This Brief presents steps towards elaborating a new interpretation of quantum mechanics based on a specific version of ukasiewicz infinite-valued logic. It begins with a short survey of main interpretations of quantum mechanics already proposed, as well as various models of many-valued logics and previous attempts to apply them for the description of quantum phenomena. The prospective many-valued interpretation of quantum mechanics is soundly based on a theorem concerning the isomorphic representation of Birkhoff-von Neumann quantum logic in the form of a special ukasiewicz infinite-valued logic endowed with partially defined conjunctions and disjunctions.

Includes supplementary material: sn.pub/extras

Autorentext
Jarosaw Pykacz, born 1952, studied physics and mathematics at the University of Gdask and received his PhD in theoretical physics in 1980. He was one of the founding fathers of the International Quantum Structures Association and served as its President in the years 2008 - 2010. He published about 50 papers on logico-philosophic foundations and application of fuzzy sets in quantum mechanics.

Inhalt
Introduction.- A brief survey of main interpretations of quantum mechanics.- A brief survey of many-valued logics.- Fuzzy sets and many-valued logics.- Many-valued logics in quantum mechanics.- Birkhoffvon Neumann quantum logic.- Birkhoffvon Neumann quantum logic as infinite-valued ukasiewicz logic.- Perspectives.- The many-valued interpretation of quantum mechanics.