Journal of Formalized Mathematics
Volume 1, 1989
University of Bialystok
Copyright (c) 1989
Association of Mizar Users
The Fundamental Logic Structure in Quantum Mechanics

Pawel Sadowski

Warsaw University, Bialystok

Andrzej Trybulec

Warsaw University, Bialystok

Konrad Raczkowski

Warsaw University, Bialystok
Summary.

In this article we present the logical structure given by four
axioms of Mackey [4] in the set of propositions of Quantum
Mechanics.
The equivalence relation (PropRel(Q)) in the set of propositions (Prop Q)
for given Quantum Mechanics Q is considered.
The main text for this article is [6]
where the structure
of quotient space and the properties of equivalence relations, classes and
partitions are studied.
MML Identifier:
QMAX_1
The terminology and notation used in this paper have been
introduced in the following articles
[8]
[3]
[12]
[10]
[13]
[14]
[15]
[1]
[2]
[11]
[7]
[5]
[9]
[6]
Contents (PDF format)
Bibliography
 [1]
Czeslaw Bylinski.
Functions and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [2]
Czeslaw Bylinski.
Functions from a set to a set.
Journal of Formalized Mathematics,
1, 1989.
 [3]
Czeslaw Bylinski.
Some basic properties of sets.
Journal of Formalized Mathematics,
1, 1989.
 [4]
G.W.Mackey.
\em The Mathematical Foundations of Quantum Mechanics.
North Holland, New York, Amsterdam, 1963.
 [5]
Andrzej Nedzusiak.
$\sigma$fields and probability.
Journal of Formalized Mathematics,
1, 1989.
 [6]
Konrad Raczkowski and Pawel Sadowski.
Equivalence relations and classes of abstraction.
Journal of Formalized Mathematics,
1, 1989.
 [7]
Andrzej Trybulec.
Domains and their Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [8]
Andrzej Trybulec.
Tarski Grothendieck set theory.
Journal of Formalized Mathematics,
Axiomatics, 1989.
 [9]
Andrzej Trybulec.
Tuples, projections and Cartesian products.
Journal of Formalized Mathematics,
1, 1989.
 [10]
Andrzej Trybulec.
Subsets of real numbers.
Journal of Formalized Mathematics,
Addenda, 2003.
 [11]
Wojciech A. Trybulec and Grzegorz Bancerek.
Kuratowski  Zorn lemma.
Journal of Formalized Mathematics,
1, 1989.
 [12]
Zinaida Trybulec.
Properties of subsets.
Journal of Formalized Mathematics,
1, 1989.
 [13]
Edmund Woronowicz.
Relations and their basic properties.
Journal of Formalized Mathematics,
1, 1989.
 [14]
Edmund Woronowicz.
Relations defined on sets.
Journal of Formalized Mathematics,
1, 1989.
 [15]
Edmund Woronowicz and Anna Zalewska.
Properties of binary relations.
Journal of Formalized Mathematics,
1, 1989.
Received December 18, 1989
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