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 D 1 can be transformed into a diagram D 2 using the rules of our system, under a set Σ of hypotheses, then it is intuitionistically true that the relation defined by diagram D 1 is a sub-relation of the one defined by diagram D 2, under the hypotheses in Σ.
Research partially sponsored by CNPq and FAPERJ.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Brown, F.M.: Boolean reasoning: the logic of Boolean equations. Dover (2003)
Foster, S., Struth, G., Weber, T.: Automated Engineering of Relational and Algebraic Methods in Isabelle/HOL. In: de Swart, H. (ed.) RAMICS 2011. LNCS, vol. 6663, pp. 52–67. Springer, Heidelberg (2011)
de Freitas, R., Veloso, P.A.S., Veloso, S.R.M., Viana, P.: A Calculus for Graphs with Complement. In: Goel, A.K., Jamnik, M., Narayanan, N.H. (eds.) Diagrams 2010. LNCS(LNAI), vol. 6170, pp. 84–98. Springer, Heidelberg (2010)
von Oheimb, D., Gritzner, T.F.: RALL: Machine-Supported Proofs for Relation Algebra. In: McCune, W. (ed.) CADE 1997. LNCS, vol. 1249, pp. 380–394. Springer, Heidelberg (1997)
Schmidt, G., Ströhlein, T.: Relation and Graphs: discrete mathematics for computer scientists. Springer, Berlin (1993)
Tarski, A., Givant, S.: A Formalization of Set Theory Without Variables. American Mathematical Society (1987)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
de Freitas, R., Viana, P. (2012). A Graph Calculus for Proving Intuitionistic Relation Algebraic Equations. In: Cox, P., Plimmer, B., Rodgers, P. (eds) Diagrammatic Representation and Inference. Diagrams 2012. Lecture Notes in Computer Science(), vol 7352. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31223-6_40
Download citation
DOI: https://doi.org/10.1007/978-3-642-31223-6_40
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-31222-9
Online ISBN: 978-3-642-31223-6
eBook Packages: Computer ScienceComputer Science (R0)