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C00002 00002	Comments on "A first order formalization of knowledge and action for
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Comments on "A first order formalization of knowledge and action for
a muliagent planning system" by Kurt Konolige

1. I doubt that the word "theory" and the expression "th(a)" are used
consistently.  On page 5, it is taken as a list of wffs.  Does this mean
that it is finite.  On page 6 it is taken as the closure of an agent's
set of facts and rules (closure of rules?) and hence infinite in general.
On p. 18, "Then the nonlogical axioms of the ML would constitute the
computer agent's theery of the world".  On page 11, we see

	∀a f. BEL(a,f) ≡ PR(th(a),f)

where if we take seriously the notion that th(a) is closed, we need
only say f ε th(a).  On page 8, we have

	FACT(th(A0), 'ON(B,C)'),

but this doesn't seem to make sense if the theory is the closure of the
set of facts, because the same theory could be the closure of different
sets of facts.  Better might be

	theory(a) = closure(facts(a))

and

	isfact(a, 'ON(B,C)')

or even

	'ON(B,C)' ε facts(a).

	With all this verbal inconsistency, it isn't clear that there is
any real difficulty.  Most likely, if a single definition were used
consistently, minor rewordings would fix the statements.


	2. I have doubts about whether the sense quotes are a mere
abbreviation, i.e. eliminable leaving a true first order language.
Their first introduction is clearly eliminable, but no elimination
rules are offered for their later extensions.  The burden of proof
is on the author not the reader.

	Their initial introduction might be avoided by writing

	p' ∧' q'

instead of

	'p ∧ q'

or

	and(p', q').

	3. The treatment of the three wise men resembles my 1975
treatment and suffers from the same weakness.  Namely, the fact that
the first two wise men don't know the colors of their spots is taken
as a hypothesis, but it is obviously a consequence of the facts.  My
1978 treatment using the accessibility relation deduces it.  My and
Ma's treatments of "Mr. S and Mr. P." use the accessibility relation
and such reasoning deriving non-knowledge is the essential to that
problem.

	The use of "any fool" alias CFACT to describe the joint knowledge
is an adhocery.  What if there were a fourth person who didn't come
on the scene till later?  It would be necessary to describe the joint
knowledge of the three without assuming that the fourth knew all the
facts that the three know jointly.  I know how to handle joint knowledge,
but I haven't written it down.

	4. The example of the pilot light is new to me.

	5. I will be interested to learn how you propose to treat
knowledge of quantified expressions.  While I treat it in my "Concepts ..."
the treatment is rather unsatisfactory.

	6. Relying so heavily on standard names is ok in that it will
solve many problems, but it won't handle the fact that sometimes one
asks "Who is Bill?" and are happy with the reply "That guy there" and
other times ask "Who is that guy there?" and are happy with the reply
"Bill".  I think that one should try to point out the limitations of
the formal devices one introduces.

	7. It seems to me that in the later formalisms of the paper, the
object language has acquired so many properties of the metalanguage that
it may not be worthwhile having a separate metalanguage.

	8. There isn't much different between your syntactic formalism
an my use of concepts - at least in whatever either of us has done
so far.  While I permit several expressions to denote the same concept,
I don't use any kind of "extensionality of concepts" for any essential
purpose.  Nor do you use the fact that you are dealing with expressions.
I think I'm marginally better off, because the equivalence relation of 
expressions for concepts is still at my disposal.