Deduction and Induction: Reasoning through Mental Models

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1 Mind & Society, 1, 2000, Vol. 1, pp , Fondazione Rosselli, Rosenberg & Sellier Deduction and Induction: Reasoning through Mental Models Bruno G. Bara a,, Monica Bucciarelli b "Centro di Seienza Cognitiva, Universitgl di Torino, via Lagrange 3, Torino, bara@psych.unito.it h Centro di Scienza Cognitiva, Universitgt di Torino, via Lagrange 3, Torino, . monica@psych.unito.it (Received July 1998, accepted April 1999) Abstract In this paper we deal with two types of reasoning: induction and deduction. First, we present a unified computational model of deductive reasoning through models, where deduction occurs in five phases: Construction, Integration, Conclusion, Falsification, and Response. Second, we make an attempt to analyze induction through the same phases. Our aim is an explorative evaluation of the mental processes possibly shared by deductive and inductive reasoning. Keywords deduction," induction; mental models Induction and deduction can be distinguished in terms of semantic information, a concept that depends on the proportion of possible states of affairs that an assertion rules out as false (see Bar-Hillel & Carnap, 1964; Johnson-Laird, 1983). Deduction is a systematic process whose goal is to draw a valid consequence from a series of premises. It requires one to consider the premises as true and to infer what conclusion, if any, follows. By definition, a valid deduction yields a conclusion that must be true given that the premises are true. Deduction does not increase semantic information; that is, the conclusion of a valid deduction rules out the same possibilities as the premises or else fewer possibilities. Here is an example. Your starting point is the premises: If Ann is at the party, then is at the party. Ann is at the party. And you infer: is at the party. The conclusion " is at the party" rules out both the possibility that is not at the party but Ann is there, and the possibility that neither nor Ann are * Corresponding author 95

2 Mind & Society, 1, 2000, Vol. 1 at the party. The premises rule out the additional possibility that is at the party but Ann is not there. Induction is a thought process that aims to draw a plausible conclusion from particular observations or premises. It increases semantic information; that is, the conclusion goes beyond the premises by excluding at least some additional possibility over and above the circumstances that the premises rule out. Here is an example. Your starting point is the premises: Sally was late; she was not admitted to the concert hall. Ben was late; he was not admitted to the concert hall. and you infer the conclusion: If you arrive late at the concert hall you are not admitted. The premises rule out the possibility that Sally and Ben were admitted to the concert hall; the conclusion rules out the additional possibility that somebody who arrives late at the concert hall is admitted. Thus, the inductive conclusion does increase the semantic information, although it is not necessarily true. Indeed, inductions are deductively closed: there is not sufficient information to determine whether the conclusion is valid. Mental Model Theory (MMT: Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991) offers an explanatory framework that can accommodate both induction and deduction. The framework offers a unified account of reasoning leading to necessary conclusions and reasoning leading to conclusions about possibilities. A conclusion is necessary - it must be true - if it holds in all the models of the premises; and a conclusion is possible - it may be true - if it holds in at least one model of the premises (Bell & Johnson-Laird, 1998) ~. MMT claims that reasoning consists in constructing and manipulating mental models. A model is an analogical representation, whose structure corresponds to the structure of what the model represents. Although it can be experienced as a visual image, what matters is its structure: entities are represented by tokens, their properties are represented by the properties of the tokens, and the relations between them are represented by the relations between the tokens. The theory rejects the idea that deduction depends on formal rules of inference (see Braine, 1990 and 1998; Rips, 1994). The two principal predictions of MMT which have been corroborated throughout the domain of deductive reasoning are: the major cause of difficulty in making deductions is the necessity of considering models of alternative possibili- Most of the time inferences concerning possibilities are inductions. However, many inferences like "possibly p", "probably p", "the probability of p is 0.5" are deductive in that they are based on background knowledge which is taken into account as an additional set of premises. An example is inferring the chance probability of an observation through a Binomial test on the frequency of some event (Johnson-Laird, Legrenzi, Girotto, Sonino, Legrenzi & Caverni, 1999). 96

