Paper: Higher Dimensional Multigraphs (at LICS 1998)

Authors: Claudio Hermida Michael Makkai A. John Power

Abstract

We introduce the notion of higher dimensional multigraph. This notion extends that of multigraph, which underlies multicategories and is essentially equivalent to the notion of context-free grammar. We develop the definition and explain how it gives a semantically coherent category theoretic approach to the notion of higher order context-free grammar. It also gives a conceptual framework in which one can study rewrites, and rewrites of rewrites, etcetera, for proofs of sequent calculus. The definition involves a subtle interaction between geometry and linearly defined syntax; we explore the latter here, outlining the geometric intuition

BibTeX

  @InProceedings{HermidaMakkaiPower-HigherDimensionalMu,
    author = 	 {Claudio Hermida and Michael Makkai and A. John Power},
    title = 	 {Higher Dimensional Multigraphs},
    booktitle =  {Proceedings of the Thirteenth Annual IEEE Symposium on Logic in Computer Science (LICS 1998)},
    year =	 {1998},
    month =	 {June}, 
    pages =      {199--206},
    location =   {Indianapolis, IN, USA}, 
    publisher =	 {IEEE Computer Society Press}
  }