Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: How Kirkwood and Probability Distributions Differ: A Coxian Perspective   Kolmogorov's first axiom of probability is probability takes values between 0
and 1; however, in Cox's derivation of probability having a maximum value of
unity is arbitrary since he derives probability as a tool to rank degrees of
plausibility. Probability can then be used to make inferences in instances of
incomplete information, which is the foundation of Baysian probability theory.
This article formulates a rule, which if obeyed, allows probability to take
complex values and still be consistent with the interpretation of probability
theory as being a tool to rank plausibility. It is then shown that Kirkwood
distributions and the conditional complex probability distributions proposed by
Hofmann do not obey this rule and therefore cannot rank plausibility. Not only
do these quasiprobability distributions relax Kolmogorov's first axiom of
probability, they also are void of the defining property of a probability
distribution from a Coxian and Baysian perspective - they lack the ability to
rank plausibility.

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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: patt-sol
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat
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The categories of this paper are: hep-ph
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: q-bio
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The categories of this paper are: eess
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: hep-th