ONT Re: Inquiry Driven Systems
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JA = Jon Awbrey
SR = Seth Russell
JA: so it's back to what kant sang, and peirce reverbed,
about the 'good' of a concept being its utility for
helping us 'reduce a manifold to a unity' (ramtau).
that is, 'manifold' is another name -- it's names
are legion -- for a 'state of uncertainty' (sou).
JA: what's all that mean in dynamic and in symbolic terms?
JA: dynamic. good question. we are asked to think of a sou
as a state of a dynamical system, and thus to consider
the moment of doubt or the weight of uncertainty of
our representative inquiring agent as one of the
state variables that determines its dynamics.
it's a bit hard to figure how to start here.
SR: It seems to me that first order logic (FOL) does not allow
automated agents to operate in dynamic systems containing
SOUs; for in FOL the agents are always quite sure of (x)
whether Fx is True or False. Nor do your truth tables,
previously provided, show states other than those fixed
two in which all things known, are known with only the
one strong certainty. Why not add at least a third
state to the body of your tables ... interpret it as
Surprise, or perhaps a state of doubt? The values
of %B% (if we like fuzzy logic) would then range
over the real numbers in the range 0 to 2 ...
(not 0 to 1). Am I using your symbol %B%
correctly here? In other words, why not
use multi vlaued logics? Would 2 state
logic ever be capable of operating
in systems containing SOUs?
SR: Some mentographs come to mind:
http://robustai.net/mentography/3laws.jpg
http://robustai.net/mentography/formOnly2.gif
http://robustai.net/mentography/lawsOfLogic.gif
http://robustai.net/mentography/3stateLogic.gif
it's like this: 'bit mind is your ordinary mind',
that is to say, a binary channel or 2-valued logic
is no real constraint, since you can always use it
to build a polycoded channel or a k-valued logic.
and fol is good enough to build, in principle,
reasonably decent-sized chunks of any other
mathematical model, fuzzy possibility space,
fussy probability space, or whatever,
that any agent might need for any
practical purpose.
the thing to grasp here is that 1-bit or 2-valued systems
are already capable of addressing states of uncertainty
and, reversely, representing information about objects
and objectives in the world, which is why we have such
a thing as information theory on a binary basis in the
first place. the state of uncertainty is not bound up
or found in the actual values that we use as indicators,
but in their patterns of distribution over the universe.
to pick a concrete example, let's go back to
the 16 boolean functions f : B^2 -> B --
i usually drop the extra formatting of
the %B%'s and when it's understood --
or think of the corresponding set
of 16 different venn diagrams
on a 2 circle universe.
http://suo.ieee.org/ontology/msg03585.html
if i say to you: "i'm thinking of something in this here
universe of discourse, and here is a proposition that is
true of it, or an indicator function that indicates it",
then you -- let's say i'm not lying -- will be more or
less informed about what thing in the universe i am
thinking about, depending on which f_j, j = 0 to 15,
that i name. actually, we should probably toss out
f_0 as being the inconsistent case where i'm really
saying "i lied about it being in this universe".
so there are 15 informative messages i can give,
and they are ordered in a lattice that tells
how they compare with respect to giving
more or less info. f_15 is the least
informative, basically just repeating
"it's somewhere in this universe",
and we notice that it has the
most uniform distribution of
1's, or highest "entropy".
jon awbrey
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