# The logic of partitions: Introduction to the dual of the logic of subsets: The logic of partitions

*Review of Symbolic Logic*3 (2):287-350 (2010)

**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.

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References found in this work BETA

An Introduction to Substructural Logics.Restall, Greg

Categories for the Working Mathematician.Maclane, Saunders

First-Order Logic.Smullyan, Raymond M.

First-Order Logic.Smullyan, Raymond M.

Introduction to Mathematical Logic.CHURCH, ALONZO

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Citations of this work BETA

An Introduction to Partition Logic.Ellerman, David

The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.Ellerman, David

On Classical and Quantum Logical Entropy.Ellerman, David

Four Ways From Universal to Particular: How Chomsky’s Principles-and-Parameters Model is Not Selectionist.Ellerman, David P.

The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.Ellerman, David

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2009-03-27

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