Now we need to define the notions which are at the heart of our account of information.
Where
is a state of affairs,
is
the type of situation that supports
. Where i is an
infon (i.e. a parametric state of affairs),
is
a parametric type, and i is the conditioning infon of
T (cond(T)). A situation s is of parametric type T
relative to f if
, where i is the conditioning
infon of T and f is defined on all of the parameters of i.
Since infons and parametric types are the entities most used from now on, we shall mean parametric types when we say `types'; nonparametric types may be thought of as the special case.
We take constraints to be states of affairs with types of situations
as constituents. Simple involvement is a binary relation.
If T involves T', then for every situation of type T, there is
one of type T'.
We
write:
Relative involvement is a ternary relation. If T involves T' relative to T'', then, for any pair of situations of the first and third types, there is a situation of the second type. We write: