How to Produce S-Tense Operators on Lattice Effect Algebras

2014 ◽  
Vol 44 (7) ◽  
pp. 792-811 ◽  
Author(s):  
Ivan Chajda ◽  
Jiří Janda ◽  
Jan Paseka
Keyword(s):  
Effect Algebras ◽  
Tense Operators ◽  
Lattice Effect

Dynamic effect algebras

2012 ◽  
Vol 62 (3) ◽  
Author(s):  
Ivan Chajda ◽  
Miroslav Kolařík
Keyword(s):  
Quantum Mechanics ◽  
Effect Algebra ◽  
Dynamic Effect ◽  
Effect Algebras ◽  
Lattice Effect Algebra ◽  
Tense Operators ◽  
Lattice Effect

AbstractWe introduce the so-called tense operators in lattice effect algebras. Tense operators express the quantifiers “it is always going to be the case that” and “it has always been the case that” and hence enable us to express the dimension of time in the logic of quantum mechanics. We present an axiomatization of these tense operators and prove that every lattice effect algebra whose underlying lattice is complete can be equipped with tense operators. Such an effect algebra is called dynamic since it reflects changes of quantum events from past to future.

Material implications in lattice effect algebras

2018 ◽  
Vol 433-434 ◽  
pp. 233-240 ◽  
Author(s):  
R.A. Borzooei ◽  
A. Dvurečenskij ◽  
A.H. Sharafi
Keyword(s):  
Effect Algebras ◽  
Lattice Effect

Effect algebras with a full set of states

2016 ◽  
Vol 66 (4) ◽  
Author(s):  
Ivan Chajda
Keyword(s):  
Temporal Logic ◽  
Effect Algebra ◽  
Effect Algebras ◽  
Tense Operators ◽  
Numerical Algebra ◽  
Full Set Of States

AbstractIt is shown that every effect algebra with a full set of states can be represented as a so-called numerical algebra introduced in the paper. For numerical algebras there are introduced tense operators which indicate dynamical changes of quantum events depending on variability of states. These operators enable to recognize an effect algebra with a full set of states as a temporal logic where events are quantified by these tense operators. The problem of representation of tense operators on a given numerical algebra is solved.

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