Product of Graphs and Hybrid Logic

  • Authors:

  • Mario R. F. Benevides;L. Menasché Schechter

  • Affiliations:

  • Computer Science Department and Systems and Computer Engineering Program, Federal University of Rio de Janeiro, Brazil;Systems and Computer Engineering Program, Federal University of Rio de Janeiro, Brazil

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2009

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Abstract

Left and right commutativity and the Church-Rosser and reverse Church-Rosser properties are necessary conditions for a graph (frame) to be a (non-trivial) product of two other graphs, but their conjunction is not a sufficient condition. This work presents a fifth property, called H-V intransitivity, that, when added to the four previous properties, results in a necessary and sufficient condition for a finite and connected graph to be a product. Then, we show that although the first four properties can be defined in a modal logic (the reverse Church-Rosser property requires a converse modality), H-V intransitivity is not modally definable. We also show that no necessary and sufficient condition for a graph to be a product can be modally definable. Finally, we present a formula in a hybrid language that defines H-V intransitivity.