3 Bara & Bucciarelli - Deduction and Induction: Reasoning through Mental Models ties; the most likely errors are conclusions that overlook such alternatives (see Johnson-Laird & Byrne, 1991). Bara, Bucciarelli & Lombardo (1999) have devised UNICORE (UNI fled computational REasoner), a unified computational model of deductive reasoning by models which offers an account of syllogistic, propositional and relational reasoning. The computer model follows the tenets of MMT and it reunifies different sorts of deductive reasoning into a single set of basic procedures. Such a mechanism constitutes the core of the deductive competence, which is performed by manipulating the model representations of deductive premises, i.e. syllogistic, propositional, or relational premises. Now, we shall briefly illustrate the five phases of deductive reasoning according to the model; then, we shall attempt an analysis of induction using the same phases. UNICORE distinguishes five phases of deduction: Construction, Integration, Conclusion, Falsification and Response (Figure 1); they constitute a more analytic version of the stages of comprehension, description and validation, as proposed by Johnson-Laird & Byrne ( 1991). F INTEGRATION Q I CONSTRUCTION I CONCLUSION ~[ FA LSIFICA TION Millstone RESPONSE I 0 Figure 1. The five phases of deduction: Construction, Integration, Conclusion, Falsification and Response. The integration procedures, and part of the falsification procedures are task independent; they form a core system that Bara et al. (1999) refer to as the Millstone. 97

4 Mind & Society, 1, 2000, Vol. 1 Such task- independent procedures are common to syllogistic, propositional and relational reasoning. 1. Construction phase. The starting points of the reasoning process are observations of the world and/or an understanding of premises, which lead to the construction of mental models. Let us proceed with an example. A conditional premise, such as "If Ann is at the party, then is at the party", calls for a model in which Ann is at the party (and thus is at the party), but the assertion is consistent with a state of affairs in which Ann is not at the party. People do not initially make the nature of this alternative explicit, but merely represent its possibility in a second model that has no explicit content: Ann where the three dots denote a model with no explicit content. This model allows for a subsequent explicit content (see below). Ann and on the same line represent the fact that they occur together; thus, each line corresponds to a model. 2. Integration phase. In this phase all the models of the premises are integrated into a single mental model (integrated model) by overlapping their identical tokens. For instance, if we consider the model of the premise "If Ann is at the party, then is at the party" (see above) together with the model built from the premise "Ann is at the party", the integration of the two results in the following model: Ann The model of the second premise is accommodated within the set of models by eliminating the second model, because "Ann" occurs in the first model. Thus, Integration is accomplished by merging the models of the premises to yield a new model whose kernel is represented by one token (Ann) generated through the match of two tokens, one per model (see Figure 2). Match implements the Integration phase: it uses the mental models provided by the Interpreter as input, and tries to return an integrated model, which is then passed to Conclusion. 3. Conclusion phase. In this phase reasoners take into account the specific deductive task at hand. They extract the relevant information from the model produced in the Integration phase, and formulate a putative conclusion. The type of conclusion can be different depending on the task: it can be an inference, a truthvalue judgment ("true" or "false"), or an action to be performed. Thus, to formulate a conclusion it is necessary to transform the requirements of the specific task into cues for extracting the relevant information from the integrated models. In our example, the requirement of the task is to make a propositional inference: the reasoner must extract the new information contained in the premise involving a 98

5 Bara & Bucciarelli - Deduction and Induction: Reasoning through Mental Models 99 connective, with respect to the situation described by the atomic proposition. The operation results in the conclusion: " is at the party". INTEGRATION l Interpreter CONSTRUCTION Search for alternatives FALSIF YATION ] CONCLUSION Extractor of ] results I Consistency & Equivalence Task independent: Millstone Task dependent RESPONSE Generator [ of responses + Figure 2. The procedures of the Millstone (Integration and Search-for-alternatives) are invariant through deductive domains. The procedures outside the Millstone (Construction, Conclusion, Consistency-&-Equivalence and Generator-of-responses) are task dependent. The Extractor-of-results implements the Conclusion phase. It takes as input an integrated model and produces as output a model which contains only the tokens and relations which represent a putative conclusion, given a task. 4. Falsification phase. In this phase, which MMT considers the core of human rationality, the reasoners attempt to falsify the putative conclusion obtained previously, by searching for alternative integrated models which are inconsistent with the conclusion. If the search fails, then the conclusion is valid; if the search is successful, the reasoner formulates a new conclusion which is consistent with all the models produced. When it is impossible to formulate a conclusion, the reasoner asserts: "No valid conclusion". Falsification consists of two procedures: the first one (Search-for-alternatives) searches for integrated models that are alternative to the first one produced in the Integration phase. The second procedure (Consistency-&-Equivalence) checks both the consistency of a conclusion with a model, and the equivalence of two models in 99

