Changes

An IR of any object is a description of that object in terms of its properties.  A successful description of a particular object usually involves a selection of properties, those that are relevant to a particular purpose.  An IR of <math>L(\text{A})\!</math> or <math>L(\text{B})\!</math> involves properties of its elementary points <math>w \in W\!</math> and properties of its elementary relations <math>\ell \in O \times S \times I.\!</math>

An IR of any object is a description of that object in terms of its properties.  A successful description of a particular object usually involves a selection of properties, those that are relevant to a particular purpose.  An IR of <math>L(\text{A})\!</math> or <math>L(\text{B})\!</math> involves properties of its elementary points <math>w \in W\!</math> and properties of its elementary relations <math>\ell \in O \times S \times I.\!</math>

To devise an IR of any relation <math>L\!</math> one needs to describe <math>L\!</math> in terms of properties of its ingredients.  Broadly speaking, the ingredients of a relation include its elementary relations or <math>n\!</math>-tuples and the elementary components of these <math>n\!</math>-tuples that reside in the relational domains.

To devise an IR of any relation R one needs to describe R in terms of properties of its ingredients.  Broadly speaking, the ingredients of a relation include its elementary relations or n tuples and the elementary components of these n-tuples that reside in the relational domains.

The poset Pos (W) of interest here is the power set Pow (W).

The poset <math>\operatorname{Pos}(W)\!</math> of interest here is the power set <math>\mathcal{P}(W) = \operatorname{Pow}(W).\!</math>

The elements of these posets are abstractly regarded as "properties" or "propositions" that apply to the elements of W.  These properties and propositions are independently given entities.  In other words, they are primitive elements in their own right, and cannot in general be defined in terms of points, but they exist in relation to these points, and their extensions can be represented as sets of points.

The elements of these posets are abstractly regarded as "properties" or "propositions" that apply to the elements of W.  These properties and propositions are independently given entities.  In other words, they are primitive elements in their own right, and cannot in general be defined in terms of points, but they exist in relation to these points, and their extensions can be represented as sets of points.