What information can or cannot be exchanged?

What information can or cannot be exchanged between different systems? Since the dawn of the computer-aided design and engineering era, interoperability has been an issue. The exchangeable set of information between different systems has been loosely defined as the intersection of information. Yet, as information flow has directionality, a general definition of "intersection" is inadequate to define an exchangeable set of information. This paper proposes a new directive set operation, semantic intersection, and discusses which information can or cannot be exchanged between different systems using the concept of semantic intersection. This opens up the possibility of predetermining or calculating the exchangeable set of information between two or more systems or the possibility of automated generation of a standard product model between different systems. This paper focuses on data exchange between systems, but the proposed theory is also applicable to data exchange between human beings.