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Re: [ontolog-forum] Truth

To: "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "doug foxvog" <doug@xxxxxxxxxx>
Date: Thu, 2 Aug 2012 12:08:10 -0400
Message-id: <543584c3ef135abf605c3a6997940b46.squirrel@xxxxxxxxxxxxxxxxx>
On Wed, July 25, 2012 21:54, Pat Hayes wrote:
> ...
> Thinking about this more, the IKL 'that' is like backquote followed by
> normalization    (01)

This normalization is very limited.  The IKL document under "Identity
Conditions for Propositions" [ref:
http://www.ihmc.us/users/phayes/IKL/GUIDE/GUIDE.html#AppendixB ]
distinguishes identical from "equivalent" propositions.  It says,
   The Interoperability WG has decided ... to allow propositional
   identity to be defined by axioms, and to include in IKL a predefined
   relation of propositional equivalence, written =p, embodying what [it]
   considers to be the most universally appropriate such conventions,
   and intended to be used as a 'practical' propositional identity relation,
   intuitively meaning 'saying the same thing'. Users who prefer to use
   a different notion may define and use other notions of propositional
   equivalence.    (02)

The axioms are all of the form
  (=p (that ([and|or|if|iff|forAll] ...) )
         (that ([and|or|not|exists|forAll] ...)))
[I would guess that "=p" should be symmetric, but i don't find it defined
as such in this document.]    (03)

This list allows:
(lacksKnowlege Joe
     (forAll ((P isSentence) (Q isSentence))
             (equals (and P Q) (and Q P))
not to be "equivalent" to    (04)

(lacksKnowlege Joe
     (forAll ((P isSentence) (Q isSentence))
             (equals (and P Q) (and P Q))
     )))    (05)

I would not consider these two statements to be equivalent, so am
pleased that IKL does not, either.    (06)

> (to make sure eg that (that (and A B)) and (that (B and A))
> are the same, etc.)    (07)

This example uses infix notation for the second inner proposition.    (08)

In IKL, "atomic sentences and terms are written in 'Lisp style', with the
relation or function name after the opening parenthesis... This same style
is used for the quantifiers and connectives, which are always written as
prefixes rather than as infixed".    (09)

Since "(isTrue (that <sentence>)) is equivalent to <sentence>", if    (010)

> (that (and A B)) and (that (B and A)) are the same    (011)

then, since (isTrue (that (and A B))) would have the same value as
(isTrue (that (B and A))), one can conclude that in IKL,
   (and A B) is equivalent to (B and A)    (012)

I guess you meant to write, "to make sure, e.g., that (that (and A B))
and (that (B and A)) are the same".    (013)

> followed,
 crucially, by a model-theortic interpretation step    (014)

My understanding of this usage of the phrase "is like", means "is similar to
in some ways, although it differs in others".  You seem to be arguing
against a much stronger claim.    (015)

-- doug f    (016)

> (which is where LISP never goes) followed by a check
> to make sure that you have a sentence. Or something like that. So, OK,
> backquote is kind of in there somewhere.
> The reason I jumped on this was to avoid giving anyone even the ghost of
> an impression that IKL "that" operator is any kind of logical quotation at
> all, back or otherwise. This is a surprisingly stubborn misapprehension
> which we spent a lot of energy trying to eradicate in the IKRIS project,
> and I don't want to ever get into that tarpit again.
> Pat
>> -chris    (017)

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