16,075 research outputs found
Probabilistic foundations of quantum mechanics and quantum information
We discuss foundation of quantum mechanics (interpretations, superposition,
principle of complementarity, locality, hidden variables) and quantum
information theory.Comment: Contextual probabilistic viewpoint to quantum cryptography projec
Contextual viewpoint to quantum stochastics
We study the role of context, complex of physical conditions, in quantum as
well as classical experiments. It is shown that by taking into account
contextual dependence of experimental probabilities we can derive the quantum
rule for the addition of probabilities of alternatives. Thus we obtain quantum
interference without applying to wave or Hilbert space approach. The Hilbert
space representation of contextual probabilities is obtained as a consequence
of the elementary geometric fact: -theorem. By using another fact from
elementary algebra we obtain complex-amplitude representation of probabilities.
Finally, we found contextual origin of noncommutativity of incompatible
observables
Real-time and Probabilistic Temporal Logics: An Overview
Over the last two decades, there has been an extensive study on logical
formalisms for specifying and verifying real-time systems. Temporal logics have
been an important research subject within this direction. Although numerous
logics have been introduced for the formal specification of real-time and
complex systems, an up to date comprehensive analysis of these logics does not
exist in the literature. In this paper we analyse real-time and probabilistic
temporal logics which have been widely used in this field. We extrapolate the
notions of decidability, axiomatizability, expressiveness, model checking, etc.
for each logic analysed. We also provide a comparison of features of the
temporal logics discussed
An Essay on the Double Nature of the Probability
Classical statistics and Bayesian statistics refer to the frequentist and
subjective theories of probability respectively. Von Mises and De Finetti, who
authored those conceptualizations, provide interpretations of the probability
that appear incompatible. This discrepancy raises ample debates and the
foundations of the probability calculus emerge as a tricky, open issue so far.
Instead of developing philosophical discussion, this research resorts to
analytical and mathematical methods. We present two theorems that sustain the
validity of both the frequentist and the subjective views on the probability.
Secondly we show how the double facets of the probability turn out to be
consistent within the present logical frame
Linear representations of probabilistic transformations induced by context transitions
By using straightforward frequency arguments we classify transformations of
probabilities which can be generated by transition from one preparation
procedure (context) to another. There are three classes of transformations
corresponding to statistical deviations of different magnitudes: (a)
trigonometric; (b) hyperbolic; (c) hyper-trigonometric. It is shown that not
only quantum preparation procedures can have trigonometric probabilistic
behaviour. We propose generalizations of -linear space probabilistic
calculus to describe non quantum (trigonometric and hyperbolic) probabilistic
transformations. We also analyse superposition principle in this framework.Comment: Added a physical discussion and new reference
von Neumann-Morgenstern and Savage Theorems for Causal Decision Making
Causal thinking and decision making under uncertainty are fundamental aspects
of intelligent reasoning. Decision making under uncertainty has been well
studied when information is considered at the associative (probabilistic)
level. The classical Theorems of von Neumann-Morgenstern and Savage provide a
formal criterion for rational choice using purely associative information.
Causal inference often yields uncertainty about the exact causal structure, so
we consider what kinds of decisions are possible in those conditions. In this
work, we consider decision problems in which available actions and consequences
are causally connected. After recalling a previous causal decision making
result, which relies on a known causal model, we consider the case in which the
causal mechanism that controls some environment is unknown to a rational
decision maker. In this setting we state and prove a causal version of Savage's
Theorem, which we then use to develop a notion of causal games with its
respective causal Nash equilibrium. These results highlight the importance of
causal models in decision making and the variety of potential applications.Comment: Submitted to Journal of Causal Inferenc
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