A theoretical device for the explanation of behavioral regularities and/or cognitive states.  Rules are generally, but not always, characterized in terms of causally-operative mental representations. See computation, symbolicism, connectionism.

At a first pass, a rule R is said to explain a person's behavior if the behavior conforms to the conditions of output specified by R. Similarly, a mental state or function is said to be governed by R if the form it takes or the output it produces conforms to the conditions specified by R.
Adapting an argument from Reber (1995), we might say that the conditions specified by a rule may be understood to  describe one or more of the following factors:
       1. a third-person construct used by an observer to describe and explain given regularities
           observed of another;
       2. a mental representation within the observed subject that comes into play in an explicit,
           causal manner as indicated by the observed output; and
       3. certain regularities in the environment or stimulus field.
Given these distinctions, an ascription of rule-following (factor 1) would follow when the ostensibly rule-governed output (factor 2) corresponds in the appropriate way to the regularities characterizing the input (factor 3).
Rules have often figured in mentalistic explanations of behavior and have played an especially important role in the description and explanation of knowledge of language. Thus for example if a person rejects the sentence S1, "I read often the newspaper on Sunday" as ungrammatical, and accepts the sentence S2, "I often read the newspaper on Sunday," we might say that he or she knows the rule of English that holds that adverbs cannot separate verbs from their objects. The ascription (corresponding to factor 1 above) would be made on the basis of the subject's rejection of S1 in favor of S2 (corresponding to factor 2 above), and on the basis of S2's embodiment of the given regularity (corresponding to factor 3 above). In this case the rule embodied in S2 is attributed to the subject on the basis of the subject's responses to S1 and S2.
Implicit/Explicit Rules
It should be noted that when a rule is invoked as a device for explaining behavior, it is understood to be explicit, that is, actually embodied in an appropriate mental state or function. Pylyshyn has described this as requiring that the system that has an explicit rule R "has an encoded representation of R and uses it to generate instances of the behavioral regularity in question" (1991, p. 248). Put another way, a rule R is explicit to the extent that R plays an actual causal role in the mental states or behavioral performances that conform to the conditions specified by R. By contrast, implicit rules are, again by Pylyshyn's definition, rules that "merely describe constraints and regularities to which the system conforms" (1991, p. 233). There is no claim, in other words, that implicit rule R is somehow a cause of the regularity it describes. In short, explicit rules cause behavior by virtue of their being actively represented, while implicit rules simply describe certain conditions met by an entity.
A further refinement can be introduced into the notion of an explicit rule. A rule R can be distinguished from the algorithms, procedures, or operations that actually implement the functions or conditions specified by R. Accordingly, R can be thought of as an abstract set of intensional (or perhaps other) specifications delineating certain output conditions that unknown or unspecified internal mechanisms must meet (c.f. 1980: 197). The point is that R, which specifies functions and conditions to be met by behaviors and/or other outputs, may be distinguished from the representational structures that would encode R.
Thus what we are committed to when we explain a given regularity as an example of rule-following is that the rule R is explicitly represented "in" the person, that R plays a causal role in the output observed, and that the regularity takes the form it does by virtue of the specific representational content ascribed to R. We are not committed to saying how R is implemented.
There is a normative dimension to rules as well in that the conditions specified by the rule tell us, in effect, what we ought to do in a given situation. This normative dimension carries important temporal implications, since a rule specifying the conditions I ought to meet in a given situation will be as valid in the future as it is in the present or was in the past. This temporal implication requires that the rule be infinitely applicable. For this reason rules are usually thought of as intensional, since an extensional rule would have to be infinite in order to specify all future applications. The mind, by contrast, is finite, and so we would expect rules to be intensional, thus offering potentially infinite application through finite means. In light of the normative requirement, then, we can think of a rule as a finite object specifying conditions to be met in a potentially infinite number of cases.
Objections to rules-based explanations have been raised on the basis of the latter's indeterminacy. Stated in weak form, the indeterminacy objection holds that independent confirmation that a rule as formulated is in fact playing the causal role attributed to it is difficult to come by. If R and the very different R1 predict the same results, on what basis can R be credited as playing the causal role required of it? (A stronger form of this objection can be found in Kripke's (1982) interpretation of Wittgenstein's comments on rule ascription (1958, #201 et passim). Kripke claims that because the same behavior can be equally well accounted for with either rule R or rule R1 , and because there is no fact about a person that would settle the case as to whether he or she is in fact following R rather than R1 , we cannot justify the assertion that the person is following the rule we might otherwise wish to ascribe to him or her. While the following response does address the general issue Kripke raises, a rebuttal of Kripke's specific objections are outside the scope of this consideration.)
Consider again the example of a language rule given above. The sentence was explained as being produced by the rule -- call it R -- that in English, adverbs cannot separate verbs from their objects. As it happens, Chomsky's explanation of the same sentence invokes a different rule -- call it R1  --- that the case assignment parameter in English takes the value of strict adjacency (1986, p. 266). Both R and R1 predict the same sentence -- how does one determine which rule is in fact operating?
Chomsky's response is that we simply choose the rule described by the best available theory, and assume that it is playing the required role. Chomsky's argument is that the indeterminacy objection is not peculiar to mentalist explanations, but rather is an example of a general problem in science, that is, the underdetermination of theory by the evidence (1980, p. 258 n. 26; 1986, p. 13 n. 5). Despite the fact that the evidence almost always underdetermines the explanatory theory chosen, we are justified in choosing a theory as the correct explanation if that theory provides the best explanation available (1986, p. 249). Thus if R1 provides the best explanation available for the evidence, we are justified in asserting that it is R1, and not R, that is playing an actual causal role in the production of the sentence.
Still, the appeal to the best available theory does not address the question of obtaining evidence independent of the theorist's attribution for justifying that attribution. One might take a different approach and argue that ascriptions of rule-following are multiply constrained by the three factors introduced above and that an ascription is justified when at least two of the three factors are in correspondence (Reber 1995, p. 120). A fourth factor may be added, and that is what it is possible for the ostensible rule-follower to know. In order to fill in a value for this variable, we would have to know something of the facts bearing on how a person learns a rule. This is easily seen in cases of explicit learning, where the terms in which the rule's specified conditions are couched are made explicitly available to the learner, who presumably will internalize the rule in those terms. In cases of implicit learning, where the learner induces the rule without explicit direction, the situation is perhaps more ambiguous, and here we may have to appeal to the concepts or theories the learner brings to the task.
The upshot is that the best available theory would be constrained by what it is possible for the rule-follower to follow, as indicated not only by what is available in the stimulus field for him or her to internalize, but perhaps also by the theoretical and conceptual repertoire he or she can draw upon. Fixing the correct rule may thus entail matching up the observer's ascribed rule with the subject's account of the rule he or she is following. But a complication arises here in that a person may not be able to describe the rule that he or she apparently is following; as has often been noted, first-person evidence is not always reliable.
Perhaps the best, albeit tentative, solution is to hold that the fourth factor is the weakest, and that it properly comes into play only to discount third-person rule ascriptions when the preponderance of other evidence does not favor the third-person ascription over the account the subject may give of his or her own performance, and if the third-person ascription involves concepts that the subject does not have, but for which he or she has (and invokes) other, functionally equivalent concepts.
It would seem then that as Chomsky has observed, ascriptions of rule-following -- like any other psychological or indeed scientific theory -- are inherently underdetermined by the evidence. But this isn't the same as saying that we cannot distinguish more from less plausible rule-attributing hypotheses, and when the appropriate constraints are borne in mind, such explanations carry considerable predictive and explanatory power.
Daniel Barbiero