Rethinking Logical Reasoning Skills from a Strategy Perspective
Description
Rethinking Logical Reasoning Skills from a Strategy Perspective
Informations
| Publié par | ufusoged |
| Nombre de lectures | 101 |
| Langue | Français |
Extrait
Rethinking Logical Reasoning Skills from a Strategy Perspective
Bradley J. Morris*
Grand Valley State University and LRDC, University of Pittsburgh, USA
Christian D. Schunn
LRDC, University of Pittsburgh, USA
Running Head: Logical Reasoning Skills
_______________________________
* Correspondence to: Department of Psychology, Grand Valley State University, 2117 AuSable Hall, One Campus Drive, Allendale, MI 49401, USA. E-mail: morrisb@gvsu.edu, Fax: 1-616-331-2480.
Morris & Schunn
Logical Reasoning Skills 2
Rethinking Logical Reasoning Skills from a Strategy Perspective
Overview
The study of logical reasoning has typically proceeded as follows: Researchers (1) discover a response pattern that is either unexplained or provides evidence against an established theory, (2) create a model that explains this response pattern, then (3) expand this model to include a larger range of situations. Researchers tend to investigate a specific type of reasoning (e.g., conditional implication) using a particular variant of an experimental task (e.g., the Wason selection task). The experiments uncover a specific reasoning pattern, for example, that people tend to select options that match the terms in the premises, rather than derive valid responses (Evans, 1972). Once a reasonable explanation is provided for this, researchers typically attempt to expand it to encompass related phenomena, such as the role of ‘bias’ in other situations like weather forecasting (Evans, 1989). Eventually, this explanation may be used to account for all performance on an entire class of reasoning phenomena (e.g. deduction) regardless of task, experience, or age. We term this a unified theory.
Some unified theory theorists have suggested thatall logical reasoning can be characterized by a single theory, such as one that is rule-based (which involves the application of transformation rules that draw valid conclusions once fired; Rips, 1994). Other theorists believe that all logical reasoning can be described as model-based (creating veridical representations of premises, and searching them for possible conclusions; Johnson-Laird, 1999). Others still have suggested yet additional approaches (e.g., matching rules, pragmatic schemas) that may unify all aspects of performance. It seems possible, however, given the range of problem types, task demands, and experience and cognitive resources of reasoners, that there may be more than one way for solving an entire class of reasoning problem.
Morris & Schunn
Logical Reasoning Skills 3
Consider the case of deduction. This involves a wide variety of tasks, from simple statement evaluation (e.g., “Is my cat black?”) to more complex tasks such as evaluating predicate syllogisms (e.g., Some A are not B, Some B are C, therefore Some A are not C; TRUE or FALSE) (Roberts, 2000; Johnson-Laird, 1999). There is no evidence that deduction occupies a particular region of the brain (Goel, Buchel, Frith, & Dolan, 2000; Osherson, Perani, Cappa, Schnur, Grassi, & Fazio, 1998). This suggests that deduction is not a special process separate from the rest of cognition, and hence it is not likely to be unified across tasks or situations. Likewise, there is no behavioral evidence that deduction is a coherent distinct process (Johnson-Laird, 1999). Moreover, cognitive psychology has identified a variety of general processes (e.g., analogy, retrieval, guessing) that could, in theory, be used. Thus, it should not be controversial to suggest that several types of process might be used to solve reasoning problems in at least some situations.
In contrast to unified theories, we propose an alternative, in which many possible strategies may be used to solve a deductive problem, rather than always the same single type of reasoning process. Thus, this is a new framework for explaining reasoning performance, incorporating simplified versions of existing theories as possible strategies (see also Roberts, 2000). We list a variety of such strategies that seem likely to be used in at least some situations. It is not crucial to the argument that all of these are actually used. However, we will propose conditions under which various strategies are particularly likely to manifest themselves, thereby developing a framework through which these can be distinguished theoretically and empirically.
It should be noted that recent research from mental models theorists (Van der Henst, Yang, & Johnson-Laird, 2002) suggests that there are individual differences in the application of mental models, for example when solving syllogisms. Although this work suggests that reasoners use various approaches (classified as strategies), all of these are derived from the same inferential mechanism: mental models. While we agree that we should investigate individual differences in approaches to reasoning, we
Morris & Schunn
Logical Reasoning Skills 4
suggest not only that there are differences in how people apply the same inferential mechanism, but also that several different mechanisms are used.
