Distinguished representatives for equivalent labelled stratified graphs and applications

  • Authors:
  • Nicolae Ţăndăreanu

  • Affiliations:
  • Faculty of Mathematics and Computer Science, University of Craiova, Str A I Cuza 13, 1100, Romania

  • Venue:
  • Discrete Applied Mathematics - Discrete mathematics & data mining (DM & DM)
  • Year:
  • 2004

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Abstract

The concept of labelled stratified graph (LSG) was introduced in Tandaeanu (Knowledge Inform. Syst. 2(4) (2000) 438) in connection with that of knowledge base with output (KBO). The aim of this paper is to present a distinct facet of this concept. We prove several algebraic properties for LSGs and we conclude that a LSG can be used independently of a KBO. In order to realize this aim we define a partial order ≤ on the set Strat(G) of all LSGs over a labelled graph G, an equivalence relation ≃ on Strat(G) and a partial order ⊑ on the factor set Strat(G)/≃. The set Strat(G)/≃ endowed with ⊑ becomes a join semilattice with greatest element. Each equivalence class C ∈ Strat(G)/≃ contains an unique LSG, which is named distinguished representative of C. This is the least element of (C, ≤). Particularly we obtain the distinguished representative for the supremum of two classes (DRS) and the greatest distinguished LSG (the least LSG of the greatest element of Strat(G)/≃, denoted GD). Two applications are presented, one for DRS and one for GD. Several opens problems are briefly exposed in the last section.