Year 1985 – The AI Magazine – Equivalence

Mathomathis would like to present an article on: Sanskrit and Artificial Intelligence by Rick Brigs | RIACS, NASA Ames Research Centeu, Moffet Field, California 94305. The following article is a continuation from the previous article: Sanskrit and Artificial Intelligence | 101

A comparison of the theories discussed in the previous article with the Indian theories of sentence analysis in the second section shows at once a few striking similarities. Both theories take extreme care to define minute details with which a language describes the relations between events in the natural world. In both instances, the analysis itself is a map of the relations between events in the universe described. In the case of the computer-oriented analysis, this mapping is a necessary prerequisite for making the speaker’s natural language digestible for the artificial processor; in the case of Sanskrit, the motivation is more elusive and probably has to do with an age-old Indo-Aryan preoccupation to discover the nature of the reality behind the the impressions we human beings receive through the operation of our sense organs.

Be it as it may, it is a matter of surprise to discover that the outcome of both trends of thinking-so removed in time, space, and culture-have arrived at a representation of linguistic events that is not only theoretically equivalent but close in form as well. The one superficial difference is that the Indian tradition was on the whole, unfamiliar with the facility of diagrammatic representation, and attempted instead to formulate all abstract notions in grammatical sentences. In the following paragraphs a number of the parallelisms of the two analyses will be pointed out to illustrate the equivalence of the two systems.

Consider the sentence: “John is going.” The Sanskrit paraphrase would be

“An Act of going is taking place in which the Agent is ‘John’ specified by singularity and masculinity.”

If we now turn to the analysis in semantic nets, the event portrayed by a set of triples is the following:

1. “going events, instance, go (this specific going event)”
2. “go, agent, John”
3. “go, time, present.”

The first equivalence to be observed is that the basic framework for inference is the same. John must be a semantic primitive, or it must have a dictionary entry, or it must be further represented (i.e. “John, number, 1” etc.) if further processing requires more detail (e.g. “HOW many people are going?“). Similarly, in the Indian analysis, the detail required in one case is not necessarily required in another case, although it can bc produced on demand (ifneeded).

The point to be made is that in both systems, an extensive degree of specification is crucial in understanding the real meaning of the sentence to the extent that it will allow inferences to be made about the facts not explicitly stated in the sentence The basic crux of the equivalence can be illustrated by a careful look at sentence

“Out of friendship, Maitra cooks rice for Devadatta in a pot over a fire ”

The semantic net is supplied in Figure 5 (below). The triples corresponding to the net are:

cause, event, friendship
friendship, objectl, Devadatta
friendship, object2, Maitra
cause, result cook
cook, agent, Maitra
cook, recipient, Devadatta
cook, instrument, fire
cook, object, rice
cook, on-lot, pot.

The sentence in the Indian analysis is rendered as follows:

The Agent is represented by Maitra, the Object
by “rice,” the Instrument by “fire,” the Recipient
by “Devadatta,” the Point of Departure (or cause)
by “friendship” (between Maitra and Devadatta),
the Locality by “pot.”

Since all of these syntactic structures represent actions auxiliary to the action “cook,” let us write cook” next to each karaka and its sentence representation:

cook, agent, Maitra
cook, object, rice
cook, instrument, fire
cook, recipient, Devadatta
cook, because-of, friendship
friendship, Maitra, Devadatta
cook, locality, pot.

The comparison of the analyses shows that the Sanskrit sentence when rendered into triples matches the analysis arrived at through the application of computer processing. That is surprising, because the form of the Sanskrit sentence is radically different from that of the English. For comparison, the Sanskrit sentence is given here:

Maitrah: sauhardyat Devadattaya odanam ghate agnina pacati.

Here the stem forms of the nouns are: Maitra-sauhardya-“friendship,” Devadatta -, odana- “gruel,” ghatu- “pot,” agni- “fire” and the verb stem is paca- “cook”. The deviations
of the stem forms occurring at the end of each word represent the change dictated by the word’s semantic and syntactic position. It should also be noted that the Indian analysis calls for the specification of even a greater amount of grammatical and semantic detail: Maitra, Devadatta, the pot, and fire would all be said to be qualified by “singularity” and “masculinity” and the act of cooking can optionally be expanded into a number of successive perceivable activities. Also note that the phrase “over a fire” on the face of it sounds like a locative of the same form as “in a pot.” However, the context indicates that the prepositional phrase describes the instrument through which the heating of the rice takes place and, therefore, is best regarded as an instrument semantically.

