Changes

A '''local incidence property''' (LIP) of a relation ''L'' is a property that depends in turn on the properties of special subsets of ''L'' that are known as its ''local flags''.  The local flags of a relation are defined in the following way:

A '''local incidence property''' (LIP) of a relation ''L'' is a property that depends in turn on the properties of special subsets of ''L'' that are known as its ''local flags''.  The local flags of a relation are defined in the following way:

Let ''L'' be a ''k''-place relation ''L'' ⊆ ''X''₁ × … × ''X''_''k''.

Let ''L'' be a ''k''-place relation ''L'' ⊆ ''X''₁ × … × ''X''_''k''.

Select a relational domain ''X''_''j'' and one of its elements ''x''.  Then ''L''_''x''.''j'' is a subset of ''L'' that is referred to as the ''flag'' of ''L'' with ''x'' at ''j'', or the ''x''.''j''-flag of ''L'', an object which has the following definition:

Select a relational domain ''X''_''j'' and one of its elements ''x''.  Then ''L''_''x''.''j'' is a subset of ''L'' that is referred to as the ''flag'' of ''L'' with ''x'' at ''j'', or the ''x''.''j''-flag of ''L'', an object which has the following definition:

:* ''L''_''x''.''j'' = { (''x''₁, …, ''x''_''j'', …, ''x''_''k'') ∈ ''L'' : ''x''_''j'' = ''x'' }.

:* ''L''_''x''.''j'' = { (''x''₁, …, ''x''_''j'', …, ''x''_''k'') ∈ ''L'' : ''x''_''j'' = ''x'' }.

Any property ''C'' of the local flag ''L''_''x''.''j'' ⊆ ''L'' is said to be a ''local incidence property'' of ''L'' with respect to the locus ''x'' at ''j''.

Any property ''C'' of the local flag ''L''_''x''.''j'' ⊆ ''L'' is said to be a ''local incidence property'' of ''L'' with respect to the locus ''x'' at ''j''.