidean and R is right serial, then R's symmetric kernel is left serial").
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
