Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: An Abstract Approach to Consequence Relations   We generalise the Blok-J\'onsson account of structural consequence relations,
later developed by Galatos, Tsinakis and other authors, in such a way as to
naturally accommodate multiset consequence. While Blok and J\'onsson admit, in
place of sheer formulas, a wider range of syntactic units to be manipulated in
deductions (including sequents or equations), these objects are invariably
aggregated via set-theoretical union. Our approach is more general in that
non-idempotent forms of premiss and conclusion aggregation, including multiset
sum and fuzzy set union, are considered. In their abstract form, thus,
deductive relations are defined as additional compatible preorderings over
certain partially ordered monoids. We investigate these relations using
categorical methods, and provide analogues of the main results obtained in the
general theory of consequence relations. Then we focus on the driving example
of multiset deductive relations, providing variations of the methods of matrix
semantics and Hilbert systems in Abstract Algebraic Logic.

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The categories of this paper are: plasm-ph
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The categories of this paper are: q-fin
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The categories of this paper are: q-bio
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The categories of this paper are: nucl-th
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The categories of this paper are: eess
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The categories of this paper are: nlin
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The categories of this paper are: econ
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The categories of this paper are: q-alg
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The categories of this paper are: stat
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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: gr-qc
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: supr-con