Hi Riccardo:

I have a question about terminology ib the context shown below:
Which one would you choose:

supported/true/correct/?
discounted/false/wrong/?

Are there formal systems that study such beliefs?

-- Karl
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Alice claims the belief B([(1,1) (2,0)], 0.6):
Alice can give Bob a weighted CNF with clauses of the form (1,1) or (2,0) only,
where Bob cannot satisfy the fraction 0.65 of the clauses.

form (k,p) means that the clause has k literals and the first p are positive.

We check the belief through an interactive protocol:
Bob questions Alice belief.
Alice gives to Bob a weighted CNF S.
(1) Bob finds an assignment J satisfying the fraction 0.6.
(2) Bob finds an assignment J satisfying the fraction 0.7.

Would you say for 
(1) Alice' belief is supported/true/correct/?
(2) Alice' belief is discounted/false/wrong/?

Note that (1) does not imply that the mathematical statement behind Alice' belief is
a theorem. (Bob might not have a good algorithm for finding an assignment) 

Note that (2) does not imply that the mathematical statement behind Alice' belief is
a not a theorem. (S might have been too easy. Alice might have chosen a harder
problem)

The mathematical statement is:
There exists a weighted CNF S with clauses of the form (1,1) or (2,0) so that for
all assignments J: fsat(S,J) < 0.65