CONTROL PROCEDURES

Let us look again at the example simplified setting procedure of the last chapter:

This means that whenever the conditional properties constituting the state of the individual take values such that the logic expression on the left in the first line is true, the component property pk will take the value zero, and when the properties are such that the logic expression on the left in the second line is true, the property pk will take the value one.

Now suppose that the expressions in parentheses in the second line are found to occur elsewhere, separately or together, in other setting procedures. We could take this as evidence for structure in the individual. The expressions in parentheses might be regarded as representing single properties even though they are made up of the simpler properties p_a, p_b, and p_c that also appear in the first line, and might well also appear elsewhere in other procedures.

We would be justified in postulating two new properties of the individual, P_d and p_e, which have internal structure as given by the expressions in parentheses. These new properties can be formally introduced by means of what are called control procedures, which explicitly represent the postulated structures in the individual. In the notation of control procedures we can write

and

where we read : as controls. Here the control procedure

simply means that whenever it becomes true that p_a has the value zero and p_c has the value one, the property p_d will take the value one with a certain time delay that can also be indicated if necessary. It also means that whenever these properties take other values so that the logic expression on the left becomes not true, then p_d will take the value of not one, i.e., zero.

Now we can substitute the two new properties for the expressions in parentheses and write the example setting procedure in a simplified form as

The difference between control procedures and setting procedures is that control procedures do not have memory, whereas setting procedures do. Each of the setting expressions in a setting procedure sets the output to the indicated value, and it retains that value even if the input conditions that set it have changed. The output is only set to the other value when the input expression in the other setting expression becomes true. In a control procedure, on the other hand, the output property retains its value only as long as the input expression remains true. If the input expression becomes false, the output property takes the other value. Thus unlike a setting procedure, which requires a separate setting expression to represent the conditions under which the output property takes its separate values, a control procedure is complete in one expression, because if the indicated conditions do not hold, the output takes the other value.

Control procedures can be used in this way to exhibit structural relations between groups of properties and to allow simplification of the logic expressions in setting procedures. They also have other uses in developing more complex constructions of properties.

MULTIVALUED CATEGORIES

It would be convenient if we had a way of representing multivalued categories. Although binary properties are completely adequate in principle, there are cases where multivalued categories would be useful. They can in fact be expected to be as widely useful in human linguistics as they are in the linguistics of language, where there are categories of case with several values for the different cases, and of gender, with sometimes three or more genders.

If F is the name of a category which has several values or conditions, we can represent the several conditions with a dot notation as F.o, F.1, F.2, and so on. Here the category name is written first with the value name following the dot.

Then if we have four input conditions A, B, C, and D, we can represent a four-valued setting procedure involving the category F as follows:

Here the input conditions could equally well be complex logic expressions, or they could be the output of control procedures containing complex logic expressions.

Of course one could and probably would use appropriate descriptive names in place of A, F, o, I, and so on. This would be analogous to the descriptive names found in the linguistics of language, where the category of case might have values of nominative, genitive, dative, and accusative. In the present notation one would write case.nominative, case.genitive, and so on.

This notation is also available for binary categories. Thus instead of using the category name only and writing A and - A as the output conditions for a setting procedure, one could use A.1 and A.0. This allows explicit names for both the category (A) and the conditions (0 and 1). Separate descriptive names for the category and for the conditions could be used here also if desired.

Whenever multivalued categories are used, they will also enter into the input expressions in setting procedures and control procedures. In this connection, the expression – S.2 would specify the condition that the category S does not have the value 2.

THE HIERARCHY OF CATEGORIES AND
CONDITIONS

Let us turn now to a matter of considerable importance: the possibility of a hierarchical structure in the categorial and conditional properties.

To take an example, suppose that an individual has a categorial property TURN, which has the value one when the individual has the turn in conversation and the value zero when he does not have the turn in conversation. And suppose there is another property CONV, which has the value one when the individual is in conversation and the value zero when the individual is not in conversation. Now note that these properties are not independent. A person cannot have the turn in conversation if he is not in conversation.

A way of representing this structural fact is to say that the property CONV is actually composed of a set of two properties: CTURN, which will have the value one if the individual is in conversation and has the turn, and CNTURN, which will have the value one if the person is in conversation and does not have the turn.

Then the property of CTURN is simply another more explicit name for the property TURN, and CONV can be recovered by a recoding with a control procedure:

CTURN v CNTURN : CONV

This means that CONV has the value one if either CTURN or CNTURN has the value one (they will never simultaneously have the value one due to their structural interrelation), and CONV will have the value zero if both CTURN and CNTURN have the value zero.

Thus there are four possibilities for the two properties CONVTURN and CNTTURN:

In general, a property may be composed in this way from two or more properties. It will then have the value one if one or more of the properties of the set has the value one, and the value zero if none of the properties in the set has the value one.

This produces a categorial-conditional hierarchy, for a property may be seen to be conditional with respect to a higher level and categorial with respect to a lower level.

In the present example we see that CONV is hierarchically related to CTURN and CNTURN. At one level we can say that the individual is either in CONVersation or not, depending on whether CONV has the value one or zero. At a lower level we can say that a person in CONVersation either has the turn or not, depending on whether CTURN has the value one or zero.

Or, taking both levels into account, we can say that the property CONV is made up of two properties such that there are three mutually exclusive values for CONV: not in CONVersation, in CONVersation and having the turn, and in CONVersation and not having the turn. In this view CTURN is conditional in nature with respect to the higher level in that it can be viewed as one of the values of CONV, and it is categorial in nature with respect to the lower level in that it has two values, one and zero, for having the turn or not at any given moment.

These several facilities already provide a great deal of flexibility for representing the structures found in the categorial and conditional properties of individuals and linkages. Other facilities can be introduced as needed.

THE USE OF FEEDBACK

Human linguistics is a dynamic theory. When a procedure executes, a dynamic process takes place in time that changes the conditional properties. An examination of the structure of procedural properties, then, is also an examination of how the temporal course of communicative behavior is controlled.

As an exercise in the structure of procedures let us consider what would happen if the output property of a procedure were connected back to the input. There would be a time delay, of course, for the execution of a procedure always involves a time delay, a period of time starting when the causal expression on the left becomes true and ending when the output property changes.

Consider the following setting procedure:

Here we will assume that the input property trigger becomes one for a short period of time and then returns to zero. Its becoming one sets the setting procedure so that the output category out takes the value one. Note that out is connected back as an input condition in the setting expression that changes out back to the value zero. But out changes to zero only after a specified delay time d that is indicated in a standard way after the comma. Therefore, when the property trigger becomes one for a short period of time, the setting procedure is triggered, and out becomes one for a specified interval of time d. We can say that we have generated a pulse of length d on the output category out. This is our first use of the principle of feedback, which is of considerable importance in human linguistics. By means of delays, with and without feedback, the temporal course of communicative events can be controlled.

EXPECTATION PROCEDURES

It is often the case that two or more setting procedures and control procedures operate together in a coordinated way. When this is the case, it is CONVenient to consider the several cooperating procedures as one complex procedure or construction.

As an example, consider the following complex procedure made up of one setting procedure and one control procedure:

Assume again that the input property trigger becomes one for a short period of time. This sets the output category expectation to one, and it will remain one until the input category event becomes one, setting it back to zero after a specified delay time d. Then in the control procedure, event and expectation simultaneously having the value one controls the output category next, which will take the value one only during the time when event is still one and expectation has not yet returned to zero. (Here we ignore the delay in the control procedure, which we will assume is short compared to d.)

We can interpret this as follows: The short trigger pulse trigger sets up an expectation that a certain event will occur (that event will become one), and this expectation will be remembered until the event does occur, at which time the expectation will be canceled (expectation becomes zero) and a pulse will be sent out on the category next to trigger the next procedure.

This is a simple example of what is called an expectation procedure. It is constructed of one setting procedure and one control procedure. Expectation procedures are widely useful in human linguistics. By means of the expectation output, which is one during the time that the event is expected, the system effectively “knows” what it is expecting, and its behavior in the interim can be controlled appropriately. For example, the expectation output can be connected to control procedures so as to interpret a potentially ambiguous change in properties as an occurrence of the expected event rather than as what it might be on other occasions. This is one of the ways in which we can handle the influence of context on communicative behavior.

TASK PROCEDURES AND THE HIERARCHY
OF TASKS

An important use for an expectation procedure is to implement what is called a task procedure, which is a procedure for controlling the execution of a task. Suppose a student executes the task of raising his hand to seek recognition in the classroom. We can make a task procedure for this out of an expectation procedure by relabeling the trigger input as raise and connecting it also to the mechanism for starting to raise the hand, so that the same short pulse will both set the expectation of the hand being raised and start the activity of raising the hand. Then we can relabel the expectation output as task-active, or hand-being-raised. The expected event, which is the completion of raising the hand, could be signaled by a pulse from a hand-up detector. So we can relabel the event input as hand-up.

When this task procedure is triggered as the task of raising the hand is started, it sets up an expectation of the completion of that task by a task-active or hand-being-raised category taking the value of one, and then when the hand is up, the expectation is canceled and the task procedure sends a next pulse on to initiate the next step in the communicative behavior.

Note that a task procedure for raising the hand may be specialized for gaining recognition in the classroom. In this case, when the task is completed an expectation for being called on would be set up. But the hand may be raised for other purposes as well, such as reaching for a high book in the bookcase. That task would be controlled by a different specialized task procedure, the completion of which would set up a task of grasping the book as the next activity, rather than an expectation of being called on. By this means the different purposes for the same act would be controlled by separate task procedures, and therefore would not be confused. Thus we see that task procedures do control tasks by placing them sequentially within larger tasks such as answering a teacher’s question or looking up an answer in a book.

Now it should already be clear that two or more task procedures can be chained together by sending the next output pulse from one procedure to the trigger input of the next procedure. Then the task procedures would be executed in temporal sequence. These sequential task procedures could control the sequential steps required in carrying out a complex task.

In this case, we could have an overall higher-level task procedure which would control this string of tasks. It would be set when they start and expect their completion. In this way we can build a task hierarchy with a number of levels of tasks and subtasks. This facility in human linguistics of representing a task hierarchy is very important for dealing with the hierarchical organization of communicative behavior in ways reminiscent of phrase structure in the linguistics of language.

SELECTION PROCEDURES

Another type of procedure important for the control of complex communicative behavior is the selection procedure. A selection procedure allows for a choice among several courses of action depending on how the conditional properties are set, thus implementing contextual dependencies of communicative behavior.

Suppose we have a case where one of four different task procedures should be selectively triggered, depending on various combinations of the values of three properties, a, b, and c. Let t be the initial trigger input to the selection procedure, and let the four outputs from the selection procedure be t1, t2, t3, and t4. These would be connected as trigger inputs to the four task procedures to be controlled. Given the required combinations of values for a, b, and c, the appropriate selection procedure can be assembled very simply from four control procedures as in the following example:

In this example an input pulse on t will cause a pulse to appear on one of the four outputs, t1, t2, t3, or t4, only if the control properties a, b, and c have the appropriate values as indicated.

THE LINGUISTIC COORDINATION OF
NONLINGUISTIC TASKS

With these facilities and others that can be constructed straightforwardly out of the available elements, we would seem to have all that is needed for handling the communicative phenomena usually associated with syntax in the linguistics of language.

Furthermore, since the significance of communicative behavior is that by its means people interact and cooperate in groups and societies, linguistic or communicative tasks can be seen as subtasks of higher-level cooperative or interactive tasks such as obtaining food, being helpful (or combative), and the like. For example, within the scope of Jill’s nonlinguistic task of getting an apple with Jack’s help, the details of the communicative subtask of enlisting his aid are rather narrowly constrained in ways that are of great interest in linguistics. Human linguistics concentrates on the lower-level communicative tasks and only moves up the hierarchy of tasks as far as it needs to for its own purposes. It does not need to provide a theory of or to model nonlinguistic phenomena in such areas as motivation, ethics, higher-level task organization, decision making, or free will.

But at the same time we do not need to close our eyes to relevant evidence from adjacent disciplines or from our prior knowledge of the nonlinguistic tasks that are being coordinated. Jack’s behavior in getting the apple for Jill and Jill’s behavior in accepting it are relevant data for the linguist even though he does not see it as his business to provide a theory of that behavior or to model it. In fact, a powerful research technique in human linguistics is the careful observation of similarities and differences of communicative behavior and the correlated nonlinguistic behavior when certain aspects of the coordinated tasks are kept constant or systematically varied. By these means we can establish the linguistic distinctions that are being made.

Thus in human linguistics there are two categories of data: observations of linguistic behavior that we wish our models to explain and predict, and related nonlinguistic observations that we do not wish our models to explain or predict, but that we can use as valuable evidence in establishing or testing our theories. In this respect human linguistics resembles the physical and biological sciences, but differs from the usual program of the linguistics of language where the set of observations used as evidence, say a corpus of utterances and judgments of grammaticality, is identical with the set of observations to be explained. This difference reflects the unity and interconnectedness of science and the relevance of human linguistics to its neighboring disciplines, and contrasts with the autonomy and comparative isolation of grammar from other disciplines noticed in chapter 5.

THE HIERARCHY OF LEVELS OF MODELING

There is a third hierarchy in addition to the categorial-conditional hierarchy and the task hierarchy. We have constructed complex procedures out of simpler ones, and we could continue the process, building still other, more-complex procedures out of the complex procedures. This hierarchy is a foundational-informational hierarchy. From this point of view, setting procedures and control procedures are foundational with respect to the expectation procedures that are built on them. At each level there are lower-level constructions in the hierarchy that serve as the foundational properties supporting the informational properties (the conditional, categorial, and procedural properties) that are built on them. This possibility is very important because it allows certain natural simplifications in representing the structures of individuals and linkages.

How about moving down in the other direction? Can we find levels in the foundational-informational hierarchy below that of the setting procedures on which our constructions have been based? It is in fact possible to build up setting procedures completely out of control procedures. This can be done by connecting control procedures together with feedback in what is called a flip-flop connection in computer science. This shows that the principle of continuity of component properties on which the construction of setting procedures rests is, as we thought, simply a convenient notational convention.

At any given level of analysis the foundational properties are considered as unanalyzed but logically required to support the properties that are constructed on them. Thus they can be considered as lying below the limit of verisimilitude of the model at the given level of analysis, the level below which the model no longer attempts to represent the object being modeled. If one were to analyze the foundational properties themselves, they would again be analyzed as informational properties, and again there would be a lower limit, a limit of verisimilitude below which there would be a new lower-level set of foundational properties. At the bottom of this hierarchy in the theory of the communicating individual lies the disciplinary boundary between linguistics and physiology.

CONTEXT AND THE DOMAIN OF CONTROL

A dynamic state system is appropriate for the individual because it allows us to take into account the continually changing context of situation for the individual as it affects communicative behavior and is in turn affected by communicative behavior. The context of situation is modeled in the state properties of the individual (the conditional properties) as they change from moment to moment. What an individual says or does communicatively at any moment depends not only on his repertory of categorial and procedural properties but also on his condition or state at that moment. What an individual understands of the communicative behavior of others depends not only on the input energy of the sounds heard and his receptive repertory, but also on his state at the moment of reception. When certain conditions in the individual obtain, certain things happen. It is for scientific research to find out what the conditions are, how they are structured, and how they help to control the dynamic changes in the individual that constitute communicative behavior.

Recall that according to the law of small changes, only a few properties change at any given moment. And according to the law of restricted causation, the number of properties entering as causes for these changes are again few. These properties which are potentially causal can be understood as constituting the central part of what is called the domain of control. Then there are other properties that are nearly ready to be changed, and again there is a limited set of properties figuring causally in possible changes of these other properties. These can be understood as being further from the center of the domain of control. The domain of control is the human-linguistic analog of the focus of attention, and like the focus of attention it can shift from moment to moment as different sets of properties stand ready to be triggered.

Our research, then, will be centrally concerned with analyzing properties in and near the domain of control. What would we expect to find there? That question in effect asks us to identify all of the conditional properties that figure causally in the communicative behavior we are examining. The causes may be of many sorts, for we understand that the constraints of context encompass all the communicative phenomena that in the linguistics of language would be studied in phonetics, phonology, morphology, syntax, semantics, and pragmatics—and more besides—indeed all of the constraints that operate causally when people communicate. And all of these constraints operate simultaneously. They are unified in the conditional properties, for many different sorts of constraints may operate as conditions in the causal expression for triggering any given procedure.

Now consider what happens when some procedures are triggered. The domain of control of necessity shifts, because new conditions now obtain and different procedures will stand ready or nearly ready to be triggered. In this way we can see how communicative behavior changes the context and affects the understanding of the communicative behavior that follows.

Thus in human linguistics we have an appropriate and ready means for handling contextual dependence of all sorts. This includes the treatment of so-called shifters and indexical expressions, contextually relative referring, tense and time reference, phenomena seen as ellipsis, and phenomena previously treated under pragmatics and presuppositions. It is a characteristic of human linguistics that it provides the means for integrating these many sorts of constraints. And it is a characteristic of the linguistics of language that its traditional theoretical structure lacks any good mechanism for handling contextual factors. Such a mechanism was not introduced into sign theory by the ancients, who focused more on the requirements of logic and the theory of knowledge than on the scientific understanding of how people communicate. Thus they placed the study of speech in the logical rather than the physical domain, where it has remained for two millennia in philosophy and in normative grammar.

THE PRINCIPLE OF EQUIVALENT COMPONENTIAL
HISTORIES

The view of causes in human linguistics, then, is that of immediate causes. The causes of a transition are represented in the conditional properties, and it is the current values of the conditional properties that are causally related to whether a certain procedure is executed or not. However, many of the causally relevant conditional properties will have acquired their current values in times past.

This fact has certain implications when considering the temporal antecedents for any given facet of communicative behavior. For a given procedure to be triggered, a logic expression must become true. In general, this could have happened in any one of a number of different ways. For each of the conditions required for triggering, there may be many ways in which that property might have been set to the current value at some earlier time, depending on the particular history of that individual. Further, different properties in the expression might be the last to change. Also, if the logic expression were a disjunction, there would be different ways in which it could become true, depending on which disjunct became true. Thus there are in general many possible histories of the individual that could have led up to the triggering of a given procedure. We can summarize this insight in the principle of equivalent componential histories:

A component property or group of properties represents in a compact fashion any one of all those different possible histories or different sets of relevant past events that would influence current communicative behavior in a certain way.

This principle is completely implied by our earlier considerations. Indeed, it is a well-known principle in other formalizations of state theories. It is one of the most important advantages of state theories, for it allows a considerable simplification. In our case it means that we do not have to know the complete details of the history of an individual in order to predict one facet of his behavior. We do not have to be omnipotent in order to make predictions in linguistics. All we have to know is the relevant aspects of the current state of the individual. That state could have been arrived at in any one of a number of different ways. That means that the doubts sometimes expressed about the possibility of a causal linguistic theory are not as well founded as has sometimes been feared.