http:^^www.cs.indiana.edu^research^dunn^ggl.html

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Date: Wed, 20 Nov 1996 19:15:16 GMT
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<html><HEAD><TITLE> Gaggle Theory </TITLE></HEAD><BODY background = "pentag8.gif"><H2> Gaggle Theory </H2><Strong>Description: </Strong> <Blockquote> Gaggle (and not giggle) isthe pronunciation of the acronym "ggl" for generalized galoislogic. 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 theideas of Jonnson and Tarski's "Boolean algebras with operators."Operators can distribute or co-distribute in various of their placesover either meet or join, and are also required to interact with eachother in a way that generalizes the notions of Galois connection andresiduation. 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 logicis interpreted using a binary accessibility relation.  While theoriginal focus was gaggles based on underlying distributive lattices,the project has been extended to underlying partial orders,semi-lattices, involuted semi-lattices, and lattices. </Blockquote><P><Strong> Associated Faculty: </Strong>  Gerard Allwein<P><Strong> Associated Graduate Students: </Strong>  Steve Crowley (Philosophy)<P><Strong> Affiliated Projects: </Strong> Chrysafis Hartonas (Universityof Ioannina, Greece), Greg Restall (Automated Reasoning Project,Australian National University) <P><Strong> Support: </Strong> College of Arts and Sciences<p> <!WA0><A HREF = "http://www.cs.indiana.edu/l/www/research/index.html"><!WA1><IMG SRC="http://www.cs.indiana.edu/research/back.gif">Return to Computer Science Research Page  </A>

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