Inconsistencies of connection for heterogeneity and a new relation discovery method that solved them

We represent the inconsistencies of the past research on the connections among such heterogeneous fields as Linked Data, Semantic Web, Bridge Ontology, and Schema Mapping as well as our own past researches. Graph structures are commonly represented as links in relationships. For the same domain, the relationships agree with each other in the domain, because the transitive and order relations are defined. However, in most heterogeneous domains, we have to define the new order relation to link heterogeneous sets. This limit exists when we consider the relation among heterogeneous fields in set theory. Three inconsistencies of linking heterogeneous resources exist: 1) the inconsistency that shows that the relation does not guarantee the future; 2) the inconsistency where no transitive relation is true, when anyone connects links for heterogeneous fields; and 3) the inconsistency where no relation in heterogeneous fields can be discovered in set theory. Closed assumption systems have already reached their limit. In the big data era, we must consider a new framework for the Three Opened Assumption's Evil. As one solution, we present a map transformation method from set theory to the Cartesian system of coordinates to interconnect these heterogeneous sets and the Three Opened Assumption's Evil by two easy mathematical proofs of transitive and order relations to interconnect the heterogeneous resources. In addition, we define a new functional predicate as an example of a map transformation from set theory to a Cartesian system of coordinates to interconnect the heterogeneous resources for our solution. We also define a “dependOn” function as an example of this framework.