Counting distinctions: on the conceptual foundations of Shannon’s information theory.
Categorical logic has shown that modern logic is essentially the logic of subsets (or “subobjects”). In “subset logic,” predicates are modeled as subsets of a universe and a predicate applies to an individual if the individual is in the subset. Partitions are dual to subsets so there is a dual logic...
| Publicado en: | Synthese Vol. 168; no. 1; pp. 119 - 150 |
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| Formato: | Artículo |
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Springer Nature
May2009
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| Acceso en línea: | Ver este registro en EBSCOhost |
| fields | @attributes: recordID: 1 pdfLink: plink: https://search.ebscohost.com/login.aspx?direct=true&db=hlh&AN=37254811&site=ehost-live header: @attributes: shortDbName: hlh uiTerm: 37254811 longDbName: Humanities International Complete uiTag: AN controlInfo: bkinfo: jinfo: jid: 00397857 4LI jtl: Synthese issn: 00397857 maglogo: N pubinfo: dt: May2009 vid: 168 iid: 1 pid: 237 pub: Springer Nature artinfo: ui: 37254811 10.1007/s11229-008-9333-7 ppf: 119 ppct: 31 formats: fmt: @attributes: type: P size: 263KB tig: atl: Counting distinctions: on the conceptual foundations of Shannon’s information theory. aug: au: Ellerman, David affil: Department of Philosophy, University of California Riverside, 4044 Mt. Vernon Ave., Riverside, CA 92507, USA su: Information theory Modern logic Borel sets Partitions (Mathematics) Predicate (Logic) Shannon's model (Communication) sug: subj: Information theory Modern logic Borel sets Partitions (Mathematics) Predicate (Logic) Shannon's model (Communication) keyword: Logic of partitions Logical entropy Shannon entropy ab: Categorical logic has shown that modern logic is essentially the logic of subsets (or “subobjects”). In “subset logic,” predicates are modeled as subsets of a universe and a predicate applies to an individual if the individual is in the subset. 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”. A predicate modeled by a partition π on U would apply to a distinction if the pair of elements was distinguished by the partition π, i.e., if u and u′ were in different blocks of π. 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 | U| pairs 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.” pubtype: Academic Journal doctype: Article src: R language: English refInfo: copyright: @attributes: flag: Y custom: Synthese is a copyright of Springer, 2009. All Rights Reserved. item: Synthese holder: Springer Nature dt: @attributes: year: 2009 holdings: @attributes: islocal: N |
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