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Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology

To: ontolog-forum@xxxxxxxxxxxxxxxx
From: John F Sowa <sowa@xxxxxxxxxxx>
Date: Sun, 06 Jul 2014 02:31:58 -0400
Message-id: <53B8ED5E.5050203@xxxxxxxxxxx>
On 7/5/2014 8:51 AM, rrovetto@xxxxxxxxxxx wrote:
> based on what's been said thus far, then it's possible to create
> non-FOL, non-syllogistic logics, correct? And are logics without
> quantifiers doable?    (01)

That depends on what you mean by 'not'.  What aspect of a logic
do you want to negate?    (02)

  1. For example, higher-order logic (HOL) is not FOL because it
     can express more kinds of statements than FOL.  But you could
     also have a non-FOL logic that expresses some subset of FOL.    (03)

  2. Propositional logic (i.e., Boolean algebra) is not FOL because
     it expresses a subset that has no quantifiers.    (04)

  3. RDF is a subset of FOL that has only one Boolean operator (and)
     and one quantifier (a blank node that says there exists something).    (05)

  4. But if you add negation to RDF, you can define all the operators
     of full FOL.  To specify all of FOL with just 'and', 'not', and
     'there exists', see http://www.jfsowa.com/talks/egintro.pdf .    (06)

There are also variations of logic that deny the option of just
two truth values {T,F}.  A three=valued logic would have an option
of unknown.  Cyc has five values:  True, True by default, Unknown,
False by default, False.  Any of these logics could use any combination
of quantifiers and Boolean operators.    (07)

There are also variations of fuzzy logic with a continuous range of
uncertainties.  Some people claim that vagueness or fuzziness is just
in the degree of knowledge, because no object can be truly vague.
But Peter Simons wrote an intriguing article about the possibility
of vague objects.  See the URL and excerpts below.    (08)

But that is a problem of ontology, not of logic.  Some people think that
identity conditions are a big deal.  I don't.  I believe that similarity
is more fundamental:  similarity is perceptible, but identity is just
a context-dependent inference.    (09)

________________________________________________________________________    (010)

https://www.academia.edu/7533490/Does_the_Sun_Exist_The_Problem_of_Vague_Objects    (011)

Does the Sun Exist? The Problem of Vague Objects    (012)


At any time, there are considerable masses of energy and matter leaving
the sun, and since there is no sharp boundary marking where the sun
stops... if all the objects that exist are exactly delimited, since
the sun is none of these, the sun does not exist...    (014)

Each of us is in the same position as the sun: at any time there are
countless molecules lurking around us, in or near us, the air, water
vapor and particles we respire, the pieces of skin about to be rubbed
off, the substances sticking to the skin, the nutrients about to cross
cell membranes from the gut, and there is no sharp fact of the matter
as when they become or cease to become parts of us...    (015)

On the other hand, if all of these everyday objects like the sun and
ourselves do exist, as common sense would have us believe, they are
vague and fail to have determinate identity conditions: there can be
an entity without identity...    (016)

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