Ellerman, David (2010) The Logic of Partitions: Introduction to the Dual of the Logic of Subsets. Review of Symbolic Logic, 3 (2). pp. 287-350.

Preview

PDF (Final preprint of published version) Logic-of-partitions5.pdf - Published Version Download (466kB)

Abstract

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. Modern categorical logic as well as the Kripke models of intuitionistic logic suggest that the interpretation of ordinary "propositional" logic might be the logic of subsets of a given universe set. 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.

---

Export/Citation:

EndNote | BibTeX | Dublin Core | ASCII/Text Citation (Chicago) | HTML Citation | OpenURL

Social Networking:

Share |

---

Item Type:	Published Article or Volume
Creators:	Creators Email ORCID Ellerman, David david@ellerman.org
Keywords:	logic of partitions, subset-partition duality, subset logic
Subjects:	Specific Sciences > Mathematics
Depositing User:	David Ellerman
Date Deposited:	23 Dec 2011 00:47
Last Modified:	23 Dec 2011 00:47
Item ID:	8966
Journal or Publication Title:	Review of Symbolic Logic
Publisher:	Association for Symbolic Logic
Subjects:	Specific Sciences > Mathematics
Date:	June 2010
Page Range:	pp. 287-350
Volume:	3
Number:	2
URI:	https://philsci-archive.pitt.edu/id/eprint/8966

Monthly Views for the past 3 years

Monthly Downloads for the past 3 years

Plum Analytics

Actions (login required)

View Item