Proofs Without Syntax

by J. D. Hughes

Venue:	Annals of Mathematics
Citations:	4 - 0 self

Datum	Value	Source
TITLE	Proofs Without Syntax	INFERENCE
AUTHOR NAME	J. D. Hughes	SVM HeaderParse 0.2
ABSTRACT	[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 φ as a graph homomorphism h: C → G(φ), where G(φ) is a graph associated with φ and C is a coloured graph. The main theorem is soundness and completeness: φ is true if and only if there exists a combinatorial proof h: C → G(φ). 1.	SVM HeaderParse 0.2
VENUE	Annals of Mathematics	INFERENCE
VENUE TYPE	JOURNAL	INFERENCE
PAGES	2006	INFERENCE
CITATIONS	23 found	ParsCit 1.0