Suppose that we have a group consisting of agents. Then we augment
the language of propositional logic by
knowledge operators
(one for each agent), and form formulae in the
obvious way. A statement like
is read ``agent 1 knows
''2.1. The state that agent
knows
that agent
knows
is formalized by
. A
formula like
is
interpreted: ``if agent
knows
and
then
he knows
''.
Formally, the language
of modal epistemic logic is
defined as follows:
The modal depth of a formula is defined by the following conditions:
for all
;
;
; and
.