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    STUDIA MATHEMATICA - Issue no. 1 / 2019  
         
  Article:   A TOPOLOGICAL REPRESENTATION OF DOUBLE BOOLEAN LATTICES.

Authors:  BRIGITTE E. BRECKNER, CHRISTIAN SĂCĂREA.
 
       
         
  Abstract:  Boolean Concept Logic has been introduced by R. Wille as a mathematical theory based on Formal Concept Analysis. Concept lattices are extended
with two new operations, negation and opposition which then lead to algebras of protoconcepts which are equationally equivalent to double Boolean algebras. In this paper, we provide a topological representation for double Boolean algebras based on the so-called DB-topological contexts. A double Boolean algebra is then represented as the algebra of clopen protoconcepts of some DB-topological context.

Mathematics Subject Classi fication (2010): 18B35, 54B30, 68T30.
Keywords:
Formal concept analysis, double boolean algebra, topological context.
 
         
     
         
         
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