Modeling by binary relations

Modeling by binary relations

In conventional data modeling usually various attribute types that provide information about the same kind of thing are grouped into entity types (or ‘object types’). As a consequence of that higher order relations (tables) are created. However, many of those higher order relations must be changed when business requirements change. Thus most conventional data models have structures that are business requirements specific.

Semantic models have a universal structure that is independent of business requirements. This is achieved by expressing all requirements by binary relations, including also higher order relations. This even increases the semantic content of the expressions, as is explained and illustrated in ‘Semantic Modeling in Formal English’.

Some people have the incorrect idea that an expression of a binary relation by definition consists of two things only. However, the expression of a binary relation consists of a (usually pretty large) collection of components, such as an identifier of the relation, the (two) related things, the kind of relation, the intention of the expression, its status and timing, validity context, possibly cardinality constraints, and various other contextual facts. The advantage of those other components is that contextual facts can be provided for every binary relation.

Forthermore, modeling with binary relations has a number of other advantages, such as:

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1. Binary relations provide flexibility.
2. Binary relations reduce model complexity.
3. Binary relations enable standardization of the language for their content.

The flexibility of a data model increases, because binary relations allow for extension of a model scope without restructuring the database. This is cause by the fact that the structure (format) of the expressions is uniform and independent of their content, whereas the structure of database tables are determined by and thus are dependent on their content.

The complexity of the information model reduces, because of the reduction of the complexity of the structure of the expressions. This is cause by the fact that all expressions have the same form, so that the number of entity types, tuples or tables reduces to one or two. Nevertheless, the content can be stored in various different interoperable tables, all with the same structure (and possible using the same language for their content).

The complexity that is inherent to the semantics of the information will remain and is the same as in conventional modeling.

Standardization of the language for binary expressions is enabled by separating the expression of business requirement from the standardization of the language in which those business requirements are expressed. This is done by formalization and standardization of natural language into Formal English, Formal German, etc., such that the expressions in the formalized language becomes unambiguously computer interpretable. The advantages of such formalization and standardization of the language for the expressions are increased interoperability and elimination of data conversions in case of data exchange and data integration.

This differs from conventional modeling, where standardization of entity types is nearly impossible because their definitions are dependent of business requirements, whereas it is very difficult to come to agreement on common business requirements between competing parties.

The basic three components of a binary expression are: a left hand object, a phrase denoting a kind of relation and a right hand object. The definition of a formalized natural language, such as Formal English, includes the definition and standardization of a large number of kinds of relations and contextual facts. The richness of the collection of kinds of relations determines the expression power and capabilities of the formal language. A main difference between Formal English and e.g. RDF and OWL (which are also based on binary relations) is that the latter hardly define any kinds of relations nor contextual facts, whereas Formal English defined many of both.

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