On 11/09/2016 04:33 AM, Linas Vepstas wrote:
So, to me, it seems like BindLink and ImplicationScopeLink are the same
thing (at least as far as (a)-syntax is concerned), but Ben says no,
they have different meanings in PLN -- one has one kind of truth value,
the other has a different kind.
Perhaps we need atoms with two different kinds of types -- a syntactic
type, which indicates what their structure is, and a semantic type,
which indicates what kind of TV formulas should be used?
We could. Another way it to have different rule-bases. I've tried in the
wiki to specify when equivalences are PLN semantics specific.
There are additional issues: for example: the
page http://wiki.opencog.org/w/ExtensionalImplicationScopeLink#Remarks
makes remarks like this:
ExtensionalImplicationScopeLink <TV>
<vardecl>
<implicant-body>
<implicand-body>
is equivalent to
ExtensionalImplicationLink <TV>
LambdaLink
<vardecl>
<implicant-body>
LambdaLink
<vardecl>
<implicand-body>
Huh ? My head spins, I have no clue how to read or understand that.
They seem to be two completely different kinds -- the second one is a
pair of combinators, the first one is not a combinator at all -- they're
not even of the same kind, so how can one convert one into the other?
and then there's this:
ExtensionalImplicationScopeLink <TV>
X
EvaluationLink
P
X
EvaluationLink
Q
X
is equivalent to
ExtensionalImplicationLink <TV>
P
Q
which cannot possibly be right -- They're not even of the same kind --
how can they possibly be convertible into one-another?
The scope forms are merely sugar, the PLN formulae are derived based on
the non scope forms/combinators/higher-level-functions.
I've updated the wiki to hopefully make it clearer.
Nil
The only part of that that does make sense to me is this:
ExtensionalImplicationScopeLink <TV>
is not equivalent to
AverageLink <TV>
Ahh!! Yes, OK, that makes sense. But this is exactly where it would be
good to decouple syntax from PLN semantics.
To recap: we seem to be using atom types to sometimes indicate (a)
syntax and sometimes (b) PLN TV value formulas. I'm thinking that
maybe there is a better way to indicate which is which.
--linas
On Tue, Nov 8, 2016 at 2:03 AM, Nil Geisweiller <ngeis...@googlemail.com
<mailto:ngeis...@googlemail.com>> wrote:
I've added some notes about that
http://wiki.opencog.org/w/ExtensionalImplicationScopeLink#Remarks
<http://wiki.opencog.org/w/ExtensionalImplicationScopeLink#Remarks>
My feeling based is that the ImplicationScopeLink (I mean, either
mixed, extensional or intensional) is what we want in most cases,
which is good given that it's syntactically simpler than wrapping an
AverageLink or ForAllLink around an implication.
Nil
On 11/08/2016 01:37 AM, Ben Goertzel wrote:
I think this may be what the
AverageQuantifierLink
used to do?
Then we could say
AverageQuantifierLink
VariableNode x
ImplicationLink
P(x)
Q(x)
and this would do what PLN needs... and if Bob had a different
kind of
logic with its own formulas he could have
BobsQuantifierLink
VariableNode x
ImplicationLink
P(x)
Q(x)
But I'm not sure this would satisfy all Nil's current requirements?
ben
On Mon, Nov 7, 2016 at 11:28 PM, Linas Vepstas
<linasveps...@gmail.com <mailto:linasveps...@gmail.com>> wrote:
OK, that makes sense. In that case, though, why not invent
a new
SpecialAllLink which has the desired properties? Inventing
one new link for
this would be more economical, and less confusing than
having six new links:
ImplicationScope
IntentionalImplicationScope
ExtensionalImplicationScope
EquivalenceScope
IntensionalEquivalenceScope
ExtensionalEquivalenceScope
which is what the current code does.
Besides, come the day you want to change the PLN formula, or
create yet
another one, you would just need a NewFormulaLink instead
of six new links.
--linas
On Mon, Nov 7, 2016 at 4:23 PM, Ben Goertzel
<b...@goertzel.org <mailto:b...@goertzel.org>> wrote:
If we have
ImplicationScopeLink
VariableNode x
P(x)
Q(x)
then e.g. PLN can assign this a truth value equal to
Sum_x ( max( P(x), Q(x)) ) / Sum_x P(x)
or
Sum_x ( P(x) * Q(x) ) / Sum_x P(x)
but may assign a quite different truth value for
ForAllLink
VariableNode x
ImplicationLink
P(x)
Q(x)
PLN does assign these two constructs different uncertain
truth values,
so this is not just a theoretical difference...
Other uncertain logic frameworks may also assign the two
constructs
different TVs, I would think...
ben
--
Ben Goertzel, PhD
http://goertzel.org
“I tell my students, when you go to these meetings, see
what direction
everyone is headed, so you can go in the opposite
direction. Don’t
polish the brass on the bandwagon.” – V. S. Ramachandran
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