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Re: [ontolog-forum] new logic

To: paoladimaio10@xxxxxxxxxxxxxx, "[ontolog-forum]" <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
Date: Tue, 17 Nov 2009 10:01:50 -0500
Message-id: <4B02BADE.5030104@xxxxxxxxxxx>
Paola, Jeff, John B, and Adrian,    (01)

I never said that:    (02)

PDM> JSowa, and others, say that there is only one type of logic, FOL    (03)

In 1998, I wrote a paper with the title "The Infinite Variety of
Logics".  And the ones that have been defined, used, and implemented
are almost as numerous as the stars in the sky (at least the visible
ones, and if you're in a big city, that's not many).    (04)

But certain varieties are brighter and shinier in the constellations.
The three most prominent are Aristotle's syllogisms, Boolean algebra,
and first-order logic.  Each of these three is very simple, and each
of them is based on excerpts from our ordinary natural languages.    (05)

But there are many, many ways of extending, restricting, or varying
the basics of those logics.  Aristotle's syllogisms, for example,
are the backbone and most widely used subset of every description
logic, including OWL.    (06)

JAS> An admittedly quick review of the paper Paola mentions (below)
 > suggests that this "new logic" is argumentation.
 > It was new, maybe, to Aristotle, as the posterior analytics portion
 > of his rhetoric. It's not new today, and has applications in such
 > areas as the law.    (07)

I agree with that assessment, but I would add that it wasn't new to
Aristotle.  In fact, the debates between Socrates and the sophists
were *inspired by* the arguments in courts of law.    (08)

The ancient Athenians were as litigious as modern Americans, but
with one major difference:  no lawyers were allowed in the courts.
Both the plaintiff and the defendant had to argue their own case
in front of the jury.    (09)

Since most people aren't good at debating, the sophists had a
lucrative business in teaching people how to prepare and argue
their cases in court.  That's why they incurred the wrath of Plato
for "making the weaker side seem the stronger."  But that is one
of the primary functions of modern law schools (which is why most
people hate lawyers).    (010)

Aristotle's goal in his first six books (the Organon, or instrument
for doing science) was to analyze the types of arguments and to
determine the criteria for distinguishing the valid ones from the
fallacies (which were among the most popular stock and trade of
the sophists).    (011)

JB> "What is a logic?" by Till Mossakowski, Joseph Goguen,
 > Razvan Diaconescu and Andrzej Tarlecki
 > but warning, there's technical content ahead ...
 > http://cseweb.ucsd.edu/users/goguen/pps/nel05.pdf    (012)

I agree that the work on institutions by Goguen and friends is
a very general and important branch of work.  However, I would
hesitate to recommend it in this discussion.  Just one excerpt:    (013)

MGDT> We extend the Lindenbaum algebra construction to a Lindenbaum category
> construction, deŻned on any institution with proofs, by identifying not only 
> alent sentences, but also equivalent proofs. We show that this construction 
>is an
> invariant, i.e., preserved up to isomorphism by our equivalence on 
> This construction extends the usual approach of categorical logic by having 
> of sentences as objects, rather than just single sentences, and thus allows 
> a much larger class of logics in a uniform way.    (014)

The "Lindenbaum algebra" is what I have been talking about for years
as the "lattice of theories", and it is hard to get the idea across.
What they are doing is generalizing it to the next level.  That is
what Robert Kent has been doing with his IFF (Information Flow
Framework).  I like the approach, but it's not easy to get the
concept across.    (015)

PDM> Here is more context for you to place the earlier link into
 > perspective
 > but a warning: it's complex!!!
http://books.google.co.uk/books?id=zVOWoXDunp8C&dq=complex+systems+logic&source=gbs_navlinks_s    (016)

I agree that it's complex, but in a very different way.  The
full title suggests why: _Chaotic Logic: Language, Thought,
and Reality from the Perspective of Complex Systems Science_.
In this book, Ben Goertzel tries to use chaos theory to provide
a perspective on all the branches of cognitive science.  Unlike
the purely formal work by Goguen & Co., which is abstracted away
from all the messy things in life, this book plunges right into
the messiness in a very big way.    (017)

AW> Actually, there's another, widely used form of logic that
 > can accurately be described as new.  New, that is, on the
 > historical timescale for logic.    (018)

Those issues are basically variations on nonmonotonic logics,
belief revision, and related points.  Peirce introduced 3-value
logic over a century ago to accommodate a middle value called
'unknown'.  Lukasiewicz and others developed it and explored
it in quite a bit of depth.  Variations of it have been used
in AI and DB systems for at least 40 years, and the term
'nonmonotonic' was introduced 30 years ago.  I agree that
those are very important issues.    (019)

And by the way, the primary difference between "classical"
logic and nonmonotonic logic is that the nonmon logics use
certain rules of inference that Aristotle called fallacies.    (020)

In summary, I agree that all of these varieties of logic are
important for kinds of applications and that it's also important
to relate them to what people do in everyday argumentation and
reasoning.    (021)

My only objection is to the word 'new' in the original
citation.  Following is a quotation from page 2:    (022)

Sutherland & Wenger> The key to intuitive logic, however, is
 > that the decision must be based on persuasive arguments.    (023)

The sophists knew that very well, and Aristotle went into quite
a bit of depth on the issues, both in the Organon and in his book
on Rhetoric.  I agree that it's important, and I'll admit that
many formal logic books ignore that point.  That's why I strongly
agree with Wittgenstein's criticisms of the "grave errors" in his
first book, which was inspired by his mentors, Frege and Russell.    (024)

John Sowa    (025)

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