To say things such as "the name of the owner", we want to string together multiple relations (viz. name and owner). Relational operators allow us to make such statements.
A relation that contains pairs of the form can be altered by swapping the elements of every pair in the relation. Mathematically, is a different from . This operation is called the converse operator. It produces a new relation from an existing one. It is denoted by writing (pronounced 'wok' or ’flip’) after the relation name. This is how converse is defined:
If has type , then has type .
The composition operator is denoted by a semicolon ; between two terms. It is pronounced as 'composed with', in this case: composed with .
The composition operation is defined as follows: Let and be two relations, with the target of r being the same as the source of s. Then the composition of and , is a relation with signature
Would you like a different explanation of the relational operators? explains the relational operators in logic. explains them in natural language. for some algebraic rules about relational operators.