A Note on Representing Adjectives and Adverbs

1. INTRODUCTION

The state-based representation, vide Cercone (1975), has been developed for use in a computer program concerned with the comprehension and manipulation of factual knowledge where such knowledge is communicated to the computer program via natural language. The representation is not based on "primitives", yet permits efficient use of semantic preferences; it is capable of accommodating unlimited amounts of information about complex concepts without loss of efficiency in the use of those concepts (Cercone, 1975, Ch 4). Modifiers, of course, complicate this endeavour.

The following discussion addresses the task of incorporating modifiers into the state-based representation. It will certainly not exhaust the myriad_problems of representing all English adverbs and adJectives. Nevertheless, theoretical (the use of functors) and methudological (the visual suggestiveness of extended semantic networks) advantages accrue from the appruach uutlined below.

2. ADJECTIVES AND RELATIVE TERMS

Bartsch and Vennemann (1972) outline a unified treatment of relative adjectives and cumparatives extending Muntague's (1972) treatment within the intensiunal logic framework. Their notion of a reference set (a set of ubjects whuse members are used for cumparison with some given ubject relative to some measurable attribute of the objects) may, however, be inadequate. For example, while it is P. ossible to define a mure or less adequate 'reference set" to account for a phrase like "a large apple", it is not immediately apparent what the reference set would be if one were to ask a child to draw a large. circle on a sheet of paper. This raises the additional question of how to infer the reference set from the context.

The use of functors (Cresswell, 1973) avoids some difficulties predetermined reference sets entail. For example 1 the "typical value" functor applied to a concept w1th some measure attribute returns a value, e.g. the typical value of size for rna~. Note that this is not the same as the typical man s size which cannot be readily determined since it is difficult to ascertain exactly what constitutes a typical man. A "typical value" functor is shown in Flg. 1. We abbreviate the typical value functor in a manner analogous to predicate collasping in the abbreviated semantic net notation (Schubert, 1974).

We treat predications a circular (abbreviated treated as a descriptive adjectives as conjoined in most cases. The sentence "Judy ate spice cake" is diagrammed in Fig. 2 notation). Spice in this sentence is kind uf cake like a chocolate cake.

a typical value of size for a man". Note the use of the "typical value" functor in Fig. 4.

Finally, Fig. 5 illustrates a non-directly oredicative 1 non-directly comparative use of a relative adJective. The sentence "Big John drinks t he whiskey is paraphrased ~n the diagram as "John drinks the whiskey and John s size is greater than the typical value of size for something and John is an instance of that something". In Fig. 5, the node immediately to the left of John represents Juhn's size (size is used as a functor in the proposition containing John and size). In genera l the treatment of relative adjectives based un ~aeasura ble attributes can be summarized as follows : The value of the "attribute" uf "x" exceeds t he value of the "attribute" which is typical for that concept (uf which x is an instance).

Ordinary discuurse admits constructiuns such a s :

John is the perfect man. Mary is the wurst cunceivable baker. Mike is the ideal fat man. In order to form a more perfect union ··.

~ 1)

~2 ~

Modifiers such as perfect, worst conceivable, and ideal are problematic to represent because of th~ way they operate on what they modify. For example, we might formulate {1} in logical terms as:

(P){[(x)[man(x)&P(x)~ =>y-approves[P(x)]]]=>P(John)}

Here y is the speaker. The formulation reads "John has,all properties such that y would approve of any man s having them". We can then easily formulate an expression for "someone is not a perfect man" by utilizing the expression above with the existential quantifier added (Ez)- and replacing P(John) with P(z). Clearly, the method of handling comparative ad jectives such as big does not work here.

At this time I make no definite proposals for handling adjectives such as perfect best cunceivable, and so on, at any adequately detailed level of analysis. However one might render the sentence "Mike is the perfect fat man" as shown in Fig. 6. Nute that the predicate "fat man" is furmed using lambda abstraction, vide Cercone (1975) Ch 3 & 4. The predicate "fat man" is then uperated un by the "perfect" functor. In the cas.:: uf d.::scriptive adjectives (cf the implicit comparative "fat" in the "fat man" example abuve) the best one cuuld du (in absence uf cuntext) is tu treat them as conjoined predications outsidE: the scop.:: of the functor uperating.

3. ADVERBIALS

Th.:: purpose of this section is to suggest plausible m.::thods for handling adverbials within the state-based framework and to reformulate an earlier version of Fig. 8 consistent with the use of functors above, s.::e Cercone and Schubert (1974).

There appear to be two major appruaches to the treatment of adverbial moaifiers. One approach, expressed in Montague (1972) 1 Bartsch and Vennemann (1972) and Zadeh (1972) is to regard comparative adjectives and adverbs as o~erators which transform predicates. Reichenbach s (1947) approach, seemingly accepted by Schank (1972) and Anderson and Bower (1973), is to regard adverbial modifiers as second-order predicates that impose constraints on a specific relation, thereby restricting the class of specific relations of wh~ch it may be a member. Bartsch and Vennemann s approach seems promising but will be seen to have serious defects.

