14 July 2005

Components of Ontology: Rules

We believe that the application of relationships between entities must be based on rules for those relationships to create semantically correct communications. There are several reasons for that, but the first (and most obvious) is that without rules governing what objects to fill the slots in a sentence (or other collection of entities for communication) open to building semantically nonsensical collections of entities. As an example of this, consider the basic structure of an American English sentence, which follows the form of SVO (Subject, Verb, Object - as in "Jack carries the ball"). Even if you follow the correct syntax, you can come up with "Banana repairs mountain", which is syntactically correct, but semantically it is nonsense. There have to be rules - rules that state how whatever the verb implies that the subject is doing, then the object can match that original pairing both syntactically and sensibly. Another reason for rules is sense making out of the number of choices. This is especially true of automated systems that are attempting to make semantic sense, as they cannot hope to make sense out of the rapidly approaching infinite number of sources, even when working with a rather small and limited taxonomy.

Grammars and Ontology

Just as we have seen earlier that both taxonomies and knowledge bases are separate from a formal ontology, so too is a grammar separate from a formal ontology.
Grammar is defined as “containing the morphologic, syntactic, and semantic rules for a specific language” [American heritage dictionary reference]. The three elements of that definition can be specifically defined as this –

  • morphology is the study of the rules for forming admissible words

  • syntax is the study of rules for forming admissible sentences

  • semantics is the study of language meaning

The grammar of a system of communications to be used for information system is very similar to this definition. We propose that instead of forming words and sentences, we are forming data elements and meaningful packets of data elements making up more complex ideas than the individual elements are capable of (just as sentences are able to convey a lot more than the individual words). A grammar for a data system is concerned with the meaning of the data elements, the formulation of admissible (able to be transmitted, and able to be received) packets of communicating information based on those elements, and finally the meaningfulness of the packets of data to both systems (the transmitter and the receiver).

A formal ontology contains these same elements, and perhaps goes further in ensuring the specific definition of the concepts, property-exhibiting concepts, and property-values of those concepts that underlay all of the elements being addressed by the grammar. A formal ontology provides a specific attempt at satisfying the needs of the semantic portion of the grammar.

Rules from Three Sources

Within a linguistics system, these rules can come from one of three different places. They can come from the transmitter imparting the communication, or speaker. They can come from the perceiver, or listener, or they can be dictated by the system in question. With spoken language, the only discriminating source is the perceiver, as that is what finally determines the meaning of what is spoken, regardless of what the speaker had in mind. The listener can ask the speaker to restate something, and they can slowly come to understanding (perhaps the speaker can eventually ensure that the listener perceives what the speaker is saying in the manner that the speaker intended, but this is not automatically so). However, with the case of computer systems, we have an advantage. That advantage has been hinted at in the previous section, and we will go over it some more here as it has a great deal of bearing on the system of rules and evaluating them.

The Benefit of Not Understanding

The advantage that an information system has when considering the rules of a system, and the "semantic" meaning of a system-to-system communication method is this - the information system doesn't really understand what is being communicated. That may seem a bit pedantic and overstating things too much at first, but it has many implications. When a person hears a sentence, they "understand" the language. They have pre-conceived opinions about words, patterns, data. An automated system does not understand the words. At best, they have an ontological map that they can use to draw patterns and formulate ingest and process based on those patterns (and the understood implications of order and syntax). But those rules for ingest and process can be delivered (or be in place) before the communication takes place. The systems can agree to share, explicitly and without pre-conceived opinion or prejudice, exactly where in the ontology of the universe of discourse the data elements being exchanged fit, and what they mean. In short, the rules for communication and formulation of semantic ideas can come from the "system" of communication, and don't rely on either the transmitter or the perceiver alone.

This has been, so far, an introduction we felt necessary for the need of rules, and how they can benefit communications. Now we must consider where they reside. Even though we have suggested that the rules are part of the "system", that still leaves a big question. Are they a part of the formal ontology, or should they be up to the collection of systems relying on the ontology for communications? We believe that the answer is both, and this is an explanation of how we see that.

When considering rules, we believe that there is the possibility for two different types:

  • Rules that apply to the possible

  • Rules that apply to the actual

The former is necessarily a superset of the latter, and should be all encompassing and non-limiting. As the formal ontology will have uses and users that the original architects of it cannot conceive of at the time of inception, all of the possible eventualities that can exist between entities should be catered to.

As systems begin to use the formal ontology for specific purposes, there will necessarily be the demands of context and occasion, and the requirements for more detail and explicitness in some areas, and less in other areas. These comprise what are commonly called business rules. These business rules limit the possible down to a set of the actual, but it is a limitation with a purpose. It should eliminate ambiguities and redundancy, and it should make the operation of the overall system of communications more efficient for the purpose at hand.

We see that we have rules divided into the possible and the actual. The first set, the possible, is almost driven by the total matrix of what is possible within the syntax of the system, and these rules should reside within the formal ontology. The second set, the actual, is based on the business rules and use cases of the systems employing the formal ontology, to a certain extent, but also to the existent and changing states of the entities and relationships within the systems communicating, and as the states of those items change, then the rules determining the actual will change. It is very use dependent, yes, but it is also very much state dependent. These rules can not, without there being an insurmountably large number of such rules covering all possibilities, exist within the formal ontology, but should exist either within the systems making use of the formal ontology. Partially, what is the actual can be derived from the changing state of the entities, through implications. For instance, if you have a number of rules governing the possible that state all wheeled vehicle entities are capable of road movement, then the changing state of the location of the wheeled vehicles (sometimes on a road, sometimes not) will be an implicit limitation to the application of this rules (the actual rules).

Rules must be based on Properties

As can be seen from the aspects of this description and definition, the rules that are applied are all based on the properties of the entities and relationships affected. Without properties, there can be no application of rules, and all relationships would be equally applicable to all entities (a system of universality that results in no system at all). There must be properties, the application of rules must be based on properties, and then the connecting of entities via relationships must be based on these rules.

It is enough, based on the section above, to allow that all of the actual limitations of the rules will take place from within the formal ontology based on the changing state of properties and property-values, however it MAY be that some of the limitations on the complete set of possible rules will be made from outside business rules. These are not for the formal ontology to define.

Method for Evaluation

The method for evaluation therefore falls, in this case, not to the use cases, rather to the potential for all possible rules. All possible rules are based on properties, which are exhibited via the range of concepts that apply to an entity or relationship (and the property-values applied to those concepts). The set of all possible rules should therefore be evaluated as to the ranges of concepts that exist to limit said rules. Are the ranges sufficiently limited to allow for the precise application of rules where necessary? And are the ranges sufficiently broad to allow for a finite and understandable set of rules to be in place? If the ranges are not sufficiently broad, then too many small rules are in place, and no system can hope to have sufficient understanding and functional cataloging of all of them.

While use cases are too specific to form the basis of an evaluation concerning the inherent rules of a formal ontology, it is true that the universe of discourse that the ontology is intended to support must be considered. If the types of communications require (generally) a great deal of precision, then the ranges of concepts can be appropriately smaller. On the other hand, if the universe of discourse is itself quite large, and the number of entities to be considered is correspondently very large, then the rules should be broader, and the evaluation of rules should consider broad ranges of concepts in a favorable light.



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