# 6.3    Logical and Physical Properties

Here the logical bulk properties, logical item properties, and physical properties used in Model D are defined.

Logical Bulk Properties

Logical properties include many properties and statistics of the data in a table. They are used during the optimization process to calculate costs and to evaluate the condition of rules. They are also used in setting the parameters of the operators in the consequent expressions created in the firing of rules.

In Model D, the logical bulk properties of a table are schema, cardinality, attribute statistics, uniqueness, candidate keys and tracked functional dependencies.

In the simplest case, a schema is just the set of attributes of the table. But after an equijoin with one equality condition, two of the attributes in the resulting set will be equivalent (by definition they have the same value). Cascades models this by defining schema to be a set of equivalence classes of attributes rather than just a set of attributes. The schema also contains statistical information on each equivalence class. When the distinction between the set of equivalence classes and a set of attributes is not important, we may refer to the schema as just a set of attributes.

Certain rules require information about candidate keys and/or functional dependencies. and so both are modeled. (Candidate keys are a special case of a functional dependency.) These rules can only be applied if certain functional dependencies apply. (Also, sometimes cardinality estimates are dependent on functional dependencies -- e.g. if a group_by list contains a functional dependency, then the functionally dependent attributes do not contribute to the cardinality of the output)

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