Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Structure of First-Order Causality (extended version)   Game semantics describe the interactive behavior of proofs by interpreting
formulas as games on which proofs induce strategies. Such a semantics is
introduced here for capturing dependencies induced by quantifications in
first-order propositional logic. One of the main difficulties that has to be
faced during the elaboration of this kind of semantics is to characterize
definable strategies, that is strategies which actually behave like a proof.
This is usually done by restricting the model to strategies satisfying subtle
combinatorial conditions, whose preservation under composition is often
difficult to show. Here, we present an original methodology to achieve this
task, which requires to combine advanced tools from game semantics, rewriting
theory and categorical algebra. We introduce a diagrammatic presentation of the
monoidal category of definable strategies of our model, by the means of
generators and relations: those strategies can be generated from a finite set
of atomic strategies and the equality between strategies admits a finite
axiomatization, this equational structure corresponding to a polarized
variation of the notion of bialgebra. This work thus bridges algebra and
denotational semantics in order to reveal the structure of dependencies induced
by first-order quantifiers, and lays the foundations for a mechanized analysis
of causality in programming languages.

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The categories of this paper are: plasm-ph
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: acc-phys
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The categories of this paper are: comp-gas
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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: mtrl-th
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The categories of this paper are: math-ph
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The categories of this paper are: astro-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: solv-int