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A semantic model describes entities in abstract terms of set theory: objects, sets and relations. The world is composed of objects. These objects belong to sets. Objects also relate to other objects through many kinds of relations. For example, assume Anne and John are married. Then Anne and John are members of the set of all people, and they are related by the marriage relation.
In mathematical notation:
Definitions:
- P = { The set of all people }
- M = {
<p, q>∈ P×P | p and q are married}
Facts:
- John ∈ P
- Anne ∈ P
- John M Anne
- Anne M John
Binary relations are enough to represent information: Unary relations are simply sets, and relations with 3 or more places can be broken into several binary relations.
In many scientific fields, a theoretical analysis or a formal definition of concepts begins with definitions from set theory: You define sets, elements which belong to sets and sometimes also relations and functions. Since fuctions are a specific case of relations, talking about relations is enough. A similar approach is taken here: Information is stored on a computer using terms like set, object and relation.
However, in pure mathematics we define some definitions using rules, e.g. we define a set using a rule which determines which elements belong to the set and which don’t. But since computers can’t iterate over infinite lists and run a test for each item, these definitions are not useful to them: In computers we take the reverse approach. First we define the rule, the common characteristic of the elements in a set. Then we define elements of the set one by one, and using the list of such elements we define (which is of course finite) the computer can recognize set elements.
This “alternative” way to represent sets is presented in the next level of the expression model.
[[reality.dia]]