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

66 Pages Posted: 26 Mar 2009 Last revised: 13 Oct 2009

Date Written: March 26, 2009

Abstract

Partitions on a set are dual to subsets of a set in the sense of the category-theoretic duality of epimorphisms and monomorphisms. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of classical "propositional" logic might be the logic of subsets of a given universe set. The propositional interpretation is isomorphic to the special case where the truth and falsity of propositions behave like the subsets of a one-element set. If classical "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 "propositional" logic. The paper goes from basic concepts up through the correctness and completeness theorems for a tableau system of partition logic.

Keywords: alternative logics, partition logic, subset logic

Suggested Citation

Ellerman, David, The Logic of Partitions: Introduction to the Dual of the Logic of Subsets (March 26, 2009). Available at SSRN: https://ssrn.com/abstract=1368796 or http://dx.doi.org/10.2139/ssrn.1368796

David Ellerman (Contact Author)

University of Ljubljana ( email )

School of Social Science
Ljubljana, CA
Slovenia

HOME PAGE: http://www.ellerman.org

Here is the Coronavirus
related research on SSRN

Paper statistics

Downloads
95
Abstract Views
735
rank
298,142
PlumX Metrics