27,445 research outputs found
On the algebraic structure of conditional events
This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts
Boolean algebras of conditionals, probability and logic
This paper presents an investigation on the structure of conditional events
and on the probability measures which arise naturally in this context. In
particular we introduce a construction which defines a (finite) {\em Boolean
algebra of conditionals} from any (finite) Boolean algebra of events. By doing
so we distinguish the properties of conditional events which depend on
probability and those which are intrinsic to the logico-algebraic structure of
conditionals. Our main result provides a way to regard standard two-place
conditional probabilities as one-place probability functions on conditional
events. We also consider a logical counterpart of our Boolean algebras of
conditionals with links to preferential consequence relations for non-monotonic
reasoning. The overall framework of this paper provides a novel perspective on
the rich interplay between logic and probability in the representation of
conditional knowledge
On the algebraic structure of conditional events: 13th European conference, ECSQARU 2015, Compiègne, France, July 15-17, 2015.
This paper initiates an investigation of conditional measures as simple measures on conditional events. As a first step towards this end we investigate the construction of conditional algebras which allow us to distinguish between the logical properties of conditional events and those of the conditional measures which we can be attached to them. This distinction, we argue, helps us clarifying both concepts
Non-classical conditional probability and the quantum no-cloning theorem
The quantum mechanical no-cloning theorem for pure states is generalized and
transfered to the quantum logics with a conditional probability calculus in a
rather abstract, though simple and basic fashion without relying on a tensor
product construction or finite dimension as required in other generalizations.Comment: 6 page
Bell inequality and common causal explanation in algebraic quantum field theory
Bell inequalities, understood as constraints between classical conditional
probabilities, can be derived from a set of assumptions representing a common
causal explanation of classical correlations. A similar derivation, however, is
not known for Bell inequalities in algebraic quantum field theories
establishing constraints for the expectation of specific linear combinations of
projections in a quantum state. In the paper we address the question as to
whether a 'common causal justification' of these non-classical Bell
inequalities is possible. We will show that although the classical notion of
common causal explanation can readily be generalized for the non-classical
case, the Bell inequalities used in quantum theories cannot be derived from
these non-classical common causes. Just the opposite is true: for a set of
correlations there can be given a non-classical common causal explanation even
if they violate the Bell inequalities. This shows that the range of common
causal explanations in the non-classical case is wider than that restricted by
the Bell inequalities
Quantum key distribution without the wavefunction
A well-known feature of quantum mechanics is the secure exchange of secret
bit strings which can then be used as keys to encrypt messages transmitted over
any classical communication channel. It is demonstrated that this quantum key
distribution allows a much more general and abstract access than commonly
thought. The results include some generalizations for the Hilbert space version
of quantum key distribution,but base upon a general non-classical extension of
conditional probability. A special state-independent conditional probability is
identified as origin of the superior security of quantum key distribution and
may have more profound implications for the foundations and interpretation of
quantum mechanics,quantum information theory, and the philosophical question
what actually constitutes physical reality.Comment: 16 pages. arXiv admin note: text overlap with arXiv:1502.0215
Conjunctive Bayesian networks
Conjunctive Bayesian networks (CBNs) are graphical models that describe the
accumulation of events which are constrained in the order of their occurrence.
A CBN is given by a partial order on a (finite) set of events. CBNs generalize
the oncogenetic tree models of Desper et al. by allowing the occurrence of an
event to depend on more than one predecessor event. The present paper studies
the statistical and algebraic properties of CBNs. We determine the maximum
likelihood parameters and present a combinatorial solution to the model
selection problem. Our method performs well on two datasets where the events
are HIV mutations associated with drug resistance. Concluding with a study of
the algebraic properties of CBNs, we show that CBNs are toric varieties after a
coordinate transformation and that their ideals possess a quadratic Gr\"{o}bner
basis.Comment: Published in at http://dx.doi.org/10.3150/07-BEJ6133 the Bernoulli
(http://isi.cbs.nl/bernoulli/) by the International Statistical
Institute/Bernoulli Society (http://isi.cbs.nl/BS/bshome.htm
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