12 research outputs found
The Generalised Liar Paradox: A Quantum Model and Interpretation
The formalism of abstracted quantum mechanics is applied in a model of the
generalized Liar Paradox. Here, the Liar Paradox, a consistently testable
configuration of logical truth properties, is considered a dynamic conceptual
entity in the cognitive sphere. Basically, the intrinsic contextuality of the
truth-value of the Liar Paradox is appropriately covered by the abstracted
quantum mechanical approach. The formal details of the model are explicited
here for the generalized case. We prove the possibility of constructing a
quantum model of the m-sentence generalizations of the Liar Paradox. This
includes (i) the truth-falsehood state of the m-Liar Paradox can be represented
by an embedded 2m-dimensional quantum vector in a (2m)^m dimensional complex
Hilbert space, with cognitive interactions corresponding to projections, (ii)
the construction of a continuous 'time' dynamics is possible: typical truth and
falsehood value oscillations are described by Schrodinger evolution, (iii)
Kirchoff and von Neumann axioms are satisfied by introduction of 'truth-value
by inference' projectors, (iv) time invariance of unmeasured state.Comment: 13 pages, to be published in Foundations of Scienc
How to play two-players restricted quantum games with 10 cards
We show that it is perfectly possible to play 'restricted' two-players,
two-strategies quantum games proposed originally by Marinatto and Weber having
as the only equipment a pack of 10 cards. The 'quantum board' of such a model
of these quantum games is an extreme simplification of 'macroscopic quantum
machines' proposed by one of the authors in numerous papers that allow to
simulate by macroscopic means various experiments performed on two entangled
quantum objectsComment: 4 pages, 3 figure
Quantum Experimental Data in Psychology and Economics
We prove a theorem which shows that a collection of experimental data of
probabilistic weights related to decisions with respect to situations and their
disjunction cannot be modeled within a classical probabilistic weight structure
in case the experimental data contain the effect referred to as the
'disjunction effect' in psychology. We identify different experimental
situations in psychology, more specifically in concept theory and in decision
theory, and in economics (namely situations where Savage's Sure-Thing Principle
is violated) where the disjunction effect appears and we point out the common
nature of the effect. We analyze how our theorem constitutes a no-go theorem
for classical probabilistic weight structures for common experimental data when
the disjunction effect is affecting the values of these data. We put forward a
simple geometric criterion that reveals the non classicality of the considered
probabilistic weights and we illustrate our geometrical criterion by means of
experimentally measured membership weights of items with respect to pairs of
concepts and their disjunctions. The violation of the classical probabilistic
weight structure is very analogous to the violation of the well-known Bell
inequalities studied in quantum mechanics. The no-go theorem we prove in the
present article with respect to the collection of experimental data we consider
has a status analogous to the well known no-go theorems for hidden variable
theories in quantum mechanics with respect to experimental data obtained in
quantum laboratories. For this reason our analysis puts forward a strong
argument in favor of the validity of using a quantum formalism for modeling the
considered psychological experimental data as considered in this paper.Comment: 15 pages, 4 figure
Coarelli et al., Table 4
Table 4. New SPG7 variants found in the analyzed cohort