Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Quantum logic. A brief outline   Quantum logic has been introduced by Birkhoff and von Neumann as an attempt
to base the logical primitives, the propositions and the relations and
operations among them, on quantum theoretical entities, and thus on the related
empirical evidence of the quantum world. We give a brief outline of quantum
logic, and some of its algebraic properties, such as nondistributivity, whereby
emphasis is given to concrete experimental setups related to quantum logical
entities. A probability theory based on quantum logic is fundamentally and
sometimes even spectacularly different from probabilities based on classical
Boolean logic. We give a brief outline of its nonclassical aspects; in
particular violations of Boole-Bell type consistency constraints on joint
probabilities, as well as the Kochen-Specker theorem, demonstrating in a
constructive, finite way the scarcity and even nonexistence of two-valued
states interpretable as classical truth assignments. A more complete
introduction of the author can be found in the book "Quantum Logic" (Springer,
1998)

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The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
4
The categories of this paper are: cond-mat
25
The categories of this paper are: patt-sol
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
32
The categories of this paper are: atom-ph
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
1
The categories of this paper are: cs
23
The categories of this paper are: solv-int
35
The categories of this paper are: mtrl-th
22
The categories of this paper are: chao-dyn
0
The categories of this paper are: hep-ph
16
The categories of this paper are: stat
31
The categories of this paper are: ao-sci