ONTOLOGICAL DISTINCTIONS AS BASIC NODE TYPES

If we follow the entailment relation "upward" between classes we will reach ever more abstract or more general distinctions, e.g. dog-> carnivore-> mammal-> vertebrate-> animal-> organism-> object. The most abstract classes can be interpreted as the philosopher's "categories", the most basic or universal distinctions which underlie our understanding of the universe. These fundamental concepts can be said to define an "ontology", i.e. a theory of the most fundamental categories of existence, such as time, space, matter, truth, cause and effect. These ontological distinctions can be interpreted as basic node types, which allow a classification of other, more concrete nodes.

Note that the word "ontology" has recently received a broader and more practical meaning in the domain of knowledge representation, where it denotes the complete system of concepts, with their definitions and relationships, that support a shared conceptualization of a domain (Uschold and Gruninger, 1996). The original philosophical meaning, which I use here, is closer to what Uschold and Gruninger call a "meta-ontology", i.e. a set of allowable types of concepts. What they call "an ontology" would correspond to the whole system of concepts in an entailment network. In that sense, CONCEPTORGANIZER could be viewed as a tool for building ontologies. As an illustration, the Principia Cybernetica Project has developed an ontology of basic systems theoretic concepts in the form of a semantic network (Joslyn, Heylighen & Bollen, 1997).

In order to develop a skeleton (meta-)ontology, or list of fundamental node types, I have posited two basic dimensions of distinction: stability (or time) and generality (Heylighen, 1991b). Stability distinguishes more from less temporally variable phenomena, while generality distinguishes abstract, universal classes from their concrete, particular instances. Although these distinction dimensions can in principle have continuous values, it is simpler to consider discrete classes. Stability can be seen as having three possible values: transitional (i.e. with no distinguished duration), temporary (with a finite duration), and stable (with an indefinite duration), and generality two: particular - general. The combination of these 3 x 2 values leads to 6 basic types of distinction (see table 1).

Table 1: 6 basic node types, generated as combinations of 3 values for the time dimension, and 2 values for the generality dimension.

For example, an object is a distinction that is stable (it is not supposed to appear or disappear while we are considering it), and particular(it is concrete, there is only of it). A property is a distinction that is general (several phenomena may be denoted by it, it represents a common feature), and temporary (it may appear or disappear, but normally it remains present during a finite time interval). An event is instantaneous (it appears and disappears within one moment), and particular(it does not denote a class of similar phenomena, but a specific instance). Events can be seen as discrete changes, as transitions in which something was present and suddenly is no longer present, or was absent and suddenly appears. Changes can be seen as classes of events or as "transformations" (in the mathematical sense of a function mapping a set of initial states onto a set of subsequent states).

Some examples will further clarify this classification. "Dog" is a class, and so is "mammal". My own dog "Fido", on the other hand, is an object that belongs to the class of dogs. "Barking" is a property that Fido may or may not have at any particular moment. "Being able to bark", on the other hand, is a class that mostly overlaps with the class of "dog". "Fido is barking" is a situation, a temporary state of affairs, which in this case involves a particular object. "The 2nd World War" is another situation. "The beginning of the 2nd World War", on the other hand, is an event. "Starting a war" is a general change.

These ontological distinctions are meant to be an aid to analysis, not an absolute statement about the structure either of the world or of the formal system. They are not at the same level of importance as the bootstrapping axiom. They should rather be seen as a checklist (cf. Heylighen, 1991a) of distinctions that are likely to be relevant. Their use is not mandatory. Indeed, it is easy to conceive of a concept in an entailment network that cannot be readily classified along either of the ontological dimensions.

Consider for example the concept of "the American democracy". Does this concept refer to a particular institution that exists in one country, or to a more general method of governing that could be applied to many instances? Does it represent the situation at this moment in time, or a system that may survive indefinitely? Different people are likely to answer these questions differently in different contexts. Yet the concept of "American democracy" is sufficiently clear that it can be meaningfully used in communicating and representing knowledge. It can therefore be represented in an entailment network, perhaps with entailments linking it to "the American senate" and "the Bill of Rights", but without needing to be linked to one of the ontological concepts of "object", "class", "situation", etc. Still, the creation of more specialised distinctions such as "the American democracy as method of governing" (class) or "the American democracy as an institution during the Reagan years" (situation) may be helpful to elucidate semantic confusions between different (p-) individuals who use the same words but speak about different things.

BASIC LINK TYPES

With these generic node types we can now produce a number of corresponding link types by considering the possible combinations of nodes between which an "if... then" link can exist. There is one constraint on these combinations, though: a more "invariant" (more stable or more general) distinction can never entail a less invariant one. Otherwise, the second would be present each type the first one is present, contradicting the hypothesis that it is less invariant than the first one. For example, a class cannot entail an object and a situation cannot entail an event. Yet, two concepts with the same type of invariance (e.g. two objects) can be connected by an entailment relation. The remaining possible combinations are summarized in figure 5.

