We introduce the calculus of neo-Peircean relations, a string diagrammatic extension of the calculus of binary relations that has the same expressivity as first order logic and comes with a complete axiomatisation. The axioms are obtained by combining two well known categorical structures: cartesian and linear bicategories.

翻译：我们引入了新皮尔士关系演算，这是二元关系演算的字符串图扩展，具有与一阶逻辑相同的表达能力，并附带完备公理化系统。这些公理是通过结合两种众所周知的范畴论结构——笛卡尔双范畴与线性双范畴——而获得的。