Strategy Use in Logical Reasoning
What does it mean, as a cognitive researcher, to think in terms of strategies? A glance at the literature suggests that unified theories have difficulty accounting for differences in performance, both between individuals, and across tasks/situations (for a review see Rips, 1994; Johnson-Laird, 1999). We suggest that these differences are due to the selection of different strategies, and that this is a function of (1) the history of success with each strategy, and (2) the match between the processing demands of the strategy and the task demands. Together, these form thesituational niche.
As stated earlier, unified theories posit a single account for the range of human performance, although there are disagreements as to which single theory is correct. We suggest a strategy selection theory to explain the same phenomena, proposing a series of specified strategies, each relegated to explaining a subset of the total range of human deductive performance. This is closely related to other models that focus on individual differences (Roberts, 2000, 1993). For example, Roberts (2000) suggests that deductive performance can be better accounted for by three strategies (spatial, verbal, task-specific) than any single theory (e.g., mental models; Johnson-Laird, 1999).
What do we gain from thislogical strategy model? It allows for a wide range of findings -- patterns of variability across problems, tasks, individuals, and different points of development - to move from theoretical embarrassment to core, theoretically -relevant phenomena, that not only can be explained, but also are crucial to understanding the cognition of logical reasoning. It also allows a variety of established theories to be incorporated into a single framework, in which all form strategies that are possible explanations of behavior, differing only in the extent to which each particular strategy has been used in similar situations, and their matches to current task demands.
Morris & Schunn
Logical Reasoning Skills 5
The match between a particular strategy and its situational niche may not be rational, but may help to explain individual and situational differences. For example, it is well established that familiar content tends to improve performance on the Wason selection task (Wason & Johnson-Laird, 1972). Hundreds of experiments have been used to investigate this phenomenon, and these have led to a variety of explanations (e.g., pragmatic reasoning schemas). These differ widely in their range of applicability: Some are specific to a particular set of materials, while others seek to explain a broader range of behavior. What has rarely been investigated is the influence of the situational niche on performance, or, more specifically how is thetask itself contributing to the response pattern? For example, take two contrasting theories: in one, specific knowledge is required to solve a problem, and in the other, abstract rules (excluding the influence of knowledge) are needed. Problem A is given in which a substantial amount of relevant content knowledge is provided. In this case, we would expect the knowledge-based strategies to be best suited. If however, Problem B were given in which no background information is supplied, then we would predict that a different solution strategy is more likely to be used. Hence the logical strategy model permits flexibility in explanation by allowing for an individual to display a range of possible solution strategies.
The logical strategy model is in stark contrast to unified theories, in which explanations of processing logical statements are confined to one type of strategy. A possible criticism at this point is that a unified theory is more parsimonious: Why suggest that individuals possess a collection of competing strategies when a single type would suffice? We provide two responses.
First, current unified theories have been unable to account for a range of performance without many ad hoc additions. For example, mental logic theory posits that logical inferences are derived by the application of a set of near-automatic conte-nt free inference rules (Rips, 1994; Braine & O’Brien, 1998). In order to explain the effect of familiar content, this theory has incorporated an additional step in the reasoning
Morris & Schunn
Logical Reasoning Skills 6
process, a “pragmatic filter”, which determines whether a statement is to be considered logical or conversational. In the former, logical inference rules are applied, while in the latter case, less formal conversational rules are applied. The result is that the theory postulates an approach to reasoning that undermines its own primary thesis. As another example, mental models theory suggests that logical inference is achieved by the creation and search of models of a problem’s premises (Johnson-Laird, Byrne, & Schaeken, 1992). This theory does not specify how models of ambiguous or metaphorical premises can be constructed without exceeding working memory capacity (Braine & O’Brien, 1998). Similar problems can be found with the universal application of all unified theories.
Second, the logical strategy model does not require a set of resources specific to logical reasoning, which is an ad hoc component of some theories. Instead, it assumes a variety of general-purpose cognitive mechanisms. Within this framework, a series of strategies can be derived, with minimal effort on the part of the cognitive system, as a result of experience with the environment. Let us return to the example given earlier. To account for reasoning in situations in which either statements are presented (1) with familiar content, or (2) without familiar content, our framework can account for empirical findings in terms of two strategies. The first situation does not trigger the use of formal rules. Instead, specific content is used to derive a plausible conclusion. In the second situation, inference rules are used because the most salient property of the problem is the relations between elements, not thecontent of the elements. The use of each strategy is specific to the situation.
