SUO: Re: IFF LOT Glossary
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Robert E. Kent wrote:
>
> OK Jon, now I have a question for you!
>
> ----- Original Message -----
> From: "Jon Awbrey" <jawbrey@att.net>
> To: "Robert E. Kent" <rekent@ontologos.org>
> Cc: "SUO" <standard-upper-ontology@ieee.org>
> Sent: Wednesday, July 02, 2003 5:36 PM
> Subject: Re: IFF LOT Glossary
>
> [snip]
>
> > Okay, I'm not trying to reduce anything, merely striving to relate things.
> > I am preparing for a happier FOL, but when I do get ready to cast it into
> > a full computational form, it's going to look a bit different, more like
> > a refit of Peirce's "Logic of Relatives" (1870) than anything you've
> > seen on the market lately. At any rate, any logic formalism is
> > just a formal language with added structure, and you know all
> > the reasons for upbuilding character bit by bit, so I'll just
> > leave it at that. Just for (auto-)tutorial purposes, though,
> > I would like to try devising some simple ZOL examples of the
> > corresponding concepts.
>
> I am very much interested in the calculus of binary relations.
> Please see Vaughn Pratt's articles referenced below. And also note
> the connection with Chu spaces, and the fact that the central category
> of Information Flow, Classification the category of classifications and
> infomorphisms, is the canonical Chu space Chu(Set, 2). And of course
> much in the IFF is based upon these ideas. Is your approach related
> to this material?
This will be in the category of Freud and Freyd:
free associative complexes, and books that I've
collected, but only sketchily looked into yet.
Don't know Pratt's work, but I did read DeMorgan and Schroeder
fairly closely some time ago, and been reading Peirce ever since.
Had some talks with Lyndon in '85-'86 as one of his sets of notes
was a big inspiration to me. Passing acquaintance with Tarski on
2-adic relations, as one of my advisors, Fatma Mili, uses a lot
from that tradition in her work. There is also Freyd & Scedrov,
'Catgories, Allegories', that explores the analogue of category
theory for binary relations.
http://www.secs.oakland.edu/~mili/
http://www.secs.oakland.edu/~mili/program-construction/
Was up with the 'Situations & Attitudes' angle in '85-'86,
when Larry Moss was at A^2 and was telling us about it,
and I collected a lot more stuff along that line,
but haven't got back to it yet.
I have glanced at some online material about Chu spaces, and it vaguely
reminds me of (1) some ideas that I was trying to work out in '80-'85 --
the last when I took a course on cartesian closed catgories, combinators,
and lambda calculus from John Gray -- well, still trying to work through
all that, about "relational arrows" and "intermediate objects", analogous
to initial and terminal objects only more middling, there was some strange
connection to the "surreal numbers" of Knuth & Conway, (2) some shapes that
I'm seeing in Peirce's 1870 LOR that I call "hypergraphs" or "spreadsheets".
This is all very fringy in my head right now,
but some material on it is somewhere in here:
http://stderr.org/pipermail/inquiry/2003-March/000184.html
...
http://stderr.org/pipermail/inquiry/2003-April/000243.html
...
http://stderr.org/pipermail/inquiry/2003-April/000302.html
Will look into it further.
Jon Awbrey
> The following two articles on the calculus
> of binary relations are accessible from:
>
> http://boole.stanford.edu/abstracts.html.
>
> Origins of the Calculus of Binary Relations
> @InProceedings( Pr92b,
> Author="Pratt, V.R.",
> Title="Origins of the Calculus of Binary Relations",
> Booktitle="Proc. 7th Annual IEEE Symp. on Logic in Computer Science",
> Address="Santa Cruz, CA",
> Month=Jun,
> Pages="248-254",
> Year=1992)
> The calculus of binary relations was introduced by De Morgan in 1860, and
> was subsequently greatly developed by Peirce and Schroeder. Half a century
> later Tarski, J'onsson, Lyndon, and Monk further developed the calculus from
> the perspective of modern model theory.
>
> The Second Calculus of Binary Relations
> @InProceedings( Pr93b,
> Author="Pratt, V.R.",
> Title="The Second Calculus of Binary Relations",
> Booktitle="MFCS'93, Gda{\'{n}}sk",
> Pages="142-155",
> Address="Poland",
> Year=1993)
> We view the Chu space interpretation of linear logic as an alternative
> interpretation of the language of the Peirce calculus of binary relations.
> Chu spaces amount to K-valued binary relations, which for K=2^n we show
> generalize n-ary relational structures. We also exhibit a four-stage unique
> factorization system for Chu transforms that illuminates their operation.
>
> Robert E. Kent
> rekent@ontologos.org
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