1. Educational Uses of WordNet
This project, which is funded by the Advanced Research Projects Agency (ARPA/CISTO/CAETI), is being carried out in collaboration with Professor George A. Miller. My component of the project has been the development of Dialectica, a suite of computer programs written in Common Lisp and that include an interface with WordNet -- a large, psychologically realistic, semantic network -- which is used to investigate and to model everyday inferences. Thus, for example, an inference such as:
The opera help business.
Therefore, the arts serve commerce.
hinges on the semantic relations between words, and WordNet allows users to establish these relations.
2. Reasoning about necessary conclusions
The main aim of this project is to develop a unified account of how individuals reason. Its theoretical background is the theory of mental models developed in collaboration with Dr. Ruth Byrne (Dublin). According to this theory, logically-untrained individuals reason by using the meaning of assertions to construct mental models of the situations that they describe. A conclusion is logically necessary if it holