Abstractrule Theory

The evidence on conditional reasoning suggests that people are not wholly rational; they fail to make valid inferences and often make invalid inferences. Abstract-rule theories maintain that people are inherently rational, that they use a mental logic (although, as we shall see later, one could argue that this is a very narrow definition of rationality). According to this account, people only make invalid inferences because they misunderstand or misrepresent the reasoning task. After their initial misunderstanding the reasoning itself is logical (Henle, 1962).

Abstract-rule theories propose that humans reason using a set of very abstract, logic-like rules that can be applied to any domain of knowledge (e.g., rules like modus ponens). These abstract rules do not take the content of the premises into account (see e.g., Braine, 1990; Johnson-Laird, 1975; O'Brien, 1995; Osherson, 1975; Rips, 1983, 1990, 1994). From this theoretical perspective, people construct proofs to reach conclusions in a manner similar to logical proofs. For example, Rips (1983, p. 40) says that "the sequence of applied rules forms a mental proof or derivation of the conclusion from the premises, where these implicit proofs are analogous to the explicit proofs of elementary logic." Although there are several variants of this theoretical position, we concentrate on a representative case: Braine and O'Brien's abstract-rule theory.

Braine and O'Brien's abstract-rule theory

Braine and O'Brien's theory maintains that deductive reasoning is mediated by basic, abstract rules or schemata (see Chapter 9). People comprehend the premises of an argument and encode them into abstract rules from which they make inferences. The theory is summarised in Panel 16.1 (see also Braine, 1978, 1990; Braine & O'Brien, 1991; Braine, Reiser, & Rumain, 1984; Braine & Rumain, 1983; Lea et al, 1990; O'Brien, 1995; O'Brien, Braine, & Yang, 1994; Rumain, Connell, & Braine, 1983). In this view people are natural logicians who are slightly fallible at the edges. When reasoning directly, people always reason validly, except for extraneous influences from the comprehension of premises or the inherent limitations of working memory. In the following sections, we elaborate how the theory accounts for the different inferences made by people.

Valid and invalid inferences

Consider the abstract-rule account of how a conclusion is drawn for the following premises:

PANEL 16.1:


• Natural language premises are encoded by comprehension mechanisms, which are sensitive to conversational implications (e.g., Grice, 1975), into a mental representation of the premises in working memory.

• In direct reasoning, abstract-rule schemas an applied to these premises to derive conclusions. Core schemas encode fundamental reasoning rules (like modus ponens) and feeder schemas are auxiliary schemas that art applied to produce intermediate conclusions for core schemas. Incompatibility rules also examine the contents of working memory for incompatible inferences, such as contradictions (e.g., inferring P and not-p).

• The application of these Schemata is controlled by a reasoning program (in essence, a production system, see Chapter 1).

• In indirect reasoning, problems that am beyond the bounds of "normal" reasoning problems are handled (e.g., the abstract selection task). People can learn other non-logical schemas that may be applied to solve such problems (like the domain-specific rules of other problem-solving systems), but they may result in bias-type responses.

• Even within direct reasoning, people can draw invalid conclusions or errors of three types: (a) comprehension errors, where the premises or conclusion art misconstrued in some fashion, (b) heuristic inadequacy errors, where a conclusion to a problem fails to be reached because the strategies far co-ordinating the application of the reasoning schemas am inadequate, (c) processing errors, resulting from lapses of attention or a failure to hold relevant information in working memory.

If I get hungry, then I will go for a walk, If P then Q,

If I go for a walk, I will feel much better, If Q then R,

I am hungry P

Most abstract-rule theories have a reasoning rule that corresponds to modus ponens; theorists assume that because people find this inference so easy, there must be an appropriate mental rule to deal with it. A conclusion to the example here can be derived by the repeated application of this modus ponens rule. First, the rule is applied to the first premise (If I get hungry then I will go for a walk) and third premise (I am hungry) to produce the intermediate conclusion of "I will go for a walk"; then the rule is applied again to the second premise "If I go for a walk, I will feel much bettef' and the intermediate conclusion "I will go for a walk" to produce the final conclusion "I will feel much better" (see Byrne, 1989b, for explicit tests of these chains of inferences). The rules are applied successively to the set of premises until a conclusion is derived.

The existence of a modus ponens rule accounts nicely for why people find this argument so easy, but why do they find the other valid form, modus tollens, so hard? In the abstract-rule theory, modus tollens is a harder inference to make because no single rule can be applied to it. Rather, a proof involving several different rules has to be formed to reach a conclusion. In general, the longer a derivation, the greater the likelihood that errors will occur or no conclusion will be reached.

In abstract-rule theories, people make the fallacious inferences, like the invalid denial of the antecedent and affirmation of the consequent inferences, as a result of comprehension errors. One account maintains that people make the conversational assumptions used in everyday life thus causing a re-interpretation of the premises (O'Brien, 1995). So, people still apply their logically valid rules but because the input to the rules is erroneous, the output is often erroneous too. Consider the detailed explanation for why people make the fallacious denial of the antecedent inference: Invalid: Denial of the antecedent

Rumain et al. (1983) maintained that the conditional premise of this argument, If P then Q, was reinterpreted as If not-P then not-Q. As Geis and Zwicky (1971) have pointed out, the statement "if you mow the lawn I will give you five dollars" invites the inference "If you don't mow the lawn, I won't give you five dollars". If one starts with this as the conditional premise then by the application of the modus ponens rule one reaches the conclusion not-Q. For example:

So, valid rules are still being applied, but to re-interpreted premises (note that this is not the only account of this effect, when one considers that the Geis & Zwicky sentence is deontic, namely a conditional promise). A similar explanation can be made for the affirmation of the consequent fallacy.

