For a visual presentation of the semantics of terms, we use Venn-diagrams.

Consider two relations: traveler[Trip*Person] and dest[Trip*Destination]. The first relation tells which persons have traveled on which trip. The diagram shows this as red dashed lines. The second relation links trips to destinations. It is depicted by dotted blue lines in the diagram.

Each pair (fact) in the diagram can be written as a fact in two ways, using the converse operator:

From the diagram, we assume that each pair represents a true statement (i.e. a fact). The statements are given both formally and in natural language. The elaborate version is a literate translation of the semantics in logic. The ordinary version tells the same in a more human sounding manner.

Consider two relations: traveler[Trip*Person] and dest[Trip*Destination]. The first relation tells which persons have traveled on which trip. The diagram shows this as red dashed lines. The second relation links trips to destinations. It is depicted by dotted blue lines in the diagram.

From this diagram, we can tell which statements are true (i.e. facts). The statements are given both formally and in natural language. The elaborate version is a literate translation of the . The ordinary version tells the same in a more human sounding manner.

The following statements do NOT follow from the population shown in the diagram:

Other explanation

Consider two relations: authorized[Account*Person] and beneficiary[Account*Person]. The first relation tells which persons are authorized to which accounts. The diagram shows this as red dashed lines. The second relation tells which persons stand to benefit from which accounts.. It is depicted by dotted blue lines in the diagram.

This diagram gives an example population of the relations authorized[Account*Person] and beneficiary[Account*Person]. Bob is authorized for account DE9382991 and Ann is authorized for account RS746620. Carl stands to benefit from account NL19RABO03992844 and Ann stands to benefit from account RS746620. Formally, we say:

By combining the relations authorized and beneficiary, we can derive the following true statements.

A different way to state the same is:

Other explanations

Would you like a different explanation of the boolean operators? This page explains them in set theory. Click here for the semantics of the boolean operators in algebra. Here you get their definitions in logic.