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)
CM:
> 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)
CS:
> 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)
http://www.jfsowa.com/pubs/fflogic.pdf
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)
John
_____________________________________________________________________ (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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