The Logic of Partitions: With Two Major Applications

Ellerman, David

ISBN 10: 1848904401 / ISBN 13: 9781848904408

Published by College Publications, 2023

About this Item

Seller Inventory # I-9781848904408

Bibliographic Details

• Title: The Logic of Partitions: With Two Major Applications
• Publisher: College Publications
• Publication Date: 2023
• Language: English
• ISBN 10: 1848904401
• ISBN 13: 9781848904408
• Binding: Soft cover
• Condition: New

About this title

Synopsis

This book is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (direct-sum decompositions or DSDs) on a vector space. Partitions of a set are categorically dual to subsets of a set. Thus the logic of partitions is, in that sense, the dual to the Boolean logic of subsets (usually presented as the special case of propositional logic).

Since partitions can be seen as the inverse image partitions of random variables or numerical attributes, partition logic is the logic of random variables or numerical attributes (abstracted from the actual values). On the lattice of partitions of an arbitrary unstructured set, there is a rich algebraic structure of dual operations of implication and co-implication - resembling a non-distributive version of Heyting and co-Heyting algebras.