A calculus for graphs with complement

Authors:
Renata de Freitas;Paulo A. S. Veloso;Sheila R. M. Veloso;Petrucio Viana
Affiliations:
Institute of Mathematics, Universidade Federal Fluminense, Niterói, Brazil;COPPE, Universidade Federal do Rio de Janeiro, Rio de Janeiro, Brazil;Systems and Computer Engin. Dept., Faculty of Engineering, Universidade do Estado do Rio de Janeiro, Rio de Janeiro, Brazil;Institute of Mathematics, Universidade Federal Fluminense, Niterói, Brazil
Venue:
Diagrams'10 Proceedings of the 6th international conference on Diagrammatic representation and inference
Year:
2010

Citing 9
Cited 1

Proofs with graphs

Science of Computer Programming - Special issue on mathematics of program construction
Relational matching for graphical calculi of relations

Information Sciences: an International Journal - Relational methods in computer science
Compiling dyadic first-order specifications into map algebra

Theoretical Computer Science - Algebraic methods in language processing
Allegories of Circuits

LFCS '94 Proceedings of the Third International Symposium on Logical Foundations of Computer Science
Algebraic Graph Derivations for Graphical Calculi

WG '96 Proceedings of the 22nd International Workshop on Graph-Theoretic Concepts in Computer Science
On a Graph Calculus for Algebras of Relations

WoLLIC '08 Proceedings of the 15th international workshop on Logic, Language, Information and Computation
A note on proofs with graphs

Science of Computer Programming
Positive Fork Graph Calculus

LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
On graph reasoning

Information and Computation

A graph calculus for proving intuitionistic relation algebraic equations

Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference

Quantified Score

Hi-index	0.00

Visualization

Abstract

We present a system for deriving inclusions between graphs from a set of inclusions between graphs taken as hypotheses. The novel features are the extended notion of graph with an explicitly representation of complement, the more involved definition of the system, and its completeness proof due to the embedding of complements. This is an improvement on former work, where complement was introduced by definition. Our calculus provides a basis on which one can construct a wide range of graph calculi for several algebras of relations.