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Types, constraints and involvement

Now we need to define the notions which are at the heart of our account of information.

Where tex2html_wrap_inline458 is a state of affairs, tex2html_wrap532 is the type of situation that supports tex2html_wrap_inline458 . Where i is an infon (i.e. a parametric state of affairs), tex2html_wrap533 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 tex2html_wrap478 , 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'.gif We write:

tex2html_wrap_inline576

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:

tex2html_wrap_inline584


John Perry
Sat Nov 16 22:19:34 PST 1996