Language Definition Principles (TOPini)

The TOPini section of the Gellish Formal English Dictionary-Taxonomy contains the basic 'Upper Ontology' that defines the core of Gellish Formal English. That section primarily defines the kinds of facts that can be expressed in Gellish and secondary it defines the generic concepts in the top of the specialization hierarchy (the subtype-supertype hierarchy or Taxonomy) of concepts in the Gellish Dictionary-Taxonomy.

The TOPini section has the form of a Gellish Expression Table. The structure (columns) of that table is defined in the document 'Definition of Universal Semantic Databases and Data Exchange Messages'. Each line (row) in that table expresses a main fact or opinion and a number of accessory facts. (Note: when we talk about facts we also mean opinions)
Each main fact that is expressed in Gellish is denoted as a separate 'object' with its own language independent unique identifier (the fact UID). Furthermore, each main fact is expressed in Gellish according to the semantic principle, as a relation between objects. Therefore, below is described how a main fact and thus how a relation is expressed in Gellish. The auxiliary facts are facts about the main fact (such as its status, date of creation and author) and facts that specify names of concepts or contexts for validity and interpretation of the expression.
Below we focus on the expression of main facts as relations between objects.

We distinguish binary relations from higher order relations.

1. Binary relations

The basic kinds of relations (also called ‘relation types’) are binary relations. A binary relation is a relation that relates two things. A binary relation can be used for expressing a fact, statement or opinion that one thing is related to one other thing.
For example, the fact that ‘the Eiffel tower is located in Paris’ is a fact that can be expressed by a binary relation, although the expression requires seven words in English. The expression uses the relation type 'location relation' that is denoted in Gellish Formal English by the standard phrase <is located in>. That relation type has as language independent unique identifier (UID) 5138. Thus the Gellish Formal English expression will be a statement as follows:

statement:  the Eiffel tower <is located in> Paris

When the Eiffel tower has UID 101, Paris has UID 102, and the whole fact has UID 201, then the language independent expression becomes:

statement 201: 101 5138 102

To support human readability this is preferably expressed in a Gellish English database or exchange file/message as:

statement 201: 101 the Eiffel tower 5138 is located in 102 Paris

or in a Gellish Expression Table form as:

UID of fact UID of left hand object Name of left hand object UID of relation type Name of relation type UID of right hand object Name of right hand object
201 101 the Eiffel tower 5138 is located in 102 Paris

The TOPini section of the Gellish Dictionary defines the semantics of all binary relation types that belong to the Gellish language. Such a definition recognizes that the two objects that are related by a binary relation each has its particular role in the relation. For example, the Eiffel tower has a role that can be classified as ‘located’, whereas Paris has a role that can be classified as ‘locator’. Furthermore, the semantics of each relation type can be defined more precisely by specifying which kinds of things may play the required roles. For example it may be specified that a role of located as well as a role of locator can only be played by a physical object, because only physical objects can be located in space. This means that the semantic definition of a relation type is specified in five steps in TOPini as follows:

  1. It specifies for each relation type that it <is a specialization of> a more general relation type and it provides a textual definition of the relation type. The specialization relations together create a subtype-supertype hierarchy of relation types (a taxonomy of relation types). The result for ‘location relation’ is, that indirectly it is defined to be a subtype of binary relation between individual things. On its turn that is one of the subtypes of relation, which is an indirect subtype of the top concept called ‘anything’.

  2. It specifies for each binary relation type what the first and the second kind of role is that is required for the normal sequence in the Gellish expression.

  3. It specifies for each kind of role what kind of thing may play such a kind of role.

  4. It specified the normal Gellish phrase and the inverse Gellish phrase. The latter phrase requires that the role players have an inverse sequence.
    For example: Paris <is the location of> the Eiffel tower.

  5. It defines each kind of role and each kind of thing that can play a role by specifying its direct supertype(s) and providing a textual definition for each of them. These specialization relations together create a subtype-supertype hierarchy of roles and other concepts. A specialization relation implies that the subtype concept inherits all facts that are true for its supertype concept(s). This means that a relation type inherits the roles that are required for its supertype concept(s). The definitions in TOPini make use of this mechanism in two ways: 1. For some relation types none or only one kind of role is specified, which means that the inherited kind of role is applicable and 2. Every specified kind of role shall be a subtype of the kind of role that is specified for the supertype relation type. 

The Gellish language enables in principle to express any kind of fact. This requires that various kinds of binary relations are defined. These include:

  • Kinds of relations that classify relations between individual things. They express real or imaginary ‘facts’, including propositions, statements, questions, answers, denials, confirmations, etc. about a state of affairs.
    For example: John Doe <is an employee of> Ford

  • Relations between kinds of things. This includes relation that express ‘facts’ that are by definition the case for all members of the related kinds of things. It includes also expressions of knowledge about what can be the case or about requirements about what shall be the case (in a particular context) for members of the kinds.
    For example: air bag <can be a part of a> car
    and: car <is a specialization of> vehicle.

  • Relations between individual things and kinds of things. This includes classification relations, but also relations between a kind of thing and an individual object, such as the expression that things of a particular kind are made by a particular company.
    For example: S40 <is made by> Volvo A.G.

  • Relations between individual things and collections of things.
    For example: V-101 <is an element of> stock of valves in company X 

  • Relations between collections.
    For example: collection A1 <is a subset of> collection A.

2. Higher order relations

Occurrences, such as activities, processes and events, and physical laws are typical examples of higher order relations, because they describe interactions or correlations between more than two things. Such higher order relations are expressed in Gellish by defining the relation as a separate object and by specifying a collection of elementary binary relations with that higher order relation. Each of those elementary relations specifies the role that a particular thing plays in the higher order relation.
For example, according to the IDEF0 terminology, an activity such as the construction of the Eiffel tower, has typically an input, an output, a control (signal) and a mechanism, usually being a performer, enabler or tool, whereas Gellish also recognizes additional roles. Such a higher order relation is the specified in Gellish by a collection of expressions of partial facts, each of which describing one of the involved physical objects and its relation to the activity. For example:

the construction of the Eiffel tower has as input x tons of steel bars
the construction of the Eiffel tower has as output the Eiffel tower
the construction of the Eiffel tower has as designer Mr. Eiffel
etc.

Each of these elementary kinds of binary relation types is defined in the TOPini section in the same way as the ordinary binary relation types.

3. Bootstrapping relation types

All facts in the TOPini table are expressed using just six relation types. Thus the facts in TOPini can be interpreted when the semantics of only those six relation types are known. Thus software that interprets the content of the table should be provided with the meaning of these bootstrapping relation types. All other relation types that are defined in the Gelish language are defined in TOPini using those six relation types. Thus, other Gellish Database tables can be interpreted only after the import and interpretation of the TOPini section.
The bootstrapping relation types are:

1146 <is a specialization of>
4731 <requires as role-1 a>
4733 <requires as role-2 a>
4714 <can have a role as a>
1981 <is a synonym of>
1986 <is an inverse of>

The definition of these relation types is provided in the TOPini section itself. 

4. Other kinds of relations

The main content of the TOPini section of the Dictionary-Taxonomy is the definition of a hierarchy (taxonomy) of kinds of relations, their required roles and allowed kinds of role players.

The kinds of relations are arranged in categories as is illustrated in the following figure.


 

The categories are for relations between individual things, relations between kinds of things, relations between an individual thing and a kind of thing and relations between collections.