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Example
- X ⊕ i = ((X ∩ {1,...,i-1}) ⋃ {i})‘‘
- New extent X ⊕ i valid iff X ≺ i X ⊕ i
- X ≺ i X ⊕ i iff i ∈ (X ⊕ i ) – X and X ∩ {1,...,i-1} = (X ⊕ i ) ∩ {1,...,i-1}
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Consider a context with G = {1,2,3} and M = {a,b,c} and incidence I = {(1,{a,b}), (2,{a}), (3,{b,c})}:
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∅‘‘ = {a,b,c} = ∅
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⇒ 1. extent: ∅
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∅ ⊕ 3
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= ((∅ ∩ {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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