6 Mind & Society, 1, 2000, Vol. I the working memory. Search-for-alternatives is task-independent; the tests of Consistency-&-Equivalence are task-dependent. The test of Consistency discards a conclusion that is inconsistent with an integrated model and attempts to formulate a new conclusion that is consistent with all the integrated models; in case of failure, it returns "No valid conclusion". The test of Equivalence discards a model which is equivalent (with respect to the task) to one previously generated. In our example, the reasoners attempt to falsify the putative conclusion " is at the party". The initial model representation of the first premise: Ann is made fully explicit: Ann not-ann not-ann not-marl to find out whether the model of the categorical premise "Ann is at the party" can be accommodated in a different way in the model representation of the first premise. As the operation results in a failure (Ann is not represented in the other models), the conclusion " is at the party" cannot be falsified, and therefore it is valid. 5. Response phase. In this phase, the reasoners translate the conclusions from the internal model format into a communicative behavior. This is the dual phase of the Construction, where the Interpreter translates the premises into the model format. Operatively, the reasoner generates the (linguistic or motorial) response that expresses the conclusion, by taking into account the task. MMT claims that people are rational in principle, but fallible in practice. People are rational because they grasp the need to falsify a conclusion; a conclusion is valid only if there is no way in which it can be false given that the premises are true. People are fallible since the actual application of the Falsification procedure may fail. Consider the premise "If Ann is at the party, then is at the party", together with the categorical premise " is at the party". The integration of the models of the two premises produces the model: Ann which supports the conclusion "Ann is at the party". Falsification produces an alternative model of the premises: not-ann which supports the conclusion "Ann is not at the party". As none of the conclusions is consistent with the two possible integrated models of the premises, the 100

7 Bara & BucciareUi - Deduction and Induction: Reasoning through Mental Models correct answer is "No valid conclusion". Thus, in this example, either people exhaust the set of the possible integrated models of the premises in the example, check that no conclusion is true in all of them, and conclude "No valid conclusion", or they stop at one of the integrated models, and draw an erroneous conclusion. To sum up, the triggering of some procedures - those that Bara et al. (1999) define as domain-dependent - depends on the specific reasoning domain (syllogistic, relational or propositional), whereas the triggering of others - those defined as domain-independent - occurs when reasoning with any sort of deductive reasoning (Figure 2). The model allows fine-grained predictions on subjects' performances in reasoning deductively with syllogisms, relational and propositional problems. In particular, the program assumes that both the working memory capacity and the ability to falsify increase with age, and it reproduces the performances of subjects of different age by positing constraints at the two levels. Is it plausible to think about induction as a sort of thinking which shares some of the basic procedures with deduction? Which are the main differences between induction and deduction? We shall now outline them: our benchmark will be the different phases of the computational model just presented. Traditionally, in psychology and philosophy induction has been considered a process yielding plausible verbal generalizations or hypotheses, which is accomplished through a mental language analog to the predicate calculus (see Michalsky, 1983). MMT proposes instead that inductions consist in the elimination of possible states of affairs (Johnson-Laird, 1993). The resulting set of models can then be described by a parsimonious proposition. Further, MMT claims that the number of models representing the initial situations affects the process of determining which models to eliminate. Proper inductions produce descriptions; inductions that result in explanations are called abductions. Here, we are not concerned with such a distinction, but with the major distinction between specific and general inductions. Specific inductions are hardly distinguishable from the activity of interpreting the world. They are concerned with specific events and look for the causes or the reasons of the events themselves. Consider, for instance, the premise: The injured man was lying on the sidewalk. together with the inferred conclusion: The man had been run over by a car. The sorts of plausible conclusions that a reasoner can draw can be reproduced by a computational model where the models of the premises are manipulated according to some dimensions of the model representation (Geminiani, Carassa & Bara, 1996). 101

