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Date: Wed, 20 Nov 1996 19:15:08 GMT
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<html><HEAD><TITLE> Structurally Free Logic </TITLE></HEAD><BODY background = "pentag8.gif"><H2> Structurally Free Logic </H2><Strong>Description: </Strong> <Blockquote> In the last few yearsthere has been great interest in so-called "substructural logics,"whereby various well-known logics are distinguished by the structuralrules that are postulated in the Gentzen systems for the logics. Mostnotorious have been thinning (relevance logic), contraction (BCKlogic), and linear logic (linear logic). But there is no reason tostop there, as people have considered non-commutative linear logic(better, the associative Lambek calculus), and people have even lookedat non-associative logice. The point of view taken in this project isthat structural rules should be done away with altogether, and theirplace taken by explicit introduction rules forcombinators. Combinators are take as "first-class' objects, and stilla cut-elimination theorem can be proven.Further the ternary relational semantics (Routley-Meyer semantics)for the Lambek calculus can be extended so as to provide a semanticsfor combinatory logic. The key idea is that a ternary relation onstates can be interpreted as an indexed action on states. So a set ofstates (a proposition) can be simultaneously be viewed as a set ofactions, and so it makes sense to talk of applying one proposition toanother (even itself).There are still a number of open problems, mostly centering about theaddition of conjunction and disjunction. These include proving the cut-theorem with respect to the distributive combination of the two, and providing a completeness theorem for their non-distributive combination.</Blockquote><P><Strong>Associated Faculty:</Strong>Michael Dunn<P><Strong> Affiliated Projects: </Strong> Robert K. Meyer(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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