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May 29, 1977
To say that S knows exactly A we can use the schema

∀p.[p ε A ⊃ Q(p)] ∧ ∀pq.[Q(p) ∧ Q(p⊃q) ⊃ Q(q)] ⊃ ∀p.[K(S,p) ⊃ Q(p)]

but this doesn't tell us how to say that S1 knows that S2 knows exactly A.
A version corresponding to the possible worlds formalism for knowledge is

[∀p.pεA ⊃ Q(p)] ∧
∧ ∀W1 W2.[∀p.[Q(p) ⊃ true(W,p)] ∧ A(S,W,W1) ⊃ ∀p.[Q(p) ⊃ true(W1,p)]]
⊃ ∀p.[true(W,K(S,p)) ⊃ Q(p)].


∀Q.
[∀p.[p ε A ⊃ Q(p)] ∧ ∀pq.[Q(p) ∧ Q(p⊃q) ⊃ Q(q)] ∧
∀Q1.∀p.[p ε A ⊃ Q1(p)] ∧ ∀pq.[Q1(p) ∧ Q1(p⊃q) ⊃ Q1(q)] ⊃ ∀p.[Q(p) ⊃ Q1(p)]]
 ⊃ ∀p.[K(S,p) ≡ Q(p)]

Political honesty of scientists

	When a scientist has it pointed out that he has been using
a non-fact in public argument, he should take the lead in publishing
a retraction.  Scientists should be asked to pledge this.  Opponents
with tape recordings or clippings should be able to request retraction
and should be able to get a consensus judgment.

Applications of minimal inference

1. The minimal schema may be an exotic way of writing.  The key
statment is that everything satisfying a predicate P is generated
from certain constants and functions, and jumping to a conclusion
consists of asserting such a schema.

2. Reduce frame problem to minimal inference.  Discuss STRIPS with
Nilsson from this point of view.

3. Wiseman problem.  Schema says that 
Wise2 knows that Wise1 knows just consequences of what Wise2 knows
he can see.  This is really a finite collection of facts so that
Wise2 can convert the quantifier into a finite conjunction of cases.

4. Converting quantified statements to finite conjunctions or
disjunctions will be the key method for AI.  In the first place,
the functions used in practice often don't generate an infinite
number of new objects.  In the second place, a quantified statement
over the integers can often be replaced by a non-quantified statement
about the set of integers.

5. If we work only with concepts, we can avoid problems with opacity,
but then there will often be an infinity of cases.  Extensional
equivalence can often reduce the number of cases to a finite number,
but then we must worry about opacity.