Now let us suppose that agent 1 believes, with strength 0.4, that
“either edge
or 
but not both, is present
in the optimal tour”. We will represent this as 
We
will not enter into the discussion of how that agent reached that belief
and we take it as a fact. Now let us suppose that another agent
believes, at a level 0.7 that 
then we write 
This is
curious, since this kind of assumption confuses our common sense. In
general we do not see any relationship between the fact that two edges
cross and that we can deduce that as a consequence one of them should be
present in the optimum tour. We can take this as a fact, as if a
“co-evolving” algorithm, is generating these predicates to guide the
search. However, note that agent 3 believes in this relationship (at a
0.7 level) for a particular pair of edges 
and
The distributed belief about
proposition 
is then stronger than any
individual belief about it, and is even stronger than what you would get
if any agent would believe the three facts. We offer now two examples on
its application.
4.1 EXAMPLE 1
The three inference rules are :
(MP) Modus Ponens from 
and 
deduce 