Fig. 5: Link types derived from the allowed combinations between node types; the straight arrows represent entailment from one type to another (more invariant) one, the circular arrows represent entailment from a concept of one type to a concept of the same type

Let us discuss the most important link types in this scheme. When an object a entails a class b, a -> b, then a is an "instance of" b. When a class a entails another class b, then a is "a kind of" b. The union of the relations "a kind of" and "instance of" may be called "is a". This is the most popular link type used in traditional semantic networks. For example, "a dog is a mammal" and "Fido is a dog". Note that the traditional "has property" relation cannot be used to link an object with a property. If you wish the express the fact that an object has a property (which because of its temporary character cannot be expressed as a class), e.g. "Fido is tired", then you must create a situation which involves (only) the object "Fido" and has the property "tired".

When an object a always entails the presence of another object b, then b must belong to or be a part of a. (If two objects entail each other, they are either identical or so tightly bound that they cannot be separated.) Note that the direction of the "has part" entailment may seem counter-intuitive, since it runs from a "larger" whole to a "smaller" part, whereas the "is a" entailment runs from a "smaller" class to a "larger" superclass, thus putting the conventional hierarchy on its head. The (physical) size of an object has nothing to do with the (logical) size of a class, though. One should beware of the intuitive tendency to see "is a kind of" as analogous to "is a part of", and remember that in terms of entailment it is equivalent to the inverse relation "has as part".

The entailment from property to class is a simple implication from temporary to stable features. E.g. if something falls it has a mass: falling -> mass, yet objects that have mass (permanently) are not permanently falling. Property entailing property is again a simple implication (or succession), now between temporary features, e.g. falling -> moving.

The application of the entailment relation to stable distinctions follows relatively closely the logical implication. However, when applied to distinctions that have an element of time, the "then" part of "if...then" can be interpreted as an indication of temporary succession. This makes it possible to express the flow of time in the formalism. The cognitive interpretation is that the main function of knowledge is anticipation: trying to predict the future on the basis of the present (Heylighen, 1993; Turchin, 1993). The simplest case is the entailment between events, which can be interpreted as "precedes or is simultaneous with". With this interpretation, my original structural language for the foundations of physics (Heylighen, 1990a) corresponds to that subset of the present representation scheme in which only events and precedence relations are considered. As shown in (Heylighen, 1990a), the network structures present in this subset are sufficient to reconstruct the primitive geometry of relativistic space-time.

The generalization of a specific event to a class of similar events corresponds to a change. When a change a entails another change b, then a and b "covary" and since a is assumed to be prior to b, we can interpret a as the cause of b. For example, "heating water (change) causes (entailment) boiling (change)". There is no direct way to express by a link that an event a causes another event b, except by noting that a precedes b, and that a and b are two instances of general change phenomena which are related by a causal relation. (This is not a shortcoming of the present knowledge representation, but a general property of causation, which can only be established after observing a repeated covariation.) A transitional phenomenon can also entail a more long lasting phenomenon. For example, "boiling (change) produces vapor (property)". Similarly, an event (e.g. "the 1939 invasion of Poland") can precede a situation (e.g. "the 2nd World War"). Sometimes this precedence can also be interpreted as a production, if event and ensuing situation can be interpreted as instances of a change producing a property (e.g. "invasions produce war"), but this is in general not the case (e.g. "the release of 'Gone with the Wind' preceded the 2nd World War") (see Fig. 6).

Fig. 6: an entailment network representing the semantic relations "the invasion of Poland produced World War II", and "'Gone with the Wind' preceded World War II".

The fact that a short-lived phenomenon (e.g. an event, change or situation) can entail a more long-lived one (e.g. a property, class or object), but not the other way around, is an illustration of the "principle of asymmetric transitions", which governs systems evolution: a transition from an unstable configuration to a stable one is possible, but the converse is not (Heylighen, 1992b). Of course, we can formulate expressions such as "the gun (stable) produced a shot (transitional)", but this is just a shorthand for saying that a particular event (transitional) involving a gun, a finger and a movement of the gun's trigger, produced another event, a shot. This example illustrates how the simple constraints inherent in the present ontology (and in entailment nets in general) force the user to make implicit--but necessary--distinctions explicit, thus avoiding ambiguities and gaps in the knowledge system.

In conclusion, the advantage of this representation scheme is that most of the intuitive and often used semantic categories (objects, classes, causality, whole-part relations, temporal precedence, etc.) can be directly expressed in it, using a simple and uniform format. The resulting representation appears general, consistent and unambiguous. This allows us to reduce a complicated set of semantic categories to an extremely simple and flexible formal structure. The disadvantage is that many more links are needed in order to reduce various link types to nodes than if the links could be simply labelled by their types. However, the burden of keeping track of all the links will normally rest on the computer, and not on the user, who could still work with a higher level representation using typed links.