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

## 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: | 09 Dec 2019 00:42 |

URI: | http://eprints.lse.ac.uk/id/eprint/49750 |

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