8 Mind & Society, 1, 2000, Vol. 1 General induction leads to a general conclusion. Consider the following series of initial observations: Sally was late; she was not admitted to the concert hall. Ben was late; he was not admitted to the concert hall. together with the conclusion: If you arrive late at the concert hall you are not admitted. Now, let us analyze the inductive process in the light of the computational model advanced by Bara et al. (1999). 1. Construction phase. The system's goals influence every thought process: therefore, they form part of the reasoning process from the Construction phase onwards. In general, an understanding of the premises leads to the construction of mental models. In deductive reasoning models' construction relies on the knowledge of the meaning of the deductive terms, and world knowledge must be carefully kept apart from the reasoning process. On the contrary, when the goal is to explain, describe or predict an event in the world - as in inductive reasoning - the premises are usually generated by perception, or by the activation of relevant knowledge. What guides perception or knowledge activation depends upon the system's needs, which seldom are so clear and defined as in deductive tasks. A major constraint in the construction phase of induction is the search for information in order to take a decision, whereas the construction phase in deduction involves just the information contained both explicitly and implicitly in the premises. In particular, the search for information is heavily involved in decisionmaking processes, where reasoners encounter the difficulty to consider a potential alternative, computing its consequences, and considering the alternatives' respective utilities (Shafir & Tversky, 1992). Thus, the tendency to focalize on the explicit information contained in the initial representation of a problem characterizes induction, as well as deduction. Legrenzi et al. (1993) show that, when the decision has to be taken in a context evoking the alternatives to the action involved in the decision, subjects also thought about potential alternatives. In addition to the system's goal, a key factor in knowledge activation is its availability. E.g. if you have a sick child, the availability of relevant knowledge about diagnosis, symptoms and treatment of diseases is crucial for adequately reasoning in that domain (see below). 2. Integration phase. The models of the premises are integrated into a single representation through the same operations involved in deductive reasoning (Match). However, induction requires a further operation, which might be called Add-information, in order to integrate the models of the premises with world knowledge. In fact, the goal of inductive inferences is to go beyond the information given in the premises. This task is accomplished by inserting the models of the premises in a broader scenario (or model representation) built by recovering specific 102

9 Bara & Bucciarelli - Deduction and Induction: Reasoning through Mental Models knowledge from long-term memory. Such a scenario provides the premises with a plausible context. Add-information is a task-dependent operation in that the sort of knowledge which is recovered from long-term memory is determined by the content of the task at hand. Which is the information in long-term memory that is relevant to the task at hand? We could define as relevant the information which is the most available to the reasoner. Indeed, the concept of knowledge availability is well accepted in the literature concerning probabilistic judgments (see Tversky & Kahneman, 1973). However, we introduce an operative definition of the concept and we state that relevance, as well as availability, can be explained in terms of models' construction and manipulation. We claim that a piece of information is relevant if it provides - along with the premises - a scenario (model representation) familiar to the reasoner. For instance, in the example concerning the injured man On the sidewalk, readers might find their belief that a frequent cause of accidents in town are cars relevant because it provides - along with the premise - a familiar scenario where a man can be injured because a car runs over him. Thus, subjective knowledge heavily enters the inferential process. 3. Conclusion phase. In this phase reasoners take account of the specific inductive task at hand to extract the relevant information from the model produced in the Integration phase. As we said above, in deductive reasoning the goal can be drawing an inference, making a judgment or determining whether or not to perform an action. Induction aims at going beyond the premises to reach a plausible conclusion. A specific goal can be to produce generalized linguistic expressions (as in the example of the concert hall), the assertion of new properties about some existent individuals (as in the example of the injured man), or the assertion of new relations between.some existent tokens (for instance, when you infer that the elder man near the bride in a church is her father). 4. Falsification phase. Falsification is accomplished by two procedures, viz. Search-for-alternatives and Consistency-&-Equivalence, which are both taskdependent in induction. Indeed, the search for alternative models through the recovery of world knowledge is guided by the content of the task. Apart from the role played by world knowledge, the main difference between deduction and induction is that the former aims at reaching a conclusion that necessarily follows from the premises, while in inductive tasks a conclusion is never necessary, but only possible. The point is to find the most plausible conclusion, to be chosen among the possible ones. Thus, the first procedure searches for scenarios providing a context for the premises that is alternative to the one previously buir. The second procedure checks the consistency of a conclusion with a model; and it accepts as a plausible alternative conclusion a conclusion which is inconsistent with a previously obtained integrated model. Equivalence discards a model which is equivalent (with respect to the task) to one previously generated. 103

