Let *W* be any non-empty set (of possible worlds). A model *M*
on *W* is a triple

where

and

Given any model *M*, we define a relation as follows:

We will write ``''
if we wish to make *M* explicit. A formula is
said to be valid in *M*, denoted by , if
for all .
(By , we mean .) Furthermore,
we will employ the following notation:

A model *M* is a KT5-model if

(M1)

(M2) for any and ,

(M3) for any and such that ,

(M4) *r*(*S*,*t*) is an equivalence relation for any and .

A set of well formed formulas is said to be
*realizable* if there exists a KT-5 model *M*
and such that .

Fri Jun 20 13:39:43 PDT 1997