Must adj.::ctives appear to be comparative in Schank (1972) diagrams adverbs as action nature regardless of their murphology. For .::xample, modifiers without further analysis. Apparently he tall, slow, hard, and so un are relative adjectives has not concerned himself with the meanings of based on some measurable attributE: of the object of genuine manner adverbials as yet (but see Schank, attention. The sentence "John is bigger than Bill" 1974, for a discussion of adverbs such as is diagrammed in Fi~. 3. The explanatory paraphrase vengefully). In the case of many adverbs (and many of Fig. 3· is "John s size is greater than Bill's adjectives) this neglect is probably justified, size". Often the comparative is implicit in the since most of the meaning content derives frum utterance. For example, in the sentence "John is a p,erceptual prucesses. For example 1 in the sentence big man", "big" serves as a comparative. The 'Mary walked gracefully" it 1s difficult tu meaning of "John is a big man" is diagrammed as paraphrase "gracefully" in more elementary terms. Fig. 4. The associated paraphrase is as follows: Essentially we know gracefulness when we see it. "Juhn is ~ man_and the _size of John is greater than Thus perceptual understanding !leeds to be supplementt:d only by a few additional facts for languagt: comprehension purposes, such as the fact that gract:ful motion is gent:rally plt:asing, is more or less the opposite of awkward motion is smooth and well-coordinated, and the like. Other advt:rbial modifiers, however, clearly require systematic analysis; "quickly" is a good example. This term appears to say something about the speed of an action or activitr, comparing it to some standard. An adequate mean ng representation for "quickly" should spell this out precisely.

Bartsch and Vennemann suggest that adverbial modifiers opt:rate on verb meanings in the same manner that adjt:ctival modifiers operate on noun meanings, i.e. they have semantic representations with functions f such that f is applied to term x to map x onto a new term f(x). One problem in this approach is illustrated by the following example.

Whereas large in {5} has as a reference set the set of cars, and John s car is large in relation to the "average" for that set~ "running quickly" cannot be analyzed so easily. Ir the analogy were perfect then the reference set operated on by "quickly" would be the set of "runnings" (whatever that means); but clearly this set of runnings must be further restricted to the set of runnin~s John is capable of performing. Thus "quickly appears to operate not on "running" alone but on "John running". As further examples consider {7} and {8}.

The cheetah is running quickly. The ant is running quickly.

Clearly "quickly" here operates on "running ant" and "running chet:tah" respectively.

Ht:nce the nature of the "runnt:r" can narrow the reference set to which we apply a measure function. In {6} "quickly" modifies running with respect to Johns runnings, or, if we don't know John, at lt:ast to human runnings (assuming that John is human). In {7} and {8} the measure function is applit:d to the runnings of cheetahs and ants respectively. Unfortunately factors other than the identity or category of the runner can also affect the meaning of "quickly", as shown by {9} to {13}.

John is running quickly on his hands and knees. l9j John is running quickly on the moon. {10 John is running quickly in Chile. { 11} { 12 }-. The cheetah is running quickly in the dense forest'.· The cheetah is running quickly on the plain. { 13}

The effect of locale on the meaning of "quickly" is st:en in the contrast between {10J and {11} and between {12} and {13}.

Consequently it appears that the context which determines the meaning of an adverbial modifier can't be circumscribed once and for all. Adverbials must be allowed to interact with any specific and general knowledge available about the participants in (and setting of) an action. Zadeh's (1972) treatment of adverbial "hedges" lacks generality since he specifies (weighted) components of each fuzzy term on which a hedge may o~erate once and for all prior to using a particular hedge". Thus we diagr.am {7}, without the adverb, as Fig. 7' (ai and (b) are based on alternative (but equivalent rt:presentations of definite descriptions. Fig. illustrates the adverbial construction, in {12} consistent with Bartsch and Vennemann s gent:ral approach, but takes into account the above considerations. In Fig. 8 tht: relationsh~p is made explicit between the speed of the cheetah s running and the typical value of speed for something that is running, a cheetah, and in dense forests.

Note that the set of cheetahs running in dense forests, required for comparison, may well be emp,ty. (if not, replace "dense forest" with "deep snow'). The "reference set" therefore, if it exists at all 1 is not of this world but of some imaginary worla which is our conception of how hard cheetahs would find the going if they were to run through forests (or snow). In our formulation we have applied the typical val~e functor_ to the lambda abstracted predicate (LAMBDAx) [cheetah(x) & running(x) & in-dense-forests ( x)] The "typical value" functor does not presume the existence of a reference set.

ACKNOWLEDGEMENTS - I am indebted to Len Schubert for contributing to the ideas herein.