Pat & Rob: (01)
Although not as well known as much of what is discussed regularly here,
Joseph Goguen's work included institutions, algebraic semiotics and
semiotic morphisms that relate category theory to semantics. (02)
The notional connections might go something like: (03)
develop semiotics from semantics
define algebraic semiotics
develop semiotic morphisms from structure preserving morphisms (04)
http://www-cse.ucsd.edu/~goguen/ (05)
Goguen, the author of the Categorical Manifesto, left a legacy that will
take a few generations to fully develop. Institutions are a pretty a
pretty good place to start ... (06)
http://www-cse.ucsd.edu/~goguen/projs/inst.html (07)
Also note, the work on the Heterogeneous Tool Set (HETS) here ... (08)
http://www.informatik.uni-bremen.de/agbkb/forschung/formal_methods/CoFI/hets/index_e.htm (09)
seems to be nicely developing a framework for Goguen's institutions ... (010)
Rick (011)
Pat Hayes wrote:
> On Sep 20, 2008, at 8:47 AM, Rob Freeman wrote:
>
>> I would welcome comments on a possible relationship between gauge
>> theories in physics, Category Theory in maths, and semantics.
>>
>
> Well, you did ask. These three topics have absolutely nothing whatever
> to do with one another. Gauge theories focus on symmetries in physical
> theory: that is, ways in which theories are invariant under various
> mathematical transformations. Category theory is a branch of pure
> mathematics, a kind of ultimate abstraction of algebra, which focusses
> on systems ('categories') defined by mappings . Semantics is concerned
> with the relationship between representations and what it is that they
> represent. One might as well ask for comments on a possible
> relationship between botany, music and gardening.
>
> Let me ask in return, what was it that suggested to you that these
> three topics might have any relationship?
>
> Pat
>
>
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> (012)
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