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