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Example

  1. X ⊕ i = ((X ∩ {1,...,i-1}) ⋃ {i})‘‘
  2. New extent X ⊕ i valid iff X ≺ i X ⊕ i
  3. X ≺ i X ⊕ i iff i ∈ (X ⊕ i ) – X and X ∩ {1,...,i-1} = (X ⊕ i ) ∩ {1,...,i-1}

 

    Consider a context with G = {1,2,3} and M = {a,b,c} and incidence I = {(1,{a,b}), (2,{a}), (3,{b,c})}:
  1. ∅‘‘ = {a,b,c} = ∅
      ⇒ 1. extent: ∅
  2. ∅ ⊕ 3
      = ((∅ ∩ {1,2}) ⋃ {3})‘‘
      = (∅ ⋃ {3})‘‘ = {3}‘‘
      = {b,c}‘ = {3}
          Is ∅ ⊕ 3 valid?
          ∅ ≺ 3 {3}, as 3 ∈ {3} - ∅ and ∅ ∩ {1,2} = {3} ∩ {1,2}
          ⇒ 2. extent: {3}

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