Paola, Chris, Pavithra, and Jeff, (01)
PDM> I am pretty sure I read it on this list (not sure when or who
> or in relation to what) some kind of categorical statement that
> 'another type of logic' is not possible, that there is only the
> FOL kind, of which all the others are subsets of. (02)
CM> No one who knows anything about logic would say such a thing. (03)
I agree with Chris, but I'd like to clarify the reason why Paola
and others have interpreted some of the discussions as being very
strongly in favor of FOL. Many of us who have been working on
Common Logic have said the following: (04)
1. Common Logic is a very general version of FOL, which includes
a large number of other versions of FOL as subsets. Among
them are the usual predicate calculus, Aristotle's syllogisms,
the Semantic Web languages, diagrams such as UML, and query
languages such as SQL when applied to a closed-world database. (05)
2. However, we have also been talking about the *nonmonotonic*
versions of logic, which deal *open worlds* for which a great
many of the cases are unknown or even unknowable. Examples
include many of the above languages (especially SQL) when they
are applied to open-world databases. Most of these languages
are versions of FOL, and they can be translated to Common Logic.
But the critical issues of the open-world unknowns must be
handled with care. (06)
3. Beyond that, we have been talking about modal logics and the
difference between the "higher order" aspects of Common Logic
and the versions of higher-order logic that have a hierarchy
of domains of higher and higher orders of infinities. There
have been many, many discussions of these points on this list. (07)
Since point #1 has been discussed more than most, it's possible
that many people may have interpreted those discussions to mean
that Common Logic can do everything. However, we have also
discussed the IKL extensions to CL, which are necessary to
cover a wider range of logics. But many of those discussions
tend to get into very esoteric issues. (08)
PK> Intuitive logic is interesting. I believe human brain can
> develop intuition after recognizing a pattern. (09)
That is extremely important, and people are trying very hard to
design computer systems that can do something like that. But
so far people (and even dogs, cats, and horses) have a lot of
"horse sense" that we still can't implement in our computers. (010)
JAS> In our discussions of "new logic," we should probably recall
> some other categorizations of logic before we wander into the
> desert. There are three that have been around a very long time.
> Their present definition is mostly from Pierce. They are:
>
> -- Deduction, which is reasoning where necessary conclusions are
> made from statements - FOL,
>
> -- Induction, which are arguments by inference, i.e., by
> likelihood, usually from experience, and
>
> -- Abduction, which forms hypotheses from observed patterns. (011)
That is another extremely important issue. A great deal of what
we call "intuition" is based on abduction, which many people are
trying very hard to implement in computers, with some success.
But it's very limited compared to dogs, cats, horses, and people. (012)
Induction is also extremely important, and the systems that do
"data mining" are essentially induction engines. Many systems
that do "learning" are mostly data mining tools. Animal learning
depends very heavily on both induction and abduction. (013)
JAS> ... in the scientific method, all three occur to some extent. (014)
Yes, indeed. Peirce defined his "logic of pragmatism" as a cycle
of induction, abduction, deduction, and testing -- and repeat as
necessary ad infinitum. That is essentially the scientific method.
Following is a diagram I drew to illustrate Peirce's cycle: (015)
http://www.jfsowa.com/figs/soup5a.gif (016)
This cycle can be traversed very rapidly for quick decisions or
very slowly and carefully for scientific research. There is a
variant called the OODA loop, which John Boyd developed for
training fighter pilots: (017)
http://www.jfsowa.com/figs/oodaloop.gif (018)
Observe corresponds to induction, orient to abduction, decide
to deduction, and act to testing. And the goal of the training
is to analyze the problems in advance and to distill a set of
predefined patterns that can be recalled almost instantly when
the crisis arises. (019)
(By the way, I did not copy those diagrams into this email
because many spam filters automatically reject email that
contains .gif or .jpg images.) (020)
John (021)
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