09/05 - Renata de Freitas

"Graph calculi for relation algebras"

Renata de Freitas
Instituto de Matemática, UFF (Niterói, RJ - Brasil)

Abstract:
Traditionally, formulas are written on a single line. S. Curtis and G.
Lowe (1995) suggest a more visually appealing alternative for the case
of relation algebra: using graphs for expressing properties and
reasoning about them in a natural way. We extended their approach to
diagrams that are sets of graphs. The basic intuitions are quite
simple, leading to playful and powerful systems for deriving
inclusions between diagrams that are consequences of sets of
inclusions between diagrams taken as hypotheses. We give a proper
formulation of these systems as logical calculi and discuss soundness,
completeness and decidability.
(Joint work with Paulo Veloso, Sheila Veloso and Petrucio Viana.)