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