In the sections that follow we will outline eight types of strategy, examining each on eight dimensions: general processing demands, task demands, influence of context, efficacy/solution time (accuracy and cost), possibility of transfer (i.e., will a solution be usable in a different context?), type of memory activated (e.g., declarative), representational form (e.g., propositional), and change in strategy as a function of experience. The results are also summarized in Table 1.
Morris & Schunn
Logical Reasoning Skills 7
These eight strategies do not reflect prescriptive norms, but represent the range that naïve or untrained subjects may use when they are given deduction tasks. Note that this is not yet an exhaustive list, and we are merely suggesting the most plausible core set. After describing the strategies, we will examine the influence of task demands on strategy selection and use. Space limitations preclude a description of the full range of possible applications. However, our model is reasonably articulated for the purposes of this paper.
1. Token-Based (Mental Models)
Overview. The token-based reasoning strategy has the following characteristics: (1) information is represented as tokens derived from natural language. These correspond to perceptual or verbal instantiations of possible states, and (2) reasoning is achieved not through the application of formal rules but by the creation, inspection, and manipulation of tokens (Johnson-Laird, 1983; Johnson-Laird, Byrne, & Schaeken, 1992). This strategy is similar to Roberts’ (2000) spatial strategy1.
Processing Demands. There are three steps in applying token-based processes: (1) propositional analysis refers to language processing, and is largely analogous to representing the surface structure of a statement, requiring sufficient verbal/spatial working memory to encode and parse language; (2)model generation refers to the creation of tokens derived from the propositional analysis, and any other relevant information in the existing knowledge base and the environment. This requires sufficient verbal/spatial working memory to create and hold tokens; (3)m odel use is the process of searching and evaluating the set of models created, and requires sufficient processing capacity to maintain these while searching for counterexamples, and evaluating truth-values. The primary limitation on processing is the working memory required to create and search models for a solution. One particular difficulty is that ambiguous premises may require multiple mental models, thus leading to a dramatic increase in the use of working memory capacity and processing time.
Morris & Schunn
Logical Reasoning Skills 8
The token-based strategy seems particularly useful in the solution of problems in which there are spatial relations because token-based representations can encode these more easily than can proposition-based ones (Johnson-Laird, 1983, 1999). For example, in the transitive problem “Bill is to the right of Fred, Fred is to the right of Sam, Is Sam to the right of Bill?” the relevant dimension is easily encoded as follows:
[Sam] [Fred] [Bill]
Summary. The token-based strategy is content/context dependent, in that the type of semantic information influences the tokens created. However, there should be consistency in the treatment of logical connectives based on their meaning (requiring the activation of procedural memory). There should be transfer between problem isomorphs, though success will vary by the degree of similar semantic content (and hence the activation of declarative elements in memory). This is an algorithmic strategy, in that under optimal conditions, processing should result in a valid/correct conclusion. Processing costs (defined as solution time) should be high because of the procedures involved in creating and searching models.
2. Verbal (Mental Logic)
Overview. Verbal theories explain logical reasoning as the result of content-free, logical transformation rules applied to linguistically derived mental structures (Rips, 1994; Braine & O’Brien, 1998).
Processing Demands. The core elements of verbal theories share basic characteristics. Input is represented and processed in a verbal form (e.g., predicate-argument structures; Braine & Rumain, 1981, 1983). Sufficient verbal working memory is required to hold formal elements and represent them. The action of transformation rules is content-free, and these are implemented as either conditio-n action pairs (Rips, 1994) or as inferential schemas (Braine & O’Brien, 1998). The output of a rule is either in the form of a conclusion, a statement that will be operated upon by additional rules, or a statement that does not trigger additional rules. Errors
Morris & Schunn
Logical Reasoning Skills 9
may be explained either by (1) a failure in the activation, or failure in the output of one (or several) rules or (2) the failure to apply an inferential rule, instead applying a pragmatic rule. As problem complexity increases, there will be an increase in the number of rules to fire, thus increasing the possibility of overall error, and hence problem difficulty.
The verbal strategy is most useful in solving abstract problems in which the focus is on relationships between elements (e.g., If A is tweeky, then B is zop). For example, the original version of the Wason selection task (Wason, 1961) is specified only by formal structure, not by content.
