  We present a very general geometrico-dynamical description of physical or
more abstract entities, called the 'general tension-reduction' (GTR) model,
where not only states, but also measurement-interactions can be represented,
and the associated outcome probabilities calculated. Underlying the model is
the hypothesis that indeterminism manifests as a consequence of unavoidable
fluctuations in the experimental context, in accordance with the
'hidden-measurements interpretation' of quantum mechanics. When the structure
of the state space is Hilbertian, and measurements are of the 'universal' kind,
i.e., are the result of an average over all possible ways of selecting an
outcome, the GTR-model provides the same predictions of the Born rule, and
therefore provides a natural completed version of quantum mechanics. However,
when the structure of the state space is non-Hilbertian and/or not all possible
ways of selecting an outcome are available to be actualized, the predictions of
the model generally differ from the quantum ones, especially when sequential
measurements are considered. Some paradigmatic examples will be discussed,
taken from physics and human cognition. Particular attention will be given to
some known psychological effects, like question order effects and response
replicability, which we show are able to generate non-Hilbertian statistics. We
also suggest a realistic interpretation of the GTR-model, when applied to human
cognition and decision, which we think could become the generally adopted
interpretative framework in quantum cognition research.
