A graph calculus for proving intuitionistic relation algebraic equations

Authors:
Renata de Freitas;Petrucio Viana
Affiliations:
Institute of Mathematics and Statistics, UFF: Universidade Federal Fluminense, Niterói, Brazil;Institute of Mathematics and Statistics, UFF: Universidade Federal Fluminense, Niterói, Brazil
Venue:
Diagrams'12 Proceedings of the 7th international conference on Diagrammatic Representation and Inference
Year:
2012

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Abstract

In this work, we present a diagrammatic system in which diagrams based on graphs represent binary relations and reasoning on binary relations is performed by transformations on diagrams. We proved that if a diagram D1 can be transformed into a diagram D2 using the rules of our system, under a set Σ of hypotheses, then it is intuitionistically true that the relation defined by diagram D1 is a sub-relation of the one defined by diagram D2, under the hypotheses in Σ.