The Many-Valued Logic of Jan Łukasiewicz in the Foundations of Quantum Mechanics

Opis książki:

1. Introduction 5
2. A brief survey of many-valued logics 7
3. Fuzzy sets and many-valued logics ... 15
3.1. Rudiments of the fuzzy set theory 15
3.2. Fuzzy sets and infinite-valued Łukasiewicz logic .. 18
4. Many-valued logics in quantum mechanics 22
5. Birkhoff — von Neumann quantum logic 26
5.1. The traditional algebraic model 27
5.2. Mączyński`s functional model .. 28
5.3. The general fuzzy set model .. 29
5.4. Two pairs of binary operations 33
6. Birkhoff — von Neumann quantum logic as oo-valued Łukasiewicz logic 40
6.1. The infinite-valued model of Birkhof F - von Neumann quantum logic 40
6.2. Application: analysis of a two-slit experiment .. 48
7. General quantum structures and infinite-valued Łukasiewicz logic 51
7.1. Effect algebras and other quantum structures ... 51
7.2. Quantum structures and Łukasiewicz connectives. 53
7.3. General effect algebras of fuzzy sets ... 56
8. Summary, discussion, and perspectives 62
8.1. Summary of results .. 62
8.2. Discussion: what is "quantum logic" and what it is not. . 63
8.3. Perspectives. 65
8.3.1. Fuzzy set models of quantum probability. 65
8.3.2. Puzzy phase space representation of quantum mechanics 68
Bibliography 71

Książka "The Many-Valued Logic of Jan Łukasiewicz in the Foundations of Quantum Mechanics" - Jarosław Pykacz - oprawa miękka - Wydawnictwo Uniwersytetu Gdańskiego.