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

Authors
David Ellerman
University of Ljubljana
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.
Keywords Boolean logic of subsets  logic of partitions
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DOI 10.1017/S1755020310000018
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References found in this work BETA

First-Order Logic.Raymond M. Smullyan - 1968 - New York [Etc.]Springer-Verlag.
Introduction to Mathematical Logic.ALONZO CHURCH - 1944 - London: Oxford University PRess.
Category Theory.S. Awodey - 2007 - Bulletin of Symbolic Logic 13 (3):371-372.

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Citations of this work BETA

An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.

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