On Sep 21, 2008, at 11:12 AM, Rick Murphy wrote: Pat & Rob:
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.
Well, he used category theory to build a very general theory of logics ('institutions'), yes. BUt that is something rather different. After all, category theory is a very general framework that can be applied to a broad range of subject-matters. (Which is why it is so widely used, of course.) Institution theory is kind of super-general mathematical approach to describing logical syntax and relating different logics to one another, and it extends to relationships defined semantically. But its not really an alternative to Tarski, so much as a very abstract generalization of it. The notional connections might go something like: develop semiotics from semantics define algebraic semiotics develop semiotic morphisms from structure preserving morphisms http://www-cse.ucsd.edu/~goguen/
I know the general idea, though admit to not having followed through on all the details. (Rod Burstall, an active collaborator with Goguen on much of this, was one of my graduate supervisors.)
I have to admit, I havnt yet seen any actual utility in this stuff, and I find the high level of abstraction rather off-putting. Though the UCSD folk are doing some interesting work in 'algebraic semiotics' based on Goguen's stuff, I will agree.
but in practice, is it anything more than a kind of organized catalog of conventional theorem=provers? What is gained by all this terminology of 'institutions'?
Pat
Rick 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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