Relational structures are models for a relational theory, that is, a logical theory whose signature is relational.
A relational structure is a tuple whose first component , is a non-empty set, and whose remaining components are relations on . (We assume that there is at least one relation given.)
In their use in the Kripke semantics of modal logics, the set is sometimes called the universe (perhaps better the domain) and the elements of are called ‘worlds’, amongst a host of other names! This leads to the terminology ‘possible world semantics’ which is sometimes used.
poset, or more generally a set, , with a family of partial orders, , on it;
transition system, , (see discussion on the transition system’s page);
a rooted tree can be considered as a relational structure on its set of nodes, by specifying properties of a successor relation;
a set with, on it, an equivalence relation, , or, more generally, a family of equivalence relations, , for is some indexing set.