Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Deducibility of Identicals, Reflection Principle and Synthetic
  Connectives   Sambin et al. (2000) introduced Basic Logic as an uniform framework for
various logics. At the same time, they also introduced the principle of
reflection as a criterion for being a connective of Basic Logic. We make
explicit a relationship between Hacking's deducibility of identicals condition
(Hacking, 1979) and the principle of reflection by proving the equivalence
between them. Moreover, despite Sambin et al.'s conjecture that only six
connectives satisfy the principle of reflection, we show the following; a
logical connective satisfies the principle of reflection if and only if the
connective is Girard's synthetic connective.

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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: nlin
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The categories of this paper are: alg-geom
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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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-ex
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The categories of this paper are: physics
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The categories of this paper are: hep-lat
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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: chem-ph