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Re: [ontolog-forum] [ontology-summit] Invitation to a brainstorming call

To: "[ontolog-forum] " <ontolog-forum@xxxxxxxxxxxxxxxx>
From: "Christopher Spottiswoode" <cms@xxxxxxxxxxxxx>
Date: Wed, 29 Dec 2010 19:41:37 +0200
Message-id: <424FBC01EF7B49EDB7C08B33B3DC5ED6@klaptop>
John,    (01)

Many thanks for your comprehensive reply (below).  I enjoyed and 
appreciated your sceptical remarks on common sense.    (02)

I could especially relate to your footnote excerpt from your 
rolelog.pdf, which had earlier struck me because Wittgenstein's 
Satzsystem/Beweissystem notion is a close cousin of what has long 
been an absolutely key notion in the architecture which I have 
from time to time incompletely tried to set out here on ontolog. 
(Those two cousins have mathematics and its interpretations as 
common grandparents.)    (03)

But I shalln't respond at this stage to your CL-related 
explanations.  On the one hand I fear it would get us bogged down 
in unhelpful analyses of words.  More positively, on the other 
hand, it would be more productive for both of us (and, I hope, 
ontologgers in general) for me to return to CL in the context of 
the fuller writeup of the above-mentioned architecture ("The 
Mainstream Architecture for Common Knowledge") that I am currently 
working on, as preparation for the further programming of an 
infrastructure for it.  I think I might be beginning to glimpse a 
most useful role there too for CL, much as there are important 
similarities I have long seen between my work and your more 
pluralistic approach to ontology.    (04)

Sorry about the punt but it will be worth it!    (05)

Christopher    (06)

----- Original Message ----- 
From: "John F. Sowa" <sowa@xxxxxxxxxxx>
To: <ontolog-forum@xxxxxxxxxxxxxxxx>
Sent: Tuesday, December 28, 2010 6:16 PM
Subject: Re: [ontolog-forum] [ontology-summit] Invitation to a 
brainstorming call for the 2011 Ontology Summit    (07)

On 12/28/2010 4:54 AM, Christopher Spottiswoode wrote:
> You seem (to me...) to be saying that every tool for a subset
> of CL or IKL can support full CL.    (08)

No.  I was elaborating the following point by Chris Menzel:    (09)

> Common Logic supports most every logic-based framework, in
> the sense that such frameworks are all Common Logic dialects.
> All that is needed in order for a framework to "support"
> Common Logic is an explicit characterization of it as such
> a dialect.  It is a mistake to think of Common Logic as some
> sort of competitor to OWL, RDF, etc. One of the central goals
> of Common Logic's design was to serve as an overarching abstract
> logical framework in which the underlying commonalities and
> differences between concrete frameworks could be easily 
> identified.    (010)

For any version of logic L, there is no such thing as a tool that
supports "full" L.  No tool could or should support every possible
method for using L in deduction, induction, abduction, analogy,
question answering, learning, data mining, knowledge discovery...    (011)

> It seems rather at odds with the usual implications of 
> subsetting languages, where tools for subsets need to be 
> expanded to handle full languages.  I am intrigued by what seem 
> to be subtle redefinitions of terms such as "subset/superset" or 
> "include ... tools".    (012)

Instead of saying "redefinition", I would claim that the words
'support' and 'full' have never been adequately defined for any
version of logic.  That's one theme of the following article:    (013)

    Fads and fallacies about logic    (014)

A programming language, such as Java or C, has a specific purpose
that determines the meaning of words like 'support' and 'full':
Each language was designed to represent algorithms that are
translated to an executable form, such as Java byte codes for
Java or machine instructions (plus supporting data) for C.    (015)

To say that tool X "supports" the "full" programming language L
means that X translates every syntactically correct statement
in L to an executable statement in the target language that
has whatever semantic effect is specified by the documentation.    (016)

But logics are declarative languages that have no single "purpose"
or "goal" or "use".  There are as many different meanings of the
words 'support' and 'full' as there are ways of using logic --
and that's probably countably infinite.  (See footnote.)    (017)

Some logic-based languages, such as Prolog or OWL, were designed
for a specific method of use.  For them, the programming-language
definition could be stretched to cover that method of use.    (018)

