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

David Ellerman
University of Ljubljana
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
Categories (categorize this paper)
DOI 10.1017/S1755020310000018
Edit this record
Mark as duplicate
Export citation
Find it on Scholar
Request removal from index
Revision history

Download options

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.

View all 17 references / Add more references

Citations of this work BETA

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

View all 6 citations / Add more citations

Similar books and articles

An Introduction to Partition Logic.David Ellerman - 2014 - Logic Journal of the IGPL 22 (1):94-125.
An Introduction to Logical Entropy and its Relation to Shannon Entropy.David Ellerman - 2013 - International Journal of Semantic Computing 7 (2):121-145.
The Spectrum of Partitions of a Boolean Algebra.J. Donald Monk - 2001 - Archive for Mathematical Logic 40 (4):243-254.
Possibility Semantics for Intuitionistic Logic.M. J. Cresswell - 2004 - Australasian Journal of Logic 2:11-29.
A Note on Dual-Intuitionistic Logic.Norihiro Kamide - 2003 - Mathematical Logic Quarterly 49 (5):519.
Forcing Closed Unbounded Subsets of Ω2.M. C. Stanley - 2001 - Annals of Pure and Applied Logic 110 (1-3):23-87.
LK, LJ, Dual Intuitionistic Logic, and Quantum Logic.Hiroshi Aoyama - 2004 - Notre Dame Journal of Formal Logic 45 (4):193-213.
S5 Knowledge Without Partitions.Dov Samet - 2010 - Synthese 172 (1):145 - 155.


Added to PP index

Total views
194 ( #43,255 of 2,326,776 )

Recent downloads (6 months)
23 ( #28,061 of 2,326,776 )

How can I increase my downloads?


My notes