Rule-Based System

Rule-Based System

The computational principles underlying rule-based reasoning are more opaque and more controversial than those of associative reasoning. One such principle, mentioned by James (1890/1950) and reasserted by Fodor and Pylyshyn (1988), is productivity. Rule-based systems are productive in that they can encode an unbounded number of propositions (i.e., rules can be combined with each other to generate an ever-larger set of propositions). To understand this, consider arithmetic, in which we can always generate a new number by adding 1 to the largest number in our set. A second principle is that rules are systematic in the sense that their ability to encode certain facts implies an ability to encode others. For example, if one can reason about John loving Mary, one also has the capacity to reason about Mary loving John. Fodor and Pylyshyn (1988) argue that the productivity, systematicity, and, therefore, compositionality of mental representations necessitate that human reasoning is generated by a language of thought that has a combinatorial syntax and semantics.

My claim is that their argument is relevant only to one form of reasoning. I call this form of reasoning rule-based because rules are the form of representation that exhibit the properties of productivity and systematicity most transparently. Rules are abstractions that apply to any and all statements that have a certain well-specified symbolic structure. Most importantly, they have both a logical structure and a set of variables. The relation is purely formal or syntactic in the sense that correct application of the rule is determined by relations amongst symbols and not by any sort of meaning that we attribute to the symbols.

Variables vary (i.e., they can be instantiated in more than one way). Because they assume a class of possible values, they are necessarily abstract. My discussion concerns rules that contain variables, and therefore rules are abstract; they can be instantiated in more than one way. This does not imply that rules have to be content independent. For instance, Cheng and Holyoak (1985) discuss sets of rules for reasoning that they call pragmatic reasoning schemas associated with particular content domains. They suggest that certain rules are associated with reasoning about situations involving domains such as permission. An example of such a rule is, “If the action is to be taken, then the precondition must be satisfied.” Such rules involve both variables (e.g., precondition and action, which must be specified on each occasion of use) and, they involve logical structure (the form if – then); therefore, I count them as rules.

Rules come in different kinds. Some rules are instructions, like statements in a computer program or a recipe; other rules are laws of nature or society or rules of logic. People are capable of following all of these rules (and of disobeying some). Rules can be normative, telling us how we should behave to reach some prespecified goal (such as the conjunction rule in order to maintain a coherent set of probabilities); or descriptive, telling us how we do behave in certain contexts. In contexts in which a normative rule obviously applies, it usually becomes descriptive as well. So, some rules are handed down to us by our culture, others we make up ourselves, and some are discovered in nature or logic. Humans can understand and apply all of these rules without external support as long as they have become internalized, as long as their analytic machinery has access to and mastery of them.

Johnson-Laird and his colleagues (e.g., 1983; Johnson-Laird & Byrne, 1991) have argued persuasively that much of everyday deduction is unlike theorem-proving. They have posited a procedure to arrive at a determination of the logical relation between the premises and conclusion of an argument that has a fundamentally different rationale and design than the sequential application of inference rules advocated by theorists such as Braine (1990) and Rips (1994). Nevertheless, their “mental models” theory shares key assumptions with rule-based theories. Both approaches depend heavily on symbols. Like rules, mental models consist entirely of symbols. Some symbols are tokens that refer to entities in the statements of an argument. Other symbols represent negation and still others represent superset–subset relations. Mental models enjoy the criterial properties that I have assigned to rules: They have both logical structure and variables. The criterial properties of the rule-based system are thus sufficiently general to encompass central aspects of the mental models theory.

Evans and Over (1996) come to a similar conclusion to mine about the dual process nature of thought. They draw their conclusion from a thorough survey of the deductive reasoning literature and related decision-making phenomena, and from the evidence supporting the distinction between implicit and explicit learning. They argue that the two systems of thought are driven by different types of rationality. The associative system is generally useful for achieving one’s goals; the rule-based system is more adept at ensuring that one’s conclusions are sanctioned by a normative theory.

Table 22.1 summarizes my characterization of the two systems. The point of this chapter is not that both systems are applied to every problem a person confronts, nor that each system has an exclusive problem domain; rather, the forms have overlapping domains that differ depending on the individual reasoner’s knowledge, skill, and experience. Table 22.1 lists some functions that show off each system’s capacities. However, the common mode of operation of the two systems is clearly interactive. Together they lend their different computational resources to the task at hand; they function as two experts who are working cooperatively to compute sensible answers. One system may be able to mimic the computation performed by the other, but only with effort and inefficiency, and even then not necessarily reliably. The systems have different goals and are specialists at different kinds of problems. However, when a person is given a problem, both systems may try to solve it, each may compute a response, and the responses may not agree. Cases can be found in every domain of reasoning that has been studied in detail in which they do not. Because the systems cannot be distinguished by the problem domains to which they apply, deciding which system is responsible for a given response is not always easy. It may not even be possible, because both systems may contribute to a particular response.