A Complete Axiomatisation for the Logic of Lattice Effect Algebras

In a recent work Foulis and Pulmannová (Stud. Logica. 100 (6), 1291–1315, 2012 ) studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras can serve as semantic models. We shall f...

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Bibliographic Details
Published inInternational journal of theoretical physics Vol. 60; no. 2; pp. 696 - 709
Main Authors Rafiee Rad, Soroush, Sharafi, Amir Hossein, Smets, Sonja
Format Journal Article
LanguageEnglish
Published New York Springer US 01.02.2021
Springer Nature B.V
Subjects
Algebra
Axioms
Elementary Particles
Mathematical and Computational Physics
Physics
Physics and Astronomy
Quantum Field Theory
Quantum Physics
Theoretical
Lattice effect algebra
Unsharp quantum logic
Sasaki arrow
Weak lattice effect algebra
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Summary:In a recent work Foulis and Pulmannová (Stud. Logica. 100 (6), 1291–1315, 2012 ) studied the logical connectives in lattice effect algebras. In this paper we extend their study and investigate further the logical calculus for which the lattice effect algebras can serve as semantic models. We shall first focus on some properties of lattice effect algebras and will then give a complete axiomatisation of this logic.
ISSN:0020-7748
1572-9575
DOI:10.1007/s10773-019-04074-y