8 research outputs found
Can many-valued logic help to comprehend quantum phenomena?
Following {\L}ukasiewicz, we argue that future non-certain events should be
described with the use of many-valued, not 2-valued logic. The
Greenberger-Horne-Zeilinger `paradox' is shown to be an artifact caused by
unjustified use of 2-valued logic while considering results of future
non-certain events. Description of properties of quantum objects before they
are measured should be performed with the use of propositional functions that
form a particular model of infinitely-valued {\L}ukasiewicz logic. This model
is distinguished by specific operations of negation, conjunction, and
disjunction that are used in it.Comment: 10 pages, no figure
Bell-type inequalities for bivariate maps on orthomodular lattices
Bell-type inequalities on orthomodular lattices, in which conjunctions of
propositions are not modeled by meets but by maps for simultaneous measurements
(s-maps), are studied. It is shown that the most simple of these inequalities,
that involves only two propositions, is always satisfied, contrary to what
happens in the case of traditional version of this inequality in which
conjunctions of propositions are modeled by meets. Equivalence of various
Bell-type inequalities formulated with the aid of bivariate maps on
orthomodular lattices is studied. Our invesigations shed new light on the
interpretation of various multivariate maps defined on orthomodular lattices
already studied in the literature. The paper is concluded by showing the
possibility of using s-maps and j-maps to represent counterfactual conjunctions
and disjunctions of non-compatible propositions about quantum systems.Comment: 14 pages, no figure
Quantum Machine and SR Approach: a Unified Model
The Geneva-Brussels approach to quantum mechanics (QM) and the semantic
realism (SR) nonstandard interpretation of QM exhibit some common features and
some deep conceptual differences. We discuss in this paper two elementary
models provided in the two approaches as intuitive supports to general
reasonings and as a proof of consistency of general assumptions, and show that
Aerts' quantum machine can be embodied into a macroscopic version of the
microscopic SR model, overcoming the seeming incompatibility between the two
models. This result provides some hints for the construction of a unified
perspective in which the two approaches can be properly placed.Comment: 21 pages, 5 figures. Introduction and Conclusions improved, minor
corrections in several sections. Accepted for publication in Foundations of
Physic
Example of a Finite Game with No Berge Equilibria at All
The problem of the existence of Berge equilibria in the sense of Zhukovskii in normal-form finite games in pure and in mixed strategies is studied. The example of a three-player game that has Berge equilibrium neither in pure, nor in mixed strategies is given
Quantum morphogenesis : A variation on Thom’s catastrophe theory
Noncommutative propositions are characteristic of both quantum and nonquantum (sociological, biological, and psychological) situations. In a Hilbert space model, states, understood as correlations between all the possible propositions, are represented by density matrices. If systems in question interact via feedback with environment, their dynamics is nonlinear. Nonlinear evolutions of density matrices lead to the phenomenon of morphogenesis that may occur in noncommutative systems. Several explicit exactly solvable models are presented, including “birth and death of an organism” and “development of complementary properties.”Non UBCReviewedFacult