Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Toward a More Natural Expression of Quantum Logic with Boolean Fractions   The fundamental algebraic concepts of quantum mechanics, as expressed by many
authors, are reviewed and translated into the framework of the relatively new
non-distributive system of Boolean fractions (also called conditional events or
conditional propositions). This system of ordered pairs (A|B) of events A, B,
can express all of the non-Boolean aspects of quantum logic without having to
resort to a more abstract formulation like Hilbert space. Such notions as
orthogonality, superposition, simultaneous verifiability, compatibility,
orthoalgebras, orthocomplementation, modularity, and the Sasaki projection
mapping are translated into this conditional event framework and their forms
exhibited. These concepts turn out to be quite adequately expressed in this
near-Boolean framework thereby allowing more natural, intuitive interpretations
of quantum phenomena. Results include showing that two conditional propositions
are simultaneously verifiable just in case the truth of one implies the
applicability of the other. Another theorem shows that two conditional
propositions (a|b) and (c|d) reside in a common Boolean sub-algebra of the
non-distributive system of conditional propositions just in case b=d, that
their conditions are equivalent. Some concepts equivalent in standard
formulations of quantum logic are distinguishable in the conditional event
algebra, indicating the greater richness of expression possible with Boolean
fractions. Logical operations and deductions in the linear subspace logic of
quantum mechanics are compared with their counterparts in the conditional event
realm. Disjunctions and implications in the quantum realm seem to correspond in
the domain of Boolean fractions to previously identified implications with
respect to various naturally arising deductive relations.

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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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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: mtrl-th
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The categories of this paper are: adap-org
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The categories of this paper are: supr-con
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: econ
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The categories of this paper are: alg-geom
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The categories of this paper are: solv-int
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The categories of this paper are: nlin
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The categories of this paper are: chao-dyn
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The categories of this paper are: acc-phys