Resumen de Proofs without syntax
Dominic J. D. Hughes
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 ¿Ó as a graph homomorphism h : C ¿¿ G(¿Ó), where G(¿Ó) is a graph associated with ¿Ó and C is a coloured graph. The main theorem is soundness and completeness: ¿Ó is true if and only if there exists a combinatorial proof h : C ¿¿ G(¿Ó).
