| Ontologies are schemas (Gk. logos = “word, description”) that order the kinds of things that exist (Gk. oon = “being”) into heirarchies of concepts expressible in the language. In this work I build on MultiNet, a computer system that formalizes the meaning of language for use with an implementation of a question-answer interface to a computer knowledge base (Hellbig, 2006). MultiNet is undergirded by a semantic net and proves to serve as a very useful and natural way to relate the semantic structure to the logical structure of the predicate calculus. Although Helbig’s publications are not well organized for learning the system from scratch, sufficient details are enumerated, particularly in Part II and the appendixes, to allow a persistent student to begin to characterize the semantic structure of English. The idea of this section is to introduce the general idea of an ontology by examples from the most general structure characterized in English. |
Ontological analysis.The semantic net consists of nodes with directed arcs connecting them. The semanticist characterizes each node using a certain set of features selected in parallel with the syntactic categories of the basic vocabulary of English (and German). These are set out on Helbig’s figure 17.1, which is reproduced and appended to using multiple figures using a rather different format. So as not to lose sight of their basis in syntax I have added an indication of the part of speech of each major class of entity. Those feature-attributes which Helbig uses are indicated using two-letter abbreviations in italics. My convention is to indicate their feature status by giving a concise label in a yellow box. Next to each leaf node of the ontology is a word from the vocabulary of English intended as typical of any words that would belong in the same class. There are three important exceptions that I take to MultiNet. 1) MultiNet puts quantity nouns and certain limiting adjectives in their own class, as if they were a separate part of speech. I have made these a subcategory of noun and part of the determiner system as well. 2) MultiNet has a formal entity, which is used as a characteristic of grammatical terms; the only examples given are proper nouns. (These are connected using yellow and green arrows in figure 2 below.) 3) MultiNet has what I call a measurement. In both English and German this is actually syntactically complex, being a number and a unit of measurement taken together as a single concept. This feature apparently exists due to the fact that science normally models these concepts mathematically as a single number. |
Conceptual objects.MultiNet is based on over 90 semantic relations — most of them binary — defined as arcs between the nodes of the net, which represent entities. The one or two-letter abbreviations used for entities throughout Helbig’s work become second nature to the student, as each relation is typed using these symbols. Each relation connects characteristic nodes as its two arguments — one being its domain and the other its range. MultiNet has in addition about a dozen functions and families of functions, which I would call functors. These are often used to relate three nodes of the net, one of them being a combination of the other two. Functors also have signatures: one for each parameter of the domain, and one for its range. Relations are in effect functors whose range consists of values of factuality. |
Common objects.Probably the simplest entities are the conceptual object that in many natural languages are denoted by the words called nouns. Figure 1 illustrates certain features that characterize a number of common nouns in English. The words in light yellow boxes on the right serve as examples of each class designated by nouns having the set of features stretching to the left. Since there are many more nouns in English, it is possible to subdivide each of these classes even further. For example, the concrete substances could be classed by the state of matter so that ice and rock are solid, water and milk are liquid, and air and breath are gaseous. At some point it becomes necessary to choose the same features on different branches. This is called cross-classification. Many common nouns cross-classify with proper nouns. |
Proper instances.Proper nouns typically denote specific instances of the classes denoted by common nouns. Figure 2, which I have altered from Helbig’s figure 4.1, is meant to illustrate a classification of the concepts belonging to certain human artifacts called buildings. The bottommost nodes belong to specific instantiations of a building. These kinds of things are often represented by constants in the predicate calculus of first order logic (FOL). In many places in MultiNet such instance nodes are at the pre-extensional level, especially when the the author has a logical or mathematical formalization of what they refer to. The relationship called reference by MultiNet is modelled as a so-called layer attribute (see below in ¶11). It is also a simple thing to indicate instances and classes by means of a reference functor. which is here drawn in red. An instance cannot be made more basic without the use of elements of a formal model for the presumptive extensional level, which by definition is ineffible. The nodes at the “class” (generalized) level are the variables or predicates of FOL and those at the “instance” (specialized) level are the constants. As it turns out, both kinds of nodes are describable by terms of the intensional level. |
| The reference function is usually expressed in English with the determiner on a common noun signifying the class. A proper noun is often equivalent to such a phrase having a definite determiner. This is particularly true when the noun requires combining with another word, which noun or adjective is its class identifier. To illustrate the possibility of expressing the reference of proper nouns in this kind of explicitly intensional language, we offer the following contextually equivalent circumlocutions (definite descriptions) available to the adequately knowledgeable English speaker: | i. | Golden Gate Bridge, e.g., “the bridge spanning the Golden Gate to San Francisco harbor” |
