A theory specifies the logical properties of a number of non-logical concepts. These properties determine what inferences can be made from information involving these concepts. For instance, in the domain of spatial relations holding among regions, the relation of `connectedness' is clearly symmetric --- i.e. if x is connected to y then y must be connected to x. Thus if we know that `the hip bone is connected to the thigh bone' we can immediately infer that `the thigh bone is connected to the hip bone'. Another example is the transitivity of the `part' relation. This means that if a is part of b and b is part of c then a is part of c (note that a similar inference involving the `connectedness' relation would not be correct).
Theories consist of a number of axioms. Each axiom specifies
some fundamental (logical) fact involving one or more concepts of the
theory. For example the symmetry and reflexivity
of the connectedness relation can be
specified by the following axioms:
