Re: sketch theory

[Zinovy Diskin <zdiskin@gsd.uwaterloo.ca>]

Let me make a few clarifying remarks

On Fri, May 22, 2009 at 8:44 PM,  <Andre.Rodin@ens.fr> wrote:

> I came across this recent paper by Diskin&Wolter
>
> http://www.cs.toronto.edu/~zdiskin/Pubs/ACCAT-07.pdf
>
> where the authors propose a version of sketch-based syntax for Computer Science
> purposes. The main idea here (as far as I understood the paper) is to use
> sketches as arities of predicates. I heard about similar ideas from Rene
> Guitart in private conversations (but Rene's approach is algebraic rather than
> logical).

our version of sketches is intended for use in software engineering,
not only in computer science. The difference between them is like the
difference between, say, electrical engineering and physics.

Predicate arities may be objects of any a priori chosen good category,
e.g., sketches built in a previous step, but this is not the main
idea. Relation of Makkai's generalized sketches to classical sketches
is, roughly, like relation of a general first-order theory a la Tarski
to a particular family of theories like, e.g., lattice theory. The
former provide a general framework, in which the user can define any
theory she likes. The latter is a family of particular instantiations
of the framework. The fact that this family is expressive enough to
specify any structure is another story.

A first-order signature contains operation and predicate symbols.
Similarly, a generalized sketch signature may contain operation
symbols too (whose arities are In-Out spans). Definitions and some
details can be found in Report referenced as [6] in the paper above.

ZD



Looking at GBLS briefly I couldn't immediately grasp if your and
> Atish Bagchi's approach to graph-based logic is based on similar ideas or your
> approach is quite different. I certainly should read GBLS more carefully for
> discussing it but I would grateful for a hint.
>
> Andrei
>
>
>
> Selon Charles Wells <charles@abstractmath.org>:
>
>> I have not kept up with the field very well, but I can recommend these
>> works:
>>
>> Peter Johnstone, *Sketches of an Elephant*, Vol. 2, OUP 2003: the chapter on
>> sketches.  (I am in rural Wisconsin at the moment asnd don't have access to
>> the book.  If OUP would make its pages available to look at on Amazon I
>> could have told you the exact page.)
>>
>> Bagchi and Wells, *Graph Based Logic and Sketches*, here:
>>
>> http://arxiv.org/PS_cache/arxiv/pdf/0809/0809.3023v1.pdf
>>
>> Also Kinoshita, et al 1997, referred to in GBLS.  There might be relevant
>> papers since 1993 mentioned in the Elephant, too.
>>
>> Category people:  If you can suggest other papers that should be included,
>> let me know soon, and I will revise the sketches paper to include them (and
>> the ones I mentioned above).
>>
>> Charles Wells
>>
>>
>
>