Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Proofs Without Syntax   "[M]athematicians care no more for logic than logicians for mathematics."
Augustus de Morgan, 1868.
  Proofs are traditionally syntactic, inductively generated objects. This paper
presents an abstract mathematical formulation of propositional calculus
(propositional logic) in which proofs are combinatorial (graph-theoretic),
rather than syntactic. It defines a *combinatorial proof* of a proposition P as
a graph homomorphism h : C -> G(P), where G(P) is a graph associated with P and
C is a coloured graph. The main theorem is soundness and completeness: P is
true iff there exists a combinatorial proof h : C -> G(P).

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The categories of this paper are: hep-ex
23
The categories of this paper are: solv-int
18
The categories of this paper are: econ
7
The categories of this paper are: hep-th
10
The categories of this paper are: q-bio
36
The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
12
The categories of this paper are: nucl-th
35
The categories of this paper are: mtrl-th
13
The categories of this paper are: quant-ph
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The categories of this paper are: bayes-an
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The categories of this paper are: q-alg
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The categories of this paper are: comp-gas
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The categories of this paper are: physics
0
The categories of this paper are: hep-ph
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The categories of this paper are: eess