2. Formal language definition: The Taxonomic Dictionary Ontology

The Taxonomic Dictionary-Ontology ('the dictionary' for short) defines the formal languages of the Gellish family of formalized languages and especially its concepts, vocabulary and possible expressions. All concepts are and shall be defined as subtypes of their direct supertype(s). The base ontology is itself the prime part of the dictionary. Thus all concepts are defined as being subtypes of the concepts that are defined in the base ontology. This means that all concepts together form one taxonomic hierarchy, with the concept 'anything' at the top of the hierarchy.
The dictionary contains relations between concepts that are BY DEFINITION the case. This implies that not only subtype-supertype relations, but also other kinds of relations are applied in the taxonomic dictionary. These other kinds of relations cause that the taxonomic dictionary is called a language defining ontology.\ The dictionary is documented in a number of tables that comply with the Gellish Expression Format. A representative subset of the dictionary is available for development and testing purposes as TSV (Tab separated variables) files in this project. The full dictionary can be licensed via the Gellish website.

Sections of the dictionary

The dictionary is subdivided in a number of sections in a hierarchical way. The top of the subtype-supertype hierarchy is called the basic ontology. All other concepts are subtypes of the concepts in this basic ontology. The basic ontology defines the standard kinds of relations, of which the phrases that represent binary relations can be used to make expressions. The basic ontology also defines for each kind of binary relation which two kinds of roles are required and for each kind of role which kind of role player can play a role of that kind in relations of the defined kinds. All three kinds of concepts, kinds of relations, roles and role players, are arranged in a taxonomic hierarchy, which means that each concept has an explicit subtype-supertype relation with at least one supertype concept of which it is a specialization.
A collection of expressions that together specify what is by definition the case for a concept is called a 'definition model' for that concept. \ Sections of the dictionary are for example:

• The base ontology with kinds of relations
• Buildings, civil and furniture
• Mechanical, electrical and control equipment and their components
• Geographic objects and countries
• Aspects, such as characteristics, properties and qualities
• Qualitative and quantitative aspects (standardized possible aspect values)
• Substances, such as chemicals, fluids, solids, materials of construction
• Organizations, persons, biologic objects
• Financial and business concepts
• Occurrences, such as activities, processes and events
• Information and documents, graphics and mathematical and geometric concepts such as shapes
• Units of measure and currencies
• Roles, usages and applications
• etc.

Supplier catalogues

For product suppliers and their customers there is an important section that covers 'product type models', which specifies what is the case for product types, such as for catalogue items. Manufacturers and suppliers who define their product types and subtypes of the concepts in the taxonomic dictionary make that they are better found by potential customers and when they express the specifications of their product types as expressions in the system independent formal language, then they enable that those models can be directly imported in the product models of their customers.

Base ontology

The base ontology consists of a collection of expressions (in the Gellish Expression Format) that uses one of the 'bootstrapping' kinds of relations. Bootstrapping kinds of relations are the few kinds that need to be interpreted by software in order to enable interpreting the first imported file that defines the kinds of relations of the formal language. Those bootstrapping kinds of relations are in English:

• 'is a kind of' or its synonym 'is a specialization of' (1146), which phrases specify subtype-supertype relations,
• 'has by definition as first role a' (5944), which defines the kind of role of a first role player in a binary relation,
• 'has by definition as second role a' (5945), which defines the kind of role of a second role player in a binary relation,
• 'is a base phrase for' (6066), which specifies a base phrase for a kind of relation in an expression, which implies that the first role player appears at the left hand side of the phrase in the expression,
• 'is an inverse phrase for' (1986), which specifies an inverse phrase for a kind of relation in an expression, which implies that the second role player appears at the left hand side of the phrase in the expression,
• 'is a synonym of' (1981), which specifies a synonym name for a concept,
• 'is by definition a role of a' (5343), which specifies for a (first or second) kind of role which kind of role player is allowed to play such a role in a relation of the applicable kind.

For examples of the application see the base ontology file.
Note: These bootstrapping kinds of relations are themselves defined in the base ontology.

All kinds of relations, kinds of roles and kinds of things (role players) are arranged in an explicit taxonomy (a subtype-supertype hierarchy). This means that kinds of roles for kinds of relations are inherited by subtype kinds of relations from their supertypes, until a new (subtype) kind of role is specified for a subtype kind of relation.

Knowledge and requirements models

In addition to the dictionary, which specifies what is by definition the case for the concepts, organizations can develop knowledge libraries or they can license the Gellish library of knowledge models. Modeled knowledge specifies _possibilities _for _kinds of things. It specifies what CAN BE the case for the concepts about which knowledge is modeled. A library of knowledge models (which is a collection of knowledge expressions) is also called a knowledge library, a knowledge base or a knowledge representing ontology. NOTE: knowledge models may only use concepts that are defined in the taxonomic dictionary (or are added in a proper way).
Such modeled knowledge is similar to modeled specifications of requirements, which specify what SHALL BE the case in the context of a particular party or in the context of an applicable standard, as a specialization of what CAN BE the case.

Product and process models

Models of individual products, called 'product models' and/or 'process models' are models in which the expressions use kinds of relations that specify what is actually the case for individual things and occurrences and their aspects. Those individual things and aspects do not belong to the language defining dictionary, but they are added on an ad-hoc basis when those things and aspects are classified (through explicit classification relations) by kinds that are already defined in the dictionary. The names of such new individual things are freely chosen by the users of the formal language, whereas the software should allocate unique identifiers according to the conventions of the language. It is a convention in Formal English that names of concepts starts with a lower case character and that names on individual things start with an upper case character. Thus John 'is classified as a' man and also Pump-1 'is classified as a' pump.

NOTE: Contrary to conventional databases, the models of individual products and processes are not 'instances' of (a finite number of) models on a conceptual level. This is caused by the fact that product and process model knowledge or requirements is not built-in (as constraints) in the definition of the structure of a Gellish database. That does not exclude that it is possible to express requirements and constraints on a conceptual level. In that case software can be constructed for verifying whether product models satisfy such requirements.