Review of Symbolic Logic 3 (2):287-350 (2010)
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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.
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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 Merrill Smullyan - 1968 - Berlin, Germany: New York [Etc.]Springer-Verlag.
An Investigation of the Laws of Thought, on Which Are Founded the Mathematical Theories of Logic and Probabilities.George Boole - 1854 - London, England: Dover Constable.
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Citations of this work BETA
Logical Information Theory: New Logical Foundations for Information Theory.David Ellerman - 2017 - Logic Journal of the IGPL 25 (5):806-835.
The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2017
The Quantum Logic of Direct-Sum Decompositions: The Dual to the Quantum Logic of Subspaces.David Ellerman - 2018 - Logic Journal of the IGPL 26 (1):1-13.
View all 6 citations / Add more citations
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