Characterizations of classical and quantum logics

PEKKA J. LAHTI

M. K. Mukherjee

Gui Qi-quan

According to philosophy of logic,quantum can be considered as a non-classical characterized by non-distributivity,and it takes scientific inference actually used by scientists of quantum mechanics as real prototypes or basis.Hillary Putnam concluded that logic can be revised globally due to reasons in terms of generation of quantum logic;while at same time he claimed that quantum logical connectives retained their classical meanings,which made him fall into a dilemma.After reexamining empirical reasons and the revision of argument on basis of several different interpretations of quantum mechanics,the authors of this paper found that metaphysical considerations are not negligible.And paper proposed that Correspondence Principle had methodological effect of resolving Putnam's Dilemma,and could explain reasonably continuity and innovation of quantum to classical logic.

Heinrich Saller

José Alejandro Fernández Cuesta, Michele Piazzai, Umberto Rivieccio

Abstract Quantum logics are non-classical logics defined from the mathematical formalism of quantum mechanics. While they are conventionally used to model inferential processes in physics, their scope of application is potentially much broader. We argue that quantum logics can serve as a framework to model human cognition, as their semantics seem able to capture not only how people make inferences about quantum mechanics, but also how they reason in general. We begin by defining quantum logics from an algebraic perspective in a classical first-order setting. Next, we present findings from cognitive science that suggest these logics are apt to characterize human reasoning. We then consider how such a connection between quantum logics and cognition contributes to longstanding philosophical debates about the epistemological status of logic and the problem of adoption. Finally, we discuss how cognitive applications of quantum logics could advance our understanding of human psychology and even quantum foundations.

Federico Holik, César Massri

In this work we study the convex set of quantum states from a quantum logical point of view. We consider an algebraic structure based on the convex subsets of this set. The relationship of this algebraic structure with the lattice of propositions of quantum logic is shown. This new structure is suitable for the study of compound systems and shows new differences between quantum and classical mechanics. This differences are linked to the nontrivial correlations which appear when quantum systems interact. They are reflected in the new propositional structure, and do not have a classical analogue. This approach is also suitable for an algebraic characterization of entanglement.