The Achilles hill of every modeling language are the relations. In human reality there are countless relations that can be set up between concepts and specifics (instances of concepts) and creating an a priori list of relations to encompass them all is simply impossible. The attempt to do so resulted in the biggest and most complex part of the terminology invention in current ontology languages: “parentOf”, “memberOf”, “derivesFrom”, “superclassOf”, “propertyOf”, and so on.
- Example 30
firstName › porpetyOf › Person
The result is both highly complex and limiting in terms of how many connections can be captured, resulting in complex yet insufficient, impossible to customize data structures that are locked into ontologies and depend heavily on the definitions the ontologies themselves define. Any new kind of relation that may arise in the future, needs modification of the ontology and introduction of a new definition in order to capture the relation.
Another problem is that the relations are static in nature. The relations cannot capture in their definition specifics that are part of a Case. Person(x) is part of a particular knowledge base, a Case, which is a manifestation of an ontology. The type Person as part of the ontology and all other types and relations must preexist any manifestation of Person, in this case Person(x). As such, Person(x) cannot be part of the definition chain of a relation.
It is important to mention that the concept of relation, just like the concept of type is in fact a result of classification, structuring, the process of creation of types. While this may be important from an analytical point of view, it has been shown int the previous chapters that from the information capturing point of view, this is detrimental. For this reason, SPInDL will avoid the use of relations altogether at the language definition level in order to allow for any possible connection between two subjects.
SPInDL introduces only two meta relation as part of the language (the divergence and the correlation). It is appropriate to call them meta relations because they are very low level containing no case specific semantics. Together with the dictionary and the meta types “Concepts” and “Specifics”, these two meta relations form the entire SPInDL ontology.
- Definition 4, The divergence
The divergence, p(S), denoted graphically by (›) is the coupling which defines the particular angle through which the connection from a subject's perspective is connected with another subject's perspective.
The notation p(S) means that the subject S is seen through the perspective of subject p.
When we try to describe a situation, a case, in reality we analyze subjects (specifics and concepts) from within the context of other specifics or concepts. Everything in our world is a concept, something from the reality around us, a feeling, a state, a time, the self, etc. and the observed fact is a combination of a subset of these concepts.
- Example 31, example of a fact
John is fast.
In example: 31 we state that a specific person is fast. When we use the word John we refer to a very specific Person. The context we use this word in implies that everybody present in the conversation (any consumer of information) has a special memory location where the specific person John, or more precisely the reference to him, resides. As such, John (which in this case is the commonly used reference to this particular memory location) is a specific from reality. The other subject used in the sentence is the concept of being. Being, referred to by the word is, is an abstract concept which has a very specific meaning that everybody in the audience understands. Fast, is yet another similar concept that implicitly brings with it the hidden concept (not appearing as a stand alone word in the sentence but rather just implied by the word fast), speed.
The object of the analyses is John and the trait observed that characterizes John is the speed that describes its being.
note: The sentence is not analyzed based on the parts of the sentence (subject, predicate, etc.) but rather from an informational perspective.
- Example 32, Perspective John is observed from
John ‹ being ‹ speed
Example: 32 illustrates how John, the specific, is observed from the perspective of the being concept, speed(being(John)), which in turn is observed from the perspective of the concept of speed and thus creating a particular perspective from which John is viewed in the context of the stated fact.
- Example 33, Correlation of John with the concept of fast
John ‹ being ‹ speed ⇢ fast
The conclusion of the analyses, the fact, states that viewed from this particular perspective John is connected to the concept of Fast, which is another well determined concept in people’s view. The relative aspect of the fastness at this point is not necessarily relevant, because it is not captured in the case, but rather it is considered as part of the greater context in which the case takes place.
- Example 34, Correlation of John with a divergence of the concept of fast
John ‹ being ‹ speed ⇢ relative › fast
If we were to be more specific about the fact that there is a relative aspect to John being fast, that would mean that we are looking at the concept of fast, from a particular perspective, that of relativeness, rather than the absolute view as depicted in the example: 33. So in this case “John is relatively fast.”, example: 34.
- Definition 5, The Correlation
The correlation, denoted (⇢), is the coupling which connects two particular perspectives of two subjects.
In the causal representations of the facts, the correlations will be replaced by a simple coma, since every fact contains a single correlation and the positions of the perspectives in the fact will give the directionality of the correlation.
Both, the divergence and the correlation are directed meta relations, because both have a sens of directionality, causality. The correlation in the examples above shows, that although the connection affects both, it is John that is connected to the concept of Fast and not vice versa. Similarly, the divergence meta relation emphasizes the perspective from which a subject is being analyzed from. It can refer an absolute subject or a perspective of it, generating an even more particular point of view.
- Definition 6, The Perspective
The Concept or Specific that sits at the starting point of the divergence shall be termed, perspective.
The actual relation, if we can talk about it in the same way as in the case of ontologies, would be the complete path, from John to Fast, in example: 34, and contains elements from both the SPInDL ontology (language elements plus the dictionary) and the particular case in discussion. However, these complete paths resemble more facts than particular types of relations.
- Definition 7, The Fact
The full path from one subject to another via the divergences and perspectives, and connected by the correlation is termed as a fact, denoted F(p1, p2).
Every fact will contain a single correlation and any number of divergences necessary to generate the particular perspective the fact needs to state, F(pn(pn-1(…(p1(p0(S1))))), qm(qm-1(…(q1(q0(S2)))))). As such, the fact is not part of the ontology but rather the case and the way these facts are formed they allow for the development of any number of facts between the subjects of the case and within the bigger context of the ontology.
Illustration 5 depicts a more complex case, in which a cat set on a cactus in the past, felt pain and will not sit on that cactus or any other cactus every again.
An important aspect of the knowledge capturing process is observable here: in SPInDL, the role of perspective can be not only played by a concept, but it can also be a taken by a specific. The fact that the Cat is correlated with Pain through the perspective of Cactus(y), in the classic ontology model would have to be provided by a parametrized relation, the definition of which would contain a great deal of complex assumptions. This would crowed the ontology with a lot of definitions that are difficult to track. SPInDL on the other hand solves the communication of the fact with a very simple construction.
In such cases when the perspective is itself part of a chain in another perspective, specifics would meet this criteria too, a notation artifice can be employed to avoid the awkwardness and confusion of opening and closing parenthesis:
pn(pn-1(…(p1,3(p1,2 (p1,1 (p1)) | p0(S1)))), instead of
pn(pn-1(…(p1,3(p1,2 (p1,1 (p1)))(p0(S1))))
In essence, the “)(“ parenthesis combination is eliminated and it is replaced by a vertical bar resulting in a perspective that has a continuation but with a single imbrication chain.
It is important to mention that information does not have an absolute character. The same information can be conveyed in many other forms, using different concepts and it is ultimately our ability to find pattern in the use of these context that gives sense to the information captured.