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THE LOGIC OF PARTITIONS: INTRODUCTION TO THE DUAL OF THE LOGIC OF SUBSETS

Published online by Cambridge University Press:  26 February 2010

DAVID ELLERMAN
DAVID ELLERMAN*
Affiliation:
Department of Philosophy, University of California/Riverside
*
*DEPARTMENT OF PHILOSOPHY, UNIVERSITY OF CALIFORNIA/RIVERSIDE, 4044 MT. VERNON AVE., RIVERSIDE, CA 92507. E-mail: [email protected]
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Abstract

Modern categorical logic as well as the Kripke and topological models of intuitionistic logic suggest that the interpretation of ordinary “propositional” logic should in general be the logic of subsets of a given universe set. Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms—which is reflected in the duality between quotient objects and subobjects throughout algebra. If “propositional” logic is thus seen as the logic of subsets of a universe set, then the question naturally arises of a dual logic of partitions on a universe set. This paper is an introduction to that logic of partitions dual to classical subset logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic.

Type
Research Article
Information
The Review of Symbolic Logic , Volume 3 , Issue 2 , June 2010 , pp. 287 - 350
Copyright
Copyright © Association for Symbolic Logic 2010

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