9 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