Date: Wed, 20 Nov 1996 19:15:16 GMT Server: Apache/1.0.3 Content-type: text/html Content-length: 1691 Last-modified: Mon, 04 Dec 1995 14:57:59 GMT Gaggle Theory

Gaggle Theory

Description:
Gaggle (and not giggle) is the pronunciation of the acronym "ggl" for generalized galois logic. This is an algebraic abstraction that covers most of existing "natural" logics (classical, modal, intuitionistic, relevant, linear, BCK, Lambek calculus, etc.). A gaggle is a great generalization of the ideas of Jonnson and Tarski's "Boolean algebras with operators." Operators can distribute or co-distribute in various of their places over either meet or join, and are also required to interact with each other in a way that generalizes the notions of Galois connection and residuation. The idea is to give a representation theorem using "Kripke frames," and to interpret an n-ary operator using a n+1 - placed accessibility relation, as for example necessity in modal logic is interpreted using a binary accessibility relation. While the original focus was gaggles based on underlying distributive lattices, the project has been extended to underlying partial orders, semi-lattices, involuted semi-lattices, and lattices.

Associated Faculty: Gerard Allwein

Associated Graduate Students: Steve Crowley (Philosophy)

Affiliated Projects: Chrysafis Hartonas (University of Ioannina, Greece), Greg Restall (Automated Reasoning Project, Australian National University)

Support: College of Arts and Sciences

Return to Computer Science Research Page