Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logics of upsets of De Morgan lattices   We study logics determined by matrices consisting of a De~Morgan lattice with
an upward closed set of designated values, such as the logic of non-falsity
preservation in a given finite Boolean algebra and Shramko's logic of
non-falsity preservation in the four-element subdirectly irreducible De Morgan
lattice. The key tool in the study of these logics is the lattice-theoretic
notion of an $n$-filter. We study the logics of all (complete, consistent, and
classical) $n$-filters on De Morgan lattices, which are non-adjunctive
generalizations of the four-valued logic of Belnap and Dunn (of the
three-valued logics of Priest and Kleene, and of classical logic). We then show
how to find a finite Hilbert-style axiomatization of any logic determined by a
finite family of prime upsets of finite De Morgan lattices and a finite
Gentzen-style axiomatization of any logic determined by a finite family of
filters on finite De Morgan lattices. As an application, we axiomatize
Shramko's logic of anything but falsehood.

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The categories of this paper are: math-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: supr-con
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: cs
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The categories of this paper are: econ
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-th
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The categories of this paper are: gr-qc
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The categories of this paper are: atom-ph
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The categories of this paper are: mtrl-th