We now define the modal system KT5. The axiom schemata for KT5 are as follows:

(A1)

(A2)

(A3)

(A4)

(A5)

(A6) , where

(A7)

We have the following two inference rules:

We write if there exists a proof of .
For any we write if
for some .
is said to be *consistent* if .

Fri Jun 20 13:39:43 PDT 1997