Year: 2004
Type: preprint
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 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).
Source: arXiv (Cornell University)
Author: Hughes, Dominic
Institution: Stanford University
Language: English
Topic: Advanced Algebra and Logic
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2952177339