This switch in the interpretation of the premise is said to occur because of Grice's (1975) co-operative principle. This principle maintains that a speaker tells a hearer exactly what they think the other needs to know. For example, if a speaker says "If it is raining, then Alicia will get wet", the hearer will assume, in the context of the conversation, that rain is the only likely event that will lead to Alicia getting wet. The hearer assumes that no other alternative Ps will play a role. So, during comprehension people make a reasonable assumption that modifies the premises. Having made this comprehension error, reasoning continues normally through the application of the various reasoning rules (see O'Brien, 1995).


If it is raining, then Alicia gets wet It is not raining.


Therefore, Alicia does not get wet.

Therefore, not Q


If it is not raining, then Alicia does not get wet It is not raining.


Therefore, Alicia does not get wet.

Therefore, not Q

Context effects

The context effects reviewed earlier are also explained in terms of these conversational assumptions. Rumain et al. (1983) predicted that alternative antecedents undo these conversational assumptions resulting in the suppression of the invalid inferences. Braine et al. (1984) took these results as evidence that there could not be rules for invalid inferences of the denial of the antecedent and the affirmation of the consequent. However, this conclusion is upset by the other context effects showing the suppression of the valid inferences by the provision of additional antecedents (see Byrne, 1989a). If the same argument is applied to Byrne's results, then abstract-rule theorists would also have to conclude that there are no mental inference rules for the valid inferences. Politzer and Braine (1991) have therefore challenged these results; they argued that Byrne's materials led subjects to doubt the truth of one of the premises because one premise was inconsistent with the other premises (see also George, 1995; O'Brien, 1993). If subjects doubted the premises then Byrne's manipulation was radically different from Rumain et al.'s. However, in reply, Byrne (1991) has shown that the conclusions drawn by subjects in her experiments were not those predicted by Politizer and Braine's account. Furthermore, Byrne et al. (1999) have explicitly tested this proposal and found no evidence that people doubt the truth of the premises (or, indeed, that they are viewed as inconsistent).

The abstract-rule theory does not do much better on the other aspects of these context effects. On the effects of uncertainty, Stevenson and Over (1995) point out that no existing abstract-rule theory (and indeed, mental model theory) can account for these effects and would have to be supplemented with a probability theory (see later section on probabilistic theory) in order to do so. This would lead to a rather baroque and psychologically implausible model. Similarly, the effects of causality (Cummins et al., 1991) and saliency (Chan & Chua, 1994) do not sit easy with the theory, as they are background knowledge effects that suggest a role for domain-specific schemata. Of course, such schemata could be entertained in Braine and O'Brien's indirect reasoning route, but this has the uncomfortable result of placing these tasks outside of reasoning proper (which would not be a generally agreed assessment).

The selection task

Braine and O'Brien also see abstract versions of the selection task as falling outside the operation of their direct reasoning routine; that is, they do not view it as a reasoning problem proper (O'Brien, 1995). As such, the theory predicts that people should not reveal much rational competence at the task, which is essentially what one finds in their behaviour. However, they do predict that people should be better on deontic versions of the task (e.g., thematic materials) because these versions have a simpler logical structure. In deontic versions of the task people are asked to judge possible violations in a regulation whose truth status is not in question, whereas in non-deontic versions they are asked for "judgements of cases that could potentially falsify descriptive statements whose truth status is uncertain" (Manktelow & Over, 1991, 1993, p. 184).

Other evidence supporting the theory's predictions

There is considerable evidence for the proposals of abstract-rule theory (see also Braine, 1990; Lea et al., 1990). For example, Braine et al. (1984) examined several predictions from the theory in a series of experiments. In one experiment, subjects were given a simple reasoning task about the presence or absence of letters on an imaginary black-board (from Osherson, 1975). So, on being given a problem such as:

If there is a T, there is an L, There is a T ? There is an L ?

subjects were asked to evaluate whether theprovided conclusion was true. These problemswere designed to be solved in a single step byone of the 16 rules proposed by the theory. Theresults showed that reasoning on these problemswas essentially error-free. Difficulty measures werederived from subjects' performance on these problems that were then used to predict behaviour onproblems that involved short chains of reasoning (on the assumption that the difficulty measuresfor single rules would be additive in more complex tasks). A

variety of measures were used todetermine problem difficulty, including subjectiveratings of difficulty, times taken to solve a problem and the number of errors made. Braine et al.found high correlations between the difficultymeasures of problems and the number of predicted inferences, from the repertoire of rules,required to solve the problems.

Evaluation of abstract-rule theories

The abstract-rule approach is very attractive in its promise to account for conditional reasoning with recourse to a limited set of reasoning rules. It also has the benefit of being consistent with models developed in problem-solving research, suggesting a unified account of problem solving and reasoning. For example, the Braine and O'Brien model can be viewed as a production system model that uses very abstract operators, rather than domain-specific ones (see also Rips, 1994).

The one main problem facing this approach is that abstract-rule theories achieve their elegance at the price of a considerable underspecification of the accompanying comprehension component. The core reasoning system is well specified and makes predictions about what inferences people will and will not make. However, some predictions are grounded in a comprehension component that is considerably less specified (e.g., predictions on invalid inferences). Although O'Brien (1995) has taken steps to specify further aspects of this component, more remains to be done. Hence, in general, its treatment of context effects leaves a lot to be desired. Furthermore, depending on one's perspective, it could be said that the theory's treatment of the selection task is weak, as it does so by excluding it from the set on explanatory phenomena to be considered.

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