Robert Rovetto wrote:
Now, my concern with this is that since syllogistic logic is not how the mind reasons, and is also very limited (in terms of producing truthful results/consequences, and expressivity, if not other things),
why isn't a non-syllogistic-based logic used for ontologies? Why is FOL used?
I have a problem with: “syllogistic logic is not how the mind reasons”.
It is rather only one of several reasoning mechanisms used by human minds. We also use induction, analogy, statistical reasoning, and a number of exotic mathematical methods.
The fundamental reasoning mechanism associated with ‘ontologies’ is inference, i.e., syllogistic logic. We create ontological models of some sets of concerns,
precisely because we have tools that implement syllogistic inference reliably, and can thus assist in solving problems of interest that involve those concerns.
The fundamental reasoning mechanism for statistical reasoning is different, and we make different models and use different tools in order to use that approach
to solving certain problems.
The fundamental reasoning mechanism for many engineering problems is the Calculus, and we make different models to use that mechanism for appropriate problems.
Mathematicians have long understood inductive reasoning, but formal induction is not statistical and it is not readily supported by tooling.
We are only beginning to have formal models for analogy that yield reliable results. In a certain sense, that is the main purpose of category theory.
And we have developed a number of hybrid approaches that beget their own models and tools, like fuzzy logics.
The point of all this is to put ontologies and syllogistic logic in their (rightful) place in the panoply of approaches to problem solving that human minds
have developed and built tools to support. Their purpose is to solve problems that can be solved by syllogistic inference, full stop.
It takes many ingredients to make the soup of human consciousness; we are just growing the leeks.
-Ed
From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx [mailto:ontolog-forum-bounces@xxxxxxxxxxxxxxxx]
On Behalf Of rrovetto@xxxxxxxxxxx
Sent: Monday, June 23, 2014 11:25 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Types of Formal (logical) Definitions in ontology
Thank you all for the feedback thus far. A couple of quick follows-ups:
@Alex Shkotin: question 3 is asking what the pro's and con's are of each non-FOL/non-syllogistic-based logic for ontology in addition to FOL-based logics.
@Dr.Sowa:
- what do you mean by "closed-form definitions"?
- I'm not sure I agree about this, and so I understand Edward Barkmeyer's reservations as well, but perhaps i'm not getting the gist of the whole context you have in mind:
"Any term, such as 'primitive concept' or 'description' that is not specified in terms of logic does not belong in a standard-- except as an informal (non-normative) comment."
To add context to my original question: I'd basically like to know what non-FOL/non-syllogism logical formalisms are there for ontologies?
This question assumes that FOL is based on Aristotelean syllogistic logic. Based on my studies in philosophy FOL is essentially presented as a modern form or translation of it.
Now, my concern with this is that since syllogistic logic is not how the mind reasons, and is also very limited (in terms of producing truthful results/consequences, and expressivity, if not other things),
why isn't a non-syllogistic-based logic used for ontologies? Why is FOL used?
If anyone can answer, or address this, I eagerly await your thoughts. Thanks.
Aside from that, please continue mentioning any other logics that are used.
On Tue, Jun 24, 2014 at 4:06 AM, Rich Cooper <rich@xxxxxxxxxxxxxxxxxxxxxx> wrote:
By the same logic, a concept can be the product of
'subordinate components', or more linguistically
aimed, 'a product of properties and behaviors'.
The choice of alternative interpretations, or the
choice of a component list, is the distinction
between Mereology and other forms of logical
representation.
So unions of alternatives and products of
component parts seem to be equivalent castings.
-Rich
Sincerely,
Rich Cooper
EnglishLogicKernel.com
Rich AT EnglishLogicKernel DOT com
9 4 9 \ 5 2 5 - 5 7 1 2
Behalf Of Barkmeyer, Edward J
Sent: Monday, June 23, 2014 2:17 PM
To: [ontolog-forum]
Subject: Re: [ontolog-forum] Types of Formal
(logical) Definitions in ontology
John makes an important addition to my list. In
addition to defining a concept as the union of a
set of 'subordinate' concepts', it is also
possible to define a 'class' or a 'term' (less
clearly a 'concept') as a specific set of named
things. This latter is also referred to as an
"extensional definition". One can define 'primary
color' as "one of red, orange, yellow, green,
blue, indigo, violet," without being at all clear
about what the distinguishing properties are.
(I tend to think that a 'concept' should have a
definition that involves specifying properties,
but then "being the color red" and "being John
Malkovich" can be considered properties.)
-Ed
> -----Original Message-----
> From: ontolog-forum-bounces@xxxxxxxxxxxxxxxx
[mailto:ontolog-forum-
> bounces@xxxxxxxxxxxxxxxx] On Behalf Of John F
Sowa
> Sent: Monday, June 23, 2014 4:47 PM
> To: ontolog-forum@xxxxxxxxxxxxxxxx
> Subject: Re: [ontolog-forum] Types of Formal
(logical) Definitions in ontology
>
> Ed and Pat,
>
> Pat raises an important point:
>
> PJH
> > If all classes are defined in terms of other
classes, where does the
> > whole process get started?
>
> All three of those methods assume you have some
classes to start:
>
> EJB
> > 1) identify a more general concept and the
delimiting characteristics
> > of the subordinate concept being defined
> > This is exactly: An A is a B that C.
> > 2) identify a list of subordinate concepts
that together cover the
> > more general concept being defined - the
union of other defined classes:
> > An A is a B or a C or a D.
> > 3) One can also define a Class as the
intersection of two or more classes,
> > but that is just a special case of (1): An
A is a B that is also a C.
>
> Those are all set forming operations. Set
theory has a starting method:
> {x | P(x)} -- the set of all x for which
some property P is true.
>
> That property P can also be specified by
enumeration:
> {x | x=a or x=b or x=c}
>
> What distinguishes a class from a set are the
identity criteria:
>
> 1. Two sets S1 and S2 are identical if they
have the same elements.
>
> 2. Two classes or concepts C1 and C2 are
identical if they have the
> same or logically equivalent defining
property or predicate P.
>
> The set of all cows, for example, changes with
every birth or death.
> But the concept cow is determined by an
unchanging predicate P.
>
> John
>
>
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