Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Replacing Nothing with Something Special: Contextuality-by-Default and
  Dummy Measurements   The object of contextuality analysis is a set of random variables each of
which is uniquely labeled by a content and a context. In the measurement
terminology, the content is that which the random variable measures, whereas
the context describes the conditions under which this content is measured (in
particular, the set of other contents being measured "together" with this one).
Such a set of random variables is deemed noncontextual or contextual depending
on whether the distributions of the context-sharing random variables are or are
not compatible with certain distributions imposed on the content-sharing random
variables. In the traditional approaches, contextuality is either restricted to
only consistently-connected systems (those in which any two content-sharing
random variables have the same distribution) or else all
inconsistently-connected systems (those not having this property) are
considered contextual. In the Contextuality-by-Default theory, an
inconsistently connected system may or may not be contextual. There are several
arguments for this understanding of contextuality, and this note adds one more.
It is related to the fact that generally not each content is measured in each
context, so there are "empty" content-context pairs. It is convenient to treat
each of these empty pairs as containing a dummy random variable, one that does
not change the degree of contextuality in a system. These dummy random
variables are deterministic ones, attaining a single value with probability 1.
The replacement of absent random variables with deterministic ones, however,
can only be made if one allows for inconsistently-connected systems.
  KEYWORDS: contextuality, dummy measurements, inconsistent connectedness,
random variables.

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The categories of this paper are: bayes-an
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The categories of this paper are: ao-sci
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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The categories of this paper are: q-bio
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: physics
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The categories of this paper are: econ
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The categories of this paper are: patt-sol
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The categories of this paper are: alg-geom
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The categories of this paper are: eess
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The categories of this paper are: cmp-lg