 The Logic of Partitions
With Two Major Applications
David Ellerman
Forthcoming.
This book is an introduction to the logic of partitions on a set as well as the (quantum) logic of partitions (directsum 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 coimplicationâ€“resembling a nondistributive version of Heyting and coHeyting algebras.
9781848904408