10 Mind & Society, 1, 2000, Vol. 1 A model plausibility is correlated with the availability of knowledge. Thus, the first conclusion that occurs to the mind is the one with the highest probability of being verified. However, plausibility can never become validity in model theory sense, i.e. always true for any model which can be constructed from the given premises. Because induction needs to add relevant knowledge to a model, it is in principle impossible to be sure that a specific conclusion may hold for any added piece of relevant knowledge. Johnson-Laird & Anderson (1989) made an experiment where the participants where given pairs of premises such as: The old man was bitten by a poisonous snake. There was no known antidote. Then, they were invited to consider what happened. Every participant replied that the old man died. However, when the experimenter said that the conclusion was possible, but not in fact true, they were able to envisage alternative models in which the old man survived. A main finding of the experiment was that the participants tended to generate ideas in approximately the same order as one another. This provides evidence of the fact that relevant knowledge is congruent with the culture. We expect that the first integrated model produced by reasoners is experienced by them as the most plausible. This fact can be explained in that reasoners, when making sense of the world, have a good capacity to take into account relevant knowledge to produce highly probable predictions. Thus, what reasoners find most plausible is frequently the case. The degree of plausibility required in order to consider a possible conclusion valid, depends upon the task's demands. Suppose your goal is only to up-date your knowledge of the environment: you may be ready to consider highly probable, and most plausible, the inference that if you perceive confusion, disorder and noise, then the kids are at home. But exactly the same evidence would be considered insufficient if your goal is to punish the kids, in case they are at home against your will: probably a direct check would make you feel more comfortable about the deserved punishment. And again, if you were asked to swear in court that the kids were at home, the degree of confidence of the same possible conclusion, based on indirect evidence, would fall below acceptability. The moral of the story is that in inductive tasks possible conclusions are generated and valued upon a plausibility scale, which in turn may change in accordance with the constraints set up by the system's goals. Now, let us work out the previous example to show the reasoning steps involved in dealing with the inductive argument. Consider, for instance, the premise: The injured man was lying on the sidewalk. and the conclusion: The man had been run over by a ear. 104

11 Bara & Bucciarelli - Deduction and Induction: Reasoning through Mental Models In the Construction phase reasoners construct a model of the premise "The injured man was lying on the sidewalk", where injured is the property of the man: injured In the Integration phase the model of the premise is integrated with information recovered from memory, according to which the accident is caused by a car: car injured Recovery of information from memory is affected by the beliefs of the reasoners: if reasoners are given the premises "The injured man was lying on the ground. It was dark in the savana" a more plausible scenario could have been one where an rhinoceros ran over him. In the Conclusion phase reasoners take into account the specific deductive task at hand, and formulate a plausible conclusion. In the example, the goal is to assert new properties about the man: the conclusion is represented by the model where the car causes the man's injuries. In the Falsification phase reasoners attempt to falsify the putative conclusion. This process is accomplished by looking for an alternative scenario where the premises are true. A plausible scenario could be one where the man has been mugged. In the Response phase the reasoners translate the conclusions from the internal model format into a communicative behavior that expresses the conclusion, for instance, the linguistic response: "The man has been mugged". To sum up, the unified computational model proposed by Bara et al. (1999) allows a detailed comparison to be made between inductive and deductive reasoning. In particular, depending on model function, Integration (Match) and part of Falsification (Search-for-alternatives) are common to deductive and inductive reasoning. However, in inductive reasoning Match and Search-for-alternatives operate along with a further operation which adds to the model of the premises the information recovered from task-relevant memory. The role of world knowledge and, consequently, the fact that an inductive conclusion is only a plausible conclusion, appears to be the main difference between deduction and induction. A crucial consequence is that Falsification is radically modified, in that all the integrated models generated are always plausible, and they only differ from one another in terms of a plausibility scale. The computational model would require a noteworthy extension to account for inductive inferences. In fact, although it is feasible to insert some constraints into the program which would allow inductive reasoning to be reproduced according to the system's goal, the simulation of world knowledge organization in long-term 105

12 Mind & Society, 1, 2000, Vol. 1 memory along with its recovery would be a noteworthy enterprise. Induction and deduction may share a set of basic procedures which are task independent, as MMT assumes. However, whereas the task-independent procedures constitute the core of human rationality in dealing with deductive tasks, in induction they are eclipsed by task-dependent procedures. Indeed, these procedures are concerned with the world knowledge that the reasoners consider relevant to the task at hand. Some recent studies on reasoning in brain-damaged subjects postulate a mechanism capable of decontextualized mental operations, and a different mechanism, the operation of which is context-bound and incapable of abstraction (see, e.g., Geminiani & Bucciarelli 1998; Savary, Whitaker & ovits 1992). Our assumptions on the mental operations involved in deduction and induction are consistent with such neuropsychological evidence: apart from a core set of basic procedures which are shared by the two sorts of reasoning, deduction invokes decontextualized operations, and induction invokes context bound operations which are concerned with world knowledge and, therefore, with the specific culture of the reasoner. As a final speculation we observe that knowledge of the requirements of the specific reasoning task itself, i.e. deductive or inductive, may depend on the culture. Traditional subjects from Middle Asia, when invited to solve syllogisms, provided an empirical answer, i.e. answers that appeal to the reasoner's experience and knowledge of relevant reality (Luria, 1976). Analogous cross-cultural investigations on syllogisms have found divergent styles of problem solutions. They suggest a tuning of the reasoning processes according to the context in which they occur. References Bara B., Bucciarelli M., Lombardo, V. (1999), Model Theory of Deduction: A unified computational approach, Cognitive Science, in press. Bar-Hillel, Y. and Camap, R. (1964). An outline of a theory of semantic information, in Y. Bar-Hillel (Ed.) Language and information (Reading, Addison-Wesley). Bell, V.A. & Johnson-Laird, P.N. (1998) A model theory of modal reasoning, Cognitive Science, in press. Braine, M. (1990) The "natural logic" approach to reasoning, in W.F. Overton (Ed.), Reasoning, Necessity, and Logic (Hove, Lawrence Erlbaum Associates), pp Braine, M. (1998) Steps towards a mental predicate logic, in M.D.S. Braine & D.P. O'Brien (Eds.), Mental Logic (Mahwah, Erlbaum). Geminiani, G.C. & Bucciarelli, M. (1998) Deductive reasoning in right-brain damaged, Proceedings of the XX Conference of the Cognitive Science Society (Madison, Morton Ann Gemsbacher & Sharon J. Derry). Geminiani, G.C., Carassa, A., Bara, B. G., (1996) Causality by contact, in A. Gamham. & J. Oakhill (Eds.) Mental Models in Cognitive Science. Essays in Honour of Phil Johnson-Laird (Hove, Lawrence Erlbaum Associates), pp Johnson-Laird, P.N. (1983) Mental models (Cambridge, Cambridge University Press). Johnson-Laird, P.N. (1993) Human and machine thinking (Hillsdale, Erlbaum). Johnson-Laird, P.N. & Anderson, T. (1989) Common-sense inference, Mimeo (Princeton University). Johnson-Laird, P.N. & Byme, R Deduction (Hillsdale, Lawrence Erlbaum Associates). Johnson-Laird, P.N., Legrenzi, P., Girotto, V., Sonino Legrenzi, M. & Cavemi, J.P. (1999) Naive probability: A mental model theory of extensional reasoning. Psychological Review, in press. 106

13 Bara & Bucciarelli - Deduction and Induction: Reasoning through Mental Models Legrenzi, P., Girotto, V. & Johnson-Laird, P.N. (1993) Focussing in reasoning and decision making. Cognition, 49, pp Luria, A.R. (1976) Cognitive development, its cultural and social foundations (Cambridge, Harvard Univ. Press). Michalsky, R.S. (1983) A theory and methodology of inductive learning, in R.S. Michalsky, J.R. Carbonell & T.M. Mitchell (Eds.), Machine learning." An artificial intelligence approach (Los Altos, Morgan Kaufmann). Rips, L.J. (1994) The psychology of proof" Deductive reasoning in human thinking (Cambridge, MIT Press). Savary, F., Whitaker, H., ovits, H. (1992) Count~rfactual reasoning deficits in right brain damage patients, Mimeo (Department of Psychology, University of Quebec at Montreal). Shafir, E. & Tversky, A. (1992) Thinking through uncertainty: Nonconsequential reasoning and choice, Cognitive Psychology, 24, pp Tversky, A. & Kahneman, D. (1973) Availability: A heuristic for judging frequency and probability. Cognitive Psychology, 5, pp Acknowledgements The article is a new version of a paper presented at the Workshop of the European Science Foundation entitled "Cognitive Theory of Social Action" held in Torino from 11 to 13 June 1998, and organized by the Rosselli Foundation as the first initiative of the scientific network of the European Science Foundation called "Human Reasoning and Decision Making". We would like to thank Vinod Goel and Philip Johnson-Laird, who read and criticized earlier versions of this paper. The research has been supported by an MPI 60% contract for