Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory
| dc.creator | Ellerman, David | |
| dc.date | 2009-02-11 | |
| dc.date.accessioned | 2026-07-07T12:40:30Z | |
| dc.date.available | 2026-07-07T12:40:30Z | |
| dc.description | Categorical logic has shown that modern logic is essentially the logic of subsets (or "subobjects"). Partitions are dual to subsets so there is a dual logic of partitions where a "distinction" [an ordered pair of distinct elements (u,u') from the universe U ] is dual to an "element". An element being in a subset is analogous to a partition p on U making a distinction, i.e., if u and u' were in different blocks of p. Subset logic leads to finite probability theory by taking the (Laplacian) probability as the normalized size of each subset-event of a finite universe. The analogous step in the logic of partitions is to assign to a partition the number of distinctions made by a partition normalized by the total number of ordered pairs |UxU| from the finite universe. That yields a notion of "logical entropy" for partitions and a "logical information theory." The logical theory directly counts the (normalized) number of distinctions in a partition while Shannon's theory gives the average number of binary partitions needed to make those same distinctions. Thus the logical theory is seen as providing a conceptual underpinning for Shannon's theory based on the logical notion of "distinctions." (forthcoming in Synthese) | |
| dc.identifier | https://arxiv.org/abs/0902.1790 | |
| dc.identifier | http://arxiv.org/abs/0902.1790 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/219464 | |
| dc.subject | Information Theory | |
| dc.subject | Logic in Computer Science | |
| dc.subject | Logic | |
| dc.title | Counting Distinctions: On the Conceptual Foundations of Shannon's Information Theory | |
| dc.type | text |