Summary. The verbal strategy is context-independent, algorithmic, and should transfer between isomorphic problem types. Processing costs should be low, because inference takes place via compiled rules that fire automatically as a result of a match to syntactic relationships. Thus the action of rules is dependent on the activation of procedural rather than declarative memory.
3. Knowledge-Based Heuristics
Overview. Heuristics are rules that do not utilize logically valid algorithms. Such a strategy need not generate a valid conclusion but may result in “logic-like” performance (Cheng & Holyoak, 1985; Cosmides, 1989). Knowledge-based heuristics are easily implemented processing rules that use content as the basis for deriving a conclusion. Unlike algorithmic procedures (e.g. a verbal strategy), these conclusions are not necessarily valid (often violating logical inference rules), yet are often pragmatically supported. An example is thepragmatic reasoning schema (Cheng & Holyoak, 1985) in which social (permission rules) and physical (causality) regularities form the basis of inference schemata.
Processing Demands. There are three steps in the use of knowledge-based heuristics: sentence parsing, detection of relations, and solution output. Sentence parsing refers to comprehension and utilises implicit and explicit information. The
Morris & Schunn
Logical Reasoning Skills 10
detection of relations occurs when the present content is similar to content for which there are available rules. For example, in permission relations, there are established rules (typically phrased as conditionals) that suggest appropriate responses. Activating content allows these rules to be accessed. Cues such as temporal sequence may suggest obligatory or causal relations between elements. For example, in the statement “Mow the lawn and I will give you five dollars” the condition is set in the first clause while the consequent is set in the second clause. Once the rules are accessed, they are applied to the specific situation of the content and a solution is produced. Previous knowledge of other exchanges (e.g., in which transactions are made on the basis of obligations) form the basis of these heuristics.
Summary. Use of a knowledge-based heuristic does not necessarily lead to a valid response. This is a context-dependent strategy that requires activation of declarative memory, through which conclusions are drawn. Thus there should be little transfer away from the domain of applicability. Processing cost should be low because little is required other than activating and applying appropriate rules.
4. Superficial Heuristics
Overview. Superficial heuristics are selective processing strategies in which solutions are derived from surface details, such as terms or common elements, rather than on content (as in knowledge-based heuristics). Two well-known examples lead to matching biases (Evans, 1989) and atmosphere effects (Woodworth & Sells, 1935).
Processing Demands. Superficial heuristics lead to selective processing, but differ from all previous strategies in that the focus is on the presence of surface elements; no specific content is accessed. They operates as follows: (1) surface structure is encoded, (2) key elements are identified, and (3) rules applied to them. For example, in the Wason selection task, subjects prefer to choose cards named in the rules rather than cards that are not named (Evans, 1972). Given “If there is an odd number on one side, then there is a vowel on the other side” the subject may focus on “odd
Morris & Schunn
Logical Reasoning Skills 11
number” and “vowel” as key elements. Then, when searching possible solutions, the subject will attend to those states that contain the key elements. Hence, a card with an odd number and a card with a vowel are selected because these match the elements in the rule. A similar processing model applies to the heuristics that lead to atmosphere effects.
Summary. Superficial heuristics are context-independent strategies that do not necessarily produce valid conclusions. Their use depends upon the activation of procedural memory. We should see transfer between tasks, but with low solution accuracy, due to focusing on surface elements. Processing cost should be low because little is required beyond matching surface content, thus solution times should be fast.
5. Analogy
Overview. Analogical reasoning utilises knowledge of existing situations to derive solutions to novel problems (Holyoak & Thagard, 1989). This is typically distinguished as a separate process from deduction, however we suggest that analogical mapping may provide resources for solving such problems. Analogies enable solution by mapping meaningful links between one already in memory (source) and the new problem (target). As an illustration, we recount the results for a 10-year-old girl enrolled in a gifted program. On a version of the Wason task framed withabstract materials (e.g., thogs, merds), she produced the correct responses, which is surprising given that few adults do so. When we asked her to explain her reasoning, she said that the question was like a chemistry experiment she had recently completed in her class. She outlined the procedure -- including allusions to confirming and disconfirming evidence -- and explained how each ‘card’ in the Wason task was like one of these options. She proceeded to explain the need for both correct options.
Processing Demands. Analogical mapping takes place in three steps (1) accessing a suitable source from memory, or current perception, that is meaningfully related to the new problem (target), (2) adapt this analog to the demands of the target,
© 2010-2024 YouScribe