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Proofs without syntax
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DOI：10.4007/annals.2006.164.1065.png)
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Abstract
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a 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 phi as a graph homomorphism h: C -> G(phi), where G(phi) is a graph associated with phi and C is a coloured graph. The main theorem is soundness and completeness: phi is true if and only if there exists a combinatorial proof h: C -> G(phi).
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