Re: The role of logic, & planning ...

From: Russell Standish <>
Date: Mon, 7 May 2001 10:49:46 +1000 (EST)

Marchal wrote:
> Hi Russell,
> I am glad you borrowed Booloses from a library and that you spent a
> while poring over my thesis.
> I want just made precise that I have never try to modelise knowledge
> by Bew(|p|).
> This is, actually, a rather sensible point. Most philosopher agree
> that S4 is a good *axiomatic* of knowledge. Precisely S4 is KT4 + MP,NEC
> or, explicitely (added to the Hilbert Ackerman axioms) :
> AXIOMS [](A -> B) -> ([]A ->[]B) K
> []A -> A T
> []A -> [][]B 4
> RULES A/[]A (A & (A->B)) / B NEC MP.
> That is, most philosopher (since Plato, but I remember having seen a
> Buddhist
> similar writing) agree that:
> -if A->B is knowable and if A is knowable, then B is knowable. (K)
> - if A is knowable then A is true. (T)
> - if A is knowable than that very fact (that A is knowable) is knowable
> (4)
> Would you agree with that? 4 makes that knowledge somehow introspective.
> Now we will see that if []A represent the formal provability of A, or
> (provability by a sound machine), i.e. Bew(|A|), although 4 and K are
> verified, we don't have T, that is, we don't have
> []A -> A
> provable for all sentence A. Bew(|A|) -> A is not always provable.
> This entails that formal provability
> cannot and should not be used for the formalisation of knowledge.

Thanks for this extended discussion. It does help a lot, and makes
even more sense if one assumes COMP (which actually I don't, but for
the sake of argument, wil do).

Just one further question. Is it possible for one machine to know p
and another machine to know -p? It seems from the above discussion,
you are only considering consistent machines, which of course
cannot know p and -p simultaneously without being
inconsistent. However, you're not ruling out a society of such
machines who argue over what statements they know to be true (just
like my ardent theists and atheists in Australia - actually this last
example is largely hypothetical - when it comes to religions,
Australians are amongst the most apathetic in the world - an important
fact in us enjoying peace and prosperity).


Dr. Russell Standish Director
High Performance Computing Support Unit, Phone 9385 6967
UNSW SYDNEY 2052 Fax 9385 6965
Room 2075, Red Centre
Received on Sun May 06 2001 - 17:54:36 PDT

This archive was generated by hypermail 2.3.0 : Fri Feb 16 2018 - 13:20:07 PST