The Logic of Partitions: With Two Major Applications
Language: English
Published by College Publications, 2023
- Softcover
- New
Seller: GreatBookPricesUK, Woodford Green, United KingdomGreatBookPricesUK
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- Title
- The Logic of Partitions: With Two Major Applications
- Author
- Ellerman, David
- Publisher
- College Publications
- Publication year
- 2023
- Condition
- New
- Binding
- Soft cover
- Language
- English
- ISBN 10
- 1848904401
- ISBN 13
- 9781848904408
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.
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