David Ellerman: New Foundations for Information Theory
Time: Fri 2017-09-15 10.00 - 11.45
Location: Room 16, building 5 kräftriket, Department of Mathematics, Stockholm University
Participating: David Ellerman — University of California at Riverside, University of Ljubljana
Abstract:
Partitions are categorically dual to subsets, so there is a logic of partitions dual to the usual Boolean logic of subsets. The quantitative version of the logic of subsets is logical probability theory and the quantitative version of partition logic is logical information theory which is the subject of the talk:
Probability : Subsets :: Information : Partitions.
Logical information theory is the foundational theory that (finally) explains what information is at the most abstract logical level. All the Shannon definitions of simple, joint, conditional, and mutual entropy can be obtained from the corresponding definitions of logical entropy by a uniform requantifying transformation. This displaces the Shannon theory from being the foundational theory to being a higher-order specialized theory for coding and communication where it has been enormously successful. The talk concludes by showing how the logical concepts extend to the quantum case to provide new foundations for quantum information theory. The background paper for the talk, “Logical Information Theory: New Foundations for Information Theory,” has come out (at least online) in The Logic Journal of the IGPL. Preprint at www.ellerman.org .