| ii. | Empire State Building, e.g., “the office building in New York, New York (the Empire State), which for many years was the tallest structure in the world” | |
| iii. | Buckingham Palace, e.g., “the palace named for the Duke of Buckingham where the British royalty reside when in London” | |
| iv. | Tower of Pisa, e.g., “the tower in Pisa, Italy, which has leaned off vertical to an exceptional degree right from the time it was built” | |
| v. | Westminster Cathedral, e.g., “the cathedral in the western part of London not far from the Parliament buildings also serving the MPs” | |
| vi. | Rita Monastery, e.g., “a certain place of religious refuge named for an ancient concept of truth found in the Uphanishads” | |
| vii. | Manti Temple, e.g., “a certain place for ritualistic worship built by the Mormons in the central Utah community of Manti” | |
Animate objects.Figure 3 consists in four diagrams illustrating features involved with animate nouns. In the first one on the top left side are three features that typically characterize the designations of proper nouns. We will abbreviate such bundles of features using tan boxes. The next two diagrams on the top show the features needed to characterize the designations of personal pronouns in the singular. The features in light gray are those most clearly part of the pre-extensional level of description. Such basic features clearly participate in cross-classification. Notice that many of the proper nouns illustrated in the figure include a determiner as part of the name. The written language usually does not capitalize such determiners, but they are required to be expressed to make the phrase grammatically acceptable. |
| Notice that there are places for given names as designating instances of human beings. The classification of family names comes under the designations for instances of certain sets of individuals (families). The fact that people may take such names as a distinguisher for themselves individually is not expressed here, but could be done by splitting up some of the existing classes and making additional classes for surnames, maiden names, etc. |
Abstract objects.Figure 4 gives possible classes for some of the many abstract objects that might have instances for which proper nouns have been applied as designators. I have put some of the aspects of culture together as “manifestations” thereof. Most of the members of this latter class may optionally appear with a definite article the. The class of ideal objects, although being often spoken of as abstract, seem to have a physical manifestation, so that they can be understood either way, according to context. |
Inanimate, movable objects.The objects included in figure 5 are concrete, but moveable, designating instruments created or devised for some purpose or extra-terrestrial objects discovered to have distinctive properties. |
Localities.The objects represented on figure 6 designate intances of places located on the surface of the earth (a locality). Those classed as “edifices” are all artificial, i.e., built by man, but the others can usually be divided between artificial and natural instances. This concludes our coverage of proper nouns in their various semantic classes. |
Situations & their descriptors.Distinct from nouns that designate conceptual objects are the other parts of speech that designate concepts for other entities. I have not developed the various subclasses and cross-classes for these concepts. Figure 7 lists only three important classes of situations designated by verbs. The careful study of syntax will reveal quite a few verbs used to designate more abstract situations, e.g., aspect, temporality, relationship, attribution, etc. The adverbs that typically modify the verbs that designate situations are called situation descriptors. It is much more common in English for this function to be handled by prepositional phrases and dependent clauses. |
Qualities & graduators.The qualities and graduators of MultiNet are classified on figure 8. The measurable qualities are those that actually have measurements that have been assigned to them by science. The non-measurable qualities are still gradable, i.e., can be modified by a graduator like very, but they don’t normally have a unit of measurement associated with them. All of the properties can be attributed to conceptual objects using a predicative construction, but the relational and functional qualities are attributed by preposing the adjective to the noun. |
Layer attributes & reference.MultiNet handles some of the atomic concepts of English as attributes assigned directly to the node being classified by the conceptual objects called entities. This mode of modification is given here also in the form of ontological charts, but these expressions are often involved directly in classification, instantiation, or other pre-extentional attributes. Figure 9 enumerates some of the important aspects of quantification, generality, extensionality, and factuality (assertion). Many of these relate directly to considerations for modeling an object as a mathematical construct required by science. The final chart given below enumerates the various words used to refer directly to a conceptual object in English. One of these forms of the determiner is almost always associated with any topic of discourse. Notice that I have repeated the abstract quantities of figure 1 (except the number one) here in another form. In figure 9 they are absolute set quantifiers. In figure 10 they refer possibly to an indeterminate set. |
