SUO: Re: Peirce's MS 514
Pat Hayes wrote:
>
> > Chris,
> >
> > I agree with your "niggling points" as I do with Pat's
> > "quibbles". (Which is bigger, a niggle or a quibble?)
>
> Not sure; but a quiggle sounds to be more than a nibble.
>
> > > Niggling point: entailment depends on notation as well,
> > > since it is always some set of statements in some notation
> > > (some language) that entails some other sentence in that notation.
> >
> > I used the word "statement" to avoid getting into details
> > about the distinction between a "statement" and a "proposition".
> > But as I have said in my KR book (Ch. 5) and many email notes,
> > I prefer to define a proposition as an equivalence class of
> > statements in multiple languages. With such a definition,
> > you can talk about entailment in a form that factors out as
> > much of the notation as you like. (The larger the equivalence
> > class, the smaller the dependence on any particular notation.)
> >
> > This kind of factoring is especially important for the SUO,
> > since we must deal with multiple languages, including CGs,
> > DAML, OIL, SQL, RDF, UML, and versions of controlled natural
> > languages, such as ACE or Aristotelian syllogisms.
> >
>
> Interesting idea, and I agree important. But to give it flesh
> you need to say what the equivalence relation is, relative to
> which the equivalence classes are defined; and that in turn
> seems to require some way to compare the semantic content
> of expressions from different languages. If they are
> all interpreted in the same structures one could see
> how this would go -- equivalent expressions denote
> the same things in all interpretations -- but the
> more general construction eludes me.
>
> If this is all in your book, I apologise for not yet getting that far.
>
> Pat
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Pat,
This is exactly the sort of problem that
Category Theory was invented to solve:
Eilenberg & MacLane, "General Theory of Natural Equivalences",
'Transactions of the American Mathematical Society, 58 (1945),
pages 231-294.
We would only need to tweak it a bit to work for sign relations.
Jon Awbrey
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