Abstract
We present a sound and complete logical system for deriving inclusions between graphs from inclusions between graphs, taken as hypotheses. Graphs provide a natural tool for expressing relations and reasoning about them. Here we extend this system to a sound and complete one to cope with proofs from hypotheses. This leads to a system dealing with complementation. Other approaches using pictures for relations use as bases the theory of allegories or rewriting systems. Our formalism is more widely applicable and provides a common denominator of these approaches.
Research partly sponsored by CNPq (Brazilian National Research Council), FAPERJ (Rio de Janeiro State Research Foundation) and FAPESP (São Paulo State Research Foundation).
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de Freitas, R., Veloso, P.A.S., Veloso, S.R.M., Viana, P. (2008). On a Graph Calculus for Algebras of Relations. In: Hodges, W., de Queiroz, R. (eds) Logic, Language, Information and Computation. WoLLIC 2008. Lecture Notes in Computer Science(), vol 5110. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69937-8_26
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