[Alta-Logic] Talk Dec 9: Katalin Bimbó, Symmetric Gaggles

[Richard Zach]

NOTE ROOM!

Tuesday, December 9, 2008, 1 pm
1253 Social Sciences

Symmetric gaggles

Katalin Bimbó (University of Alberta, Philosophy)

Lambek calculus has been extended in various ways. Grishin 
duplicated Lambek calculus based on algebraic considerations;
this leads to questions of interactions between the operations.
Dunn and Hardegree proved that for an algebraic cut rule to
hold, certain (weak) distribution has to obtain between 
(intensional) conjunction and disjunction. Recently, 
Kurtonina and Moortgat argued for similar principles based
on linguistic examples.

This talk is about symmetric gaggles that are ggl's (generalized 
Galois logics) in which there is some distributivity between 
operations from the fusion (o) and fission (+) families. I will 
present representation (including isomorphic representation) 
theorems based on topological relational frames. The topological 
frames are algebraically realizable that yields duality theorems. 
Interestingly, the various distributivity principles turn out to 
be canonical independently of each other.

The talk is based on a joint paper (that is not yet published) 
by J. M. Dunn and me.