Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Rosser provability and normal modal logics   In this paper, we investigate Rosser provability predicates whose provability
logics are normal modal logics. First, we prove that there exists a Rosser
provability predicate whose provability logic is exactly the normal modal logic
${\sf KD}$. Secondly, we introduce a new normal modal logic ${\sf KDR}$ which
is a proper extension of ${\sf KD}$, and prove that there exists a Rosser
provability predicate whose provability logic includes ${\sf KDR}$.

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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: adap-org
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The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: ao-sci
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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: chao-dyn
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The categories of this paper are: nucl-th
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The categories of this paper are: acc-phys
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The categories of this paper are: solv-int