Mathomathis - Sanskrit AI - Fig 5
Mathomathis – Sanskrit AI – Fig 5

Of course, many versions of semantic nets have been proposed, some of which match the Indian system better than others do in terms of specific concepts and structure. The important point is that the same ideas are present in both traditions and that in the case of many proposed semantic net systems it is the Indian analysis which is more specific.

A third important similarity between the two treatments of the sentence is its focal point which in both cases is the verb. The Sanskrit here is more specific by rendering the activity as a “going-event”, rather than “going.” This procedure introduces a new necessary level of abstraction, for in order to keep the analysis properly structured, the focal point ought to be phrased: “there is an event taking place which is one of cooking,” rather than “there is cooking taking place”, in order for the computer to distinguish between the levels of unspecified “doing” (vyapara) and the result of the doing (phala).

A further similarity between the two systems is the striving for un-ambiguity. Both Indian and AI schools encode in a very clear, often apparently redundant way, in order to make the analysis accessible to inference. Thus, by using the distinction of phala and vyapara, individual processes are separated into components which in term are decomposable. For example, “to cook rice” was broken down as “placing a pot on the fire, adding fuel, fanning, etc.” Cooking rice also implies a change of state, realized by the phala, which is the heated softened rice. Such specifications are necessary to make logical pathways, which otherwise would remain unclear. For example, take the following sentence:

“Maitra cooked rice for Devadatta who burned his mouth while eating it.”

The semantic nets used earlier do not give any information about the logical connection between the two clauses. In order to fully understand the sentence, one has to be able to make the inference that the cooking process involves the process of “heating” and the process of “making palatable.” The Sanskrit grammarians bridged the logical gap by the employment of the phalu/ vyapara distinction. Semantic nets could accomplish the same in a variety of ways:

1. By mapping “cooking” as a change of state, which would involve an excessive amount of detail with too much compulsory inference;
2. By representing the whole statement as a cause (event-result), or
3. By including dictionary information about cooking.

A further comparison between the Indian system and the theory of semantic nets points to another similarity: The passive and the active transforms of the same sentence are given the same analysis in both systems. In the Indian system the notion of the “intention of the speaker” (tatparya, vivaksa) is adduced as a cause for distinguishing the two transforms semantically. The passive construction is said to emphasize the object, the nonpassive emphasizes the agent. But the explicit triples are not different. This observation indicates that both systems extract the meaning from the syntax.

Finally, a point worth noting is the Indian analysis of the intransitive phrase describing the leaf falling from the tree. The semantic net analysis resembles the Sanskrit analysis remarkably, but the latter has an interesting flavor. Instead of a change from one location to another, as the semantic net analysis prescribes, the Indian system views the process as a uniting and disuniting of an agent. This process is equivalent to the concept of addition to and deletion from sets.

Leaf Falling - Mathomathis

A leaf falling to the ground can be viewed as a leaf disuniting from the set of leaves still attached to the tree followed by a uniting with (addition to) the set of leaves already on the ground. This theory is very useful and necessary to formulate changes or statements of state, such as “The hill is in the valley.” In the Indian system, inference is very complete indeed. There is the notion that in an event of “moving”, there is, at each instant, a disunion with a preceding point (the source, the initial state), and a union with the following point, toward the destination, the final state. This calculus-like concept facilitates inference. If it is stated that a process occurred, then a language processor could answer queries about the state of the world at any point during the execution of the process. As has been shown, the main point in which the two lines of thought have converged is that the decomposition of each prose sentence into karalca-representations of action and focal verbal-action, yields the same set of triples as those which result from the decomposition of a semantic net into nodes, arcs, and labels.

It is interesting to speculate as to why the Indians found it worthwhile to pursue studies into unambiguous coding of natural language into semantic elements. It is tempting to think of them as computer scientists without the hardware, but a possible explanation is that a search for clear, unambiguous understanding is inherent in the human being. Let us not forget that among the great accomplishments of the Indian thinkers were the invention of zero, and of the binary number system a thousand years before the West re-invented them. Their analysis of language casts doubt on the humanistic distinction between natural and artificial intelligence, and may throw light on how research in AI may finally solve the natural language understanding and machine translation problems.