Graph calculi for relational reasoning Renata de Freitas and Petrucio Viana Department of Mathematics and Statistics
Traditionally, formulas are written on a single line. S. Curtis and G. Lowe suggested a more visually appealing alternative for the case of binary relations: using graphs for expressing properties and reasoning about relations in a natural way. We extended their approach to diagrams that are sets of graphs. More specifically, in this setting, diagrams corresponds to sentences and transformations on graphs/diagrams correspond to inference rules, that can be used to infer a diagram from a set of diagram taken as hypothesis. The basic intuitions are quite simple, leading to playful and powerful systems. Our systems treat positive, negative, and intuitionistic information. In this minicourse we summarize these achievements, presenting proper formulations of these systems as logical calculi and discussing soundness, completeness and decidability. The course has no pre-requisites besides some familiarity with formal reasoning and with the basic logic ideas on the syntax and semantics of formal systems. Besides, all the necessary background will be presented as necessary.
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Bibliography Renata de Freitas and Petrucio Viana. Renata de Freitas, Sheila R.M. Veloso, Paulo A.S. Veloso, and Petrucio Viana.
Positive Fork Graph Calculus.
LFCS'09, LNCS 5407:152-163 (2009) | ||||
