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As we explain in Logical Database Design (forthcoming), LDD assigns the meaning of terms in conceptual models (CMs)—properties, entities, groups, multigroup—to non-logical symbols of a formal logic theory.

If the theory is RDM, the symbols stand for sets—domains/attributes, tuples, relations, database—adapted for database management. For each CM the theory acquires an interpretation, which produces a LM (application) of the theory for database representation and manipulation.

Here are the adapted sets symbolized in RDM which acquire the interpretation of the terms in CMs.

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Database domains 

Each:

           ·  Is an abstract data type that consists of:

        §   a name;

        §   an intension: domain predicate;

        §   an extension: set of values;

        §   an associated set of operators exclusively on domain values.

         · Acquires interpretation of a 1^st order property (1OP) in a CM;

         ·  Is:

§   defined intensionally (preferred), or extensionally;

         §   identified by name (as a referent to);

§   treated as atomic (non-decomposable) by the relational algebra/data sublanguage.

Domains that represent inferred 1OPs that are not directly observable have one or more appearances in one or more relations (for example, the domain COMPENSATION appears as attribute SALARY in an EMPLOYEES relation, and as attribute COMMISSION in the SALESMEN relation).

 

Attributes 

 Each:

· Acquires interpretation of a 1^st order property in (group) context in a CM;

· Is an appearance of a database domain in a relation that consists of:

§   a name;

§   an intension: attribute predicate;

§   extension: set of domain values;

§   an associated (possibly subset) of domain operators exclusively on attributes values.

              ·  Is:

§   defined intensionally on a domain;

§   identified by name (as a referent to predicate);

§   treated as atomic (non-decomposable) by the relational algebra/data sublanguage.

 

Attributes defined on the same domain (that correspond to 1OPics) that appear one or more time in one or more relations can be viewed as distinct roles that the domain plays in the relations—they are the domain constrained in distinct ways by group context for consistency with those roles.

Details in Database Domains. 

 

Database tuples

Each:

· Acquires an interpretation of a (fact) about an entity in a CM.

· Is a unique n-valued set of unordered attribute values that consists of:

§   intension: tuple predicate (TP);

§   extension: set of attribute values.

· Is:

     §   defined intensionally or extensionally;

     §   identified by primary key value.

 

A tuple is in a state: either active (asserted to be a member of a relation) at a point in time, or not (see below). 

 

Database relations

· Acquires the interpretation of  a group of entities of a single type in the CM. 

· Is a set of unordered active tuples (a subset of the Cp of attributes) that consists of:

§   a name;

§   an intension: relation predicate (RP);

§   an extension: set of tuples;

§   an associated set of exclusive RA operators exclusively on  relations.

· Is:

    §   defined intensionally;

    §   identified by name (as a referent to RP).

 

  Database

                  ·   Acquires interpretation of a multigroup in a CM.

                 ·    Is a set of related relations that consists of:

§   a name;

§   an intension: database predicate (DBP);

§   an extension: set of related relations.

                 ·    Is:

§   defined intensionally;

§   identified by name (as a referent to DBP).