| An ontology is a schema that orders the kinds of things that exist (Gk. oon = “being”) into hierarchies of concepts expressible in the language (Gk. logos = “word, description”). The ontologies here begin with those of 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 itself to be a very useful and natural way to relate the semantic structure to the basic structure of the various logical calculi (cf. The Languages of Science). 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. It must, however, be pointed out that cognative scientists and theoretical linguists have not developed the representation of knowledge and semantic universals very well at this time. In science the desire is to handle the structural and conceptual requirements of any and all languages. In our case it will be mainly the structure of English that will inform us of the semantic structure. The idea of this section is to introduce the most important ontologies with examples from English. |
Semantic net.The semantic net consists of nodes with directed arcs connecting them. The semanticist working with MultiNet characterizes each node using a certain set of features selected in parallel with the syntactic categories of the basic vocabulary of English (and German). Thus the results seem to be guided by something like the prototypical grammatical structures of the last section. These are set out on Helbig’s figure 17.1, the top of which is reproduced here in figure 4 in a rather different format. |
| I have freely extended the sorts and appended additional information to them spreading them out into multiple additional figures. 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. Helbig uses certain two-letter abbreviations in italics for feature-attributes. These are indicated next to each class on the figures and in the glossary entry. My convention is to indicate their feature status by giving a fuller but 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, which |
| Most quantifiers have been made subcategory of noun and some are made part of the determiner system. Examples of formal entities are represented by the nodes in figure 6 that are connected using yellow and green arrows below. Measurement, in both English and German, is actually syntactically complex, being a number together with a unit of measurement taken as a single concept. This feature apparently exists in MultiNet due to the fact that in the idiom of science these concepts are normally modeled 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 in my work in logic are called 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 could be viewed as functors whose range consists of the true and false values of factuality. In this case the signature of the relation would become the domain parameters of the functor. |
Common objects.Probably the simplest entities are the conceptual objects that in many natural languages are denoted by the words called nouns. Figure 5 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 such 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. These examples are sometimes count nouns, e.g., a rock, a breath, and sometimes non-count, e.g., some ice, some air. The reader is advised to click on some of the classes (semantic features) and see how they are defined in the glossary. At some point it becomes necessary to choose the same features on different branches. This is called cross-classification. Chapter 11 contains a discussion of a grammatical cross-classification of nouns denoting substances. The next few paragraphs discuss some of the many grammatically common nouns that cross-classify with corresponding proper nouns. |
Specific instances.Proper nouns typically denote specific instances of the classes denoted by common nouns. Figure 6, 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) (cf. The Languages of Science). In many places MultiNet consciously diagrams such instance nodes at the pre-extensional level. This level is the appropriate place to represent a formalization of knowledge that is so close to reality that a logical or mathematical model is possible. The semantic features of the objects at this level correspond to certain basic features of logical constructs, viz. individuals, sets, sets of sets, sets of sets of sets, etc. Any of these objects may be modeled mathematically by either a variable or a constant. In MultiNet these features constitute the “extensionality” of the conceptual object, which features are rendered here in light gray boxes. They are at the lower levels of another functor which MultiNet calls reference. Reference is typically expressed in English using the various reflexes of the determiner. Hence, the nodes in the figure representing instances and classes are provided with their reference functor, 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 ultimately 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. Both kinds of nodes are describable by terms of the intensional level. The special MultiNet signs on the legend to figure 6 may be interpreted as follows: |
| Whereas the reference functor is usually expressed in English with the determiner on a common noun signifying the class, a corresponding proper noun is often equivalent to such a phrase with a definite determiner. This is particularly true when the noun requires combining with another word, which noun or adjective is its class identifier. Many proper nouns illustrated in figure 6 may include a determiner as part of the name. The written language usually does not capitalize these determiners, but they are required to be expressed to make the phrase grammatically acceptable. To illustrate the possibility of expressing the reference of proper nouns in 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.Figures 7 and 8 illustrate certain features important when characterizing animate objects. In the section on the left of figure 7 are six features that typically characterize the designations of proper nouns. It will be convenient to abbreviate such bundles of features as virtual and ad hoc features through the use of tan boxes. The equals mark is meant to indicate that these virtual features are to be taken as equivalent to the features listed in bundle below them. The diagram on the right shows the features needed to characterize the designations of personal pronouns in the singular. Not included here are the plural pronouns, whose interpretation is more ambiguous, and it, which is quite general in its use and meaning, even though grammars often classify it too as “personal.” |
| The virtual feature of proper in figure 8 is given a plus sign to indicate that the feature bundle is to be ’unified” with the features listed below in the box and those characterizing the lexical items. Unification grammars describe the sharing of such features by words in a construction by means of that process. Inasmuch as proper nouns are included in the lexicon, their features would already be brought together there. |
| Notice also 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. A similar expansion is readily possible for the various classes (and subclasses) of the social institutions listed. The diagram is meant simply as suggestive of the structure needed for an ontology of these classes. |