When mathematicians talk about logic, they think "theorem 
proving".  But look at the Thousands of Problems for Theorem 
Provers (tptp.org).  The tools that score the best overall are 
hybrids composed of many specialized tools optimized for various 
tasks:  translating source notations to some internal form or 
forms; analyzing problem statements (axioms + goal) to determine 
what strategy or strategies to use; breaking down the top-level 
goal to subgoals processed by different methods for special cases; 
storing and reusing previous results...    (019)

Cyc could be used to prove theorems in "full" CL, but Doug Lenat 
said that CycL is equivalent to CL + the IKL extensions.  The 
IKRIS project showed that IKL can be used as the interchange 
language for interoperability of CycL and other logics used in AI. 
But Cyc itself is actually a hybrid that uses techniques similar 
to the TPTP tools.    (020)

In fact, Cyc and many other AI systems go beyond theorem proving 
to implement some subset of the infinite variety of uses for 
logic.  Lenat likes to use the term 'commonsense reasoning', but I 
consider that a catch-all term with no fixed definition.  In fact, 
common sense is a moving target that changes with every innovation 
in science and even every political and/or religious motivation. 
(And by politics and religion, I include academic and commercial 
politics and faiths.)    (021)

_____________________________________________________________________    (022)

Footnote:  Excerpt from  http://www.jfsowa.com/pubs/rolelog.pdf    (023)

5. Steps Toward Formalization    (024)

In his Philosophical Remarks from the transitional period of 
1929-30, Wittgenstein analyzed some “minor” inconsistencies in the 
Tractatus. His analysis led to innovations that form a bridge 
between his early system and the far more flexible language games. 
Shanker (1987) noted two new terms that are key to Wittgenstein’s 
transition:    (025)

    1. Satzsystem:  a system of sentences or propositions stated
        in a given syntax and vocabulary.    (026)

    2. Beweissystem:  a proof system that defines a logic for a
        Satzsystem.    (027)

Formally, the combination of a Satzsystem with a Beweissystem
corresponds to what logicians call a theory — the deductive 
closure of a set of axioms. Informally, Wittgenstein’s remarks 
about Satzsysteme are compatible with his later discussions of 
language games. In conversations reported by Waismann (1979:48), 
Wittgenstein said that outside a Satzsystem, a word is like “a 
wheel turning idly.” Instead of a separate mapping of each 
proposition to reality, as in the Tractatus, the Satzsystem is 
mapped as a complete structure: “The Satzsystem is like a ruler 
(Maßstab) laid against reality. An entire system of propositions 
is now compared to reality, not a single proposition.” 
(Wittgenstein 1964, §82).    (028)

For a given logic (Beweissystem), each Satzsystem can be 
formalized as a theory that defines the ontology of a narrow 
subject. The multiplicity of Satzsysteme implies that any word 
that is used in more than one system will have a different sense 
in each. For natural languages, that principle is far more 
realistic than the monolithic logic and ontology of the Tractatus. 
Yet Wittgenstein illustrated his Philosophical Remarks primarily 
with mathematical examples. That turning point, as Shanker called 
it, implies that the goal of a unified foundation for all of 
mathematics, as stated in the Principia Mathematica, is 
impossible. That implication alarmed Russell, who observed “The 
theories contained in this new work of Wittgenstein’s are novel, 
very original, and indubitably important. Whether they are true, I 
do not know. As a logician who likes simplicity, I should wish to 
think that they are not.”    (029)

 From the mid 1930s to the end of his life, Wittgenstein focused 
on language games as a more general basis for a theory of meaning. 
But he continued to teach and write on mathematical topics, and he 
compared language games to the multiple ways of using words such 
as number in mathematics:  “We can get a rough picture of [the 
variety of language games] from the changes in mathematics.” These 
remarks imply that Satzsysteme can be considered specialized 
language games. The crucial addition for natural language is the 
intimate integration of language games with social activity and 
even the “form of life.” As Wittgenstein said in his notebooks, 
language is an “extension of primitive behavior. (For our language 
game is behavior.)” (Zettel, §545) The meaning of a word, a chess 
piece, or a mathematical symbol is its use in a game — a 
Sprachspiel or a Beweissystem.    (030)

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