The Quasi-lattice of Indiscernible Elements

Studia Logica 97 (1):101-126 (2011)
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Abstract

The literature on quantum logic emphasizes that the algebraic structures involved with orthodox quantum mechanics are non distributive. In this paper we develop a particular algebraic structure, the quasi-lattice ( $${\mathfrak{I}}$$ -lattice), which can be modeled by an algebraic structure built in quasi-set theory $${\mathfrak{Q}}$$. This structure is non distributive and involve indiscernible elements. Thus we show that in taking into account indiscernibility as a primitive concept, the quasi-lattice that ‘naturally’ arises is non distributive.

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Décio Krause
Federal University of Santa Catarina

References found in this work

Modal Logic: Graph. Darst.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - New York: Cambridge University Press. Edited by Maarten de Rijke & Yde Venema.
An algebraic approach to non-classical logics.Helena Rasiowa - 1974 - Warszawa,: PWN - Polish Scientific Publishers.
Identity in physics: a historical, philosophical, and formal analysis.Steven French & Décio Krause - 2006 - New York: Oxford University Press. Edited by Decio Krause.
Modal Logic.Patrick Blackburn, Maarten de Rijke & Yde Venema - 2001 - Studia Logica 76 (1):142-148.

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