Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Incarnation in Ludics and maximal cliques of paths   Ludics is a reconstruction of logic with interaction as a primitive notion,
in the sense that the primary logical concepts are no more formulas and proofs
but cut-elimination interpreted as an interaction between objects called
designs. When the interaction between two designs goes well, such two designs
are said to be orthogonal. A behaviour is a set of designs closed under
bi-orthogonality. Logical formulas are then denoted by behaviours. Finally
proofs are interpreted as designs satisfying particular properties. In that
way, designs are more general than proofs and we may notice in particular that
they are not typed objects. Incarnation is introduced by Girard in Ludics as a
characterization of "useful" designs in a behaviour. The incarnation of a
design is defined as its subdesign that is the smallest one in the behaviour
ordered by inclusion. It is useful in particular because being "incarnated" is
one of the conditions for a design to denote a proof of a formula. The
computation of incarnation is important also as it gives a minimal denotation
for a formula, and more generally for a behaviour. We give here a constructive
way to capture the incarnation of the behaviour of a set of designs, without
computing the behaviour itself. The method we follow uses an alternative
definition of designs: rather than defining them as sets of chronicles, we
consider them as sets of paths, a concept very close to that of play in game
semantics that allows an easier handling of the interaction: the unfolding of
interaction is a path common to two interacting designs.

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The categories of this paper are: math-ph
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The categories of this paper are: adap-org
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: dg-ga
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The categories of this paper are: ao-sci
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The categories of this paper are: chem-ph
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The categories of this paper are: physics
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The categories of this paper are: funct-an
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The categories of this paper are: nucl-ex
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The categories of this paper are: plasm-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: supr-con
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The categories of this paper are: stat