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Operator algebras and quantum logic

Rédei, Miklós ORCID: 0000-0001-5298-1443 (2004) Operator algebras and quantum logic. In: Weingartner, Paul, (ed.) Alternative Logics: Do Sciences Need Them? Springer, Dordrecht, pp. 349-360. ISBN 9783642073915

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Identification Number: 10.1007/978-3-662-05679-0_23

Abstract

Let K = (p, q...; &, ∨, ~) be a zeroth-order formal language with sentence variables p, q..., two place connectives & (and), ∨ (or) and negation sign ~, and let F be the formula algebra (set of well-formed formulas in K defined in the standard way by induction from the sentence variables). If v is an assignment of truth values 1(true), 0(f alse) to the sentence variables p, q..., then classical propositional logic is characterized by extending v by induction from p, q... to the formula algebra F in such a manner that the extension (called interpretation and also denoted by v) be a “homomorphism” from F into the two-element Boolean algebra B 2 ≡ (1, 0, ⋂, ⋃, ⊥), where “homomorphism” means that the following hold υ(q&p)=υ(q)∩υ(p)υ(q∨p)=υ(q)∪υ(p)υ(∼q)=υ(q)⊥.

Item Type: Book Section
Official URL: http://www.springer.com/
Additional Information: © 2004 Springer
Divisions: Philosophy, Logic and Scientific Method
Subjects: B Philosophy. Psychology. Religion > B Philosophy (General)
Q Science > QC Physics
Sets: Departments > Philosophy, Logic and Scientific Method
Date Deposited: 19 Apr 2013 09:13
Last Modified: 08 Jun 2020 23:04
URI: http://eprints.lse.ac.uk/id/eprint/49750

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