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Directory:Jon Awbrey/Papers/Inquiry Driven Systems : Part 6 (view source)
Revision as of 22:30, 15 November 2012
, 22:30, 15 November 2012→6.31. Relations in General
In order to speak of generalized orders of relations I need to outline the dimensions of variation along which I intend the characters of already familiar orders of relations to be broadened. Generally speaking, the taxonomic features of <math>n\!</math>-place relations that I wish to liberalize can be read off from their ''local incidence properties'' (LIPs).
In order to speak of generalized orders of relations I need to outline the dimensions of variation along which I intend the characters of already familiar orders of relations to be broadened. Generally speaking, the taxonomic features of <math>n\!</math>-place relations that I wish to liberalize can be read off from their ''local incidence properties'' (LIPs).
'''Definition.''' A ''local incidence property'' of a <math>k\!</math>-place relation <math>L \subseteq X_1 \times \ldots \times X_k\!</math> is one that is based on the following type of data. Pick an element <math>x\!</math> in one of the domains <math>X_j\!</math> of <math>L.\!</math> Let <math>L_{x \,\text{at}\, j}\!</math> be a subset of <math>L\!</math> called the ''flag of <math>L\!</math> with <math>x\!</math> at <math>j\!</math>'', or the ''<math>x \,\text{at}\, j\!</math> flag of <math>L.\!</math>'' The ''local flag'' <math>L_{x \,\text{at}\, j} \subseteq L\!</math> is defined as follows.
'''Definition.''' A ''local incidence property'' of a <math>k\!</math>-place relation <math>L \subseteq X_1 \times \ldots \times X_k\!</math> is one that is based on the following type of data. Pick an element <math>x\!</math> in one of the domains <math>X_j\!</math> of <math>L.\!</math> Let <math>L_{x \,\text{at}\, j}\!</math> be a subset of <math>L\!</math> called the ''flag of <math>L\!</math> with <math>x\!</math> at <math>j,\!</math>'' or the ''<math>x \,\text{at}\, j\!</math> flag of <math>L.\!</math>'' The ''local flag'' <math>L_{x \,\text{at}\, j} \subseteq L\!</math> is defined as follows.
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