Towards many-valued/fuzzy interpretation of quantum mechanics

被引：9
作者：
Pykacz, Jaroslaw [1 ]
机构：
[1] Univ Gdansk, Inst Matemat, PL-80952 Gdansk, Poland
来源：
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS | 2011年 / 40卷 / 01期
关键词：
interpretation of quantum mechanics; quantum logic; fuzzy sets; many-valued logic; LUKASIEWICZ LOGIC;
D O I：
10.1080/03081079.2010.507331
中图分类号：
TP301 [理论、方法];
学科分类号：
081202 ;
摘要：
In this paper, we propose a new interpretation of quantum mechanics according to which Born probabilities are interpreted as many-valued truth values of statements concerning results of not-yet-performed experiments on quantum objects, or equivalently [0,1]-valued degrees to which quantum objects possess all their properties prior to measurements. The interpretation is based on mathematical results already published by the author, according to which any Birkhoff-von Neumann quantum logic can be isomorphically represented as a family of fuzzy sets or, equivalently, many-valued propositional functions.
引用
收藏
页码：11 / 21
页数：11
相关论文
共 50 条
[21]   Some algebraic structures for many-valued logics [J].
Cattaneo, G ;
Dalla Chiara, ML ;
Giuntini, R .
TATRA MOUNTAINS MATHEMATICAL PUBLICATIONS, VOL 15, 1998: QUANTUM STRUCTURES II, 1998, :173-195
[22]   A Talmudic norms approach to many-valued logic [J].
Lethen, Tim .
JOURNAL OF LOGIC AND COMPUTATION, 2021, 31 (05) :1195-1205
[23]   An exercise on the generation of many-valued dynamic logics [J].
Madeira, Alexandre ;
Neves, Renato ;
Martins, Manuel A. .
JOURNAL OF LOGICAL AND ALGEBRAIC METHODS IN PROGRAMMING, 2016, 85 (05) :1011-1037
[24]   Quantum logic circuit design of many-valued galois reversible expansions and fast transforms [J].
Al-Rabadi, Anas N. .
JOURNAL OF CIRCUITS SYSTEMS AND COMPUTERS, 2007, 16 (05) :641-671
[25]   ON THE MONOTONICITY OF THE FUZZY SYSTEMS BASED UPON GENUINE MANY-VALUED IMPLICATIONS-SISO CASES [J].
Qin, Feng ;
Wang, Defa .
QUANTITATIVE LOGIC AND SOFT COMPUTING, 2012, 5 :565-572
[26]   Quine–McCluskey method for many-valued logical functions [J].
Milan Petrík .
Soft Computing, 2008, 12 :393-402
[27]   A relational formalisation of a generic many-valued modal logic [J].
Konikowska, B ;
Orlowska, E .
RELATIONAL METHODS FOR COMPUTER SCIENCE APPLICATIONS, 2001, 65 :183-202
[28]   MANY-VALUED LOGIC SYSTEM FOR LINGUISTIC MODEL PROCESSING [J].
DRUCKMULLER, M .
INTERNATIONAL JOURNAL OF GENERAL SYSTEMS, 1991, 20 (01) :31-37
[29]   Many-valued logics-implications and semantic consequences [J].
Pasztor Varga, Katalin ;
Alagi, Gabor ;
Varteresz, Magda .
ACTA UNIVERSITATIS SAPIENTIAE INFORMATICA, 2013, 5 (02) :145-166
[30]   Structural Completeness in Many-Valued Logics with Rational Constants [J].
Gispert, Joan ;
Hanikova, Zuzana ;
Moraschini, Tommaso ;
Stronkowski, Michal .
NOTRE DAME JOURNAL OF FORMAL LOGIC, 2022, 63 (03) :261-299
12345