Geodesic
Proofs without syntax
Dominic J. D. Hughes1
1 Department of Mathematics, Stanford University, Stanford, CA 94305, United States
Annals of mathematics, Tome 164 (2006) no. 3, pp. 1065-1076.

Voir la notice de l'article provenant de la source Annals of Mathematics website

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 $h:C\to G(\phi)$, 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 $h:C\to G(\phi)$.
DOI : 10.4007/annals.2006.164.1065

Dominic J. D. Hughes 1

1 Department of Mathematics, Stanford University, Stanford, CA 94305, United States 
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Dominic J. D. Hughes. Proofs without syntax. Annals of mathematics, Tome 164 (2006) no. 3, pp. 1065-1076. doi : 10.4007/annals.2006.164.1065. http://geodesic.mathdoc.fr/articles/10.4007/annals.2006.164.1065/

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