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The Logic of Partitions: Introduction to the Dual of the Logic of Subsets

Ellerman, David (2010) The Logic of Partitions: Introduction to the Dual of the Logic of Subsets. [Published Article]

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    Abstract

    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. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets of a given universe set. 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.


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    Item Type: Published Article
    Keywords: logic of partitions, subset-partition duality, subset logic
    Subjects: Specific Sciences > Mathematics
    Depositing User: David Ellerman
    Date Deposited: 22 Dec 2011 19:47
    Last Modified: 22 Dec 2011 19:47
    Item ID: 8966
    Journal or Publication Title: Review of Symbolic Logic
    Publisher: Association for Symbolic Logic
    URI: http://philsci-archive.pitt.edu/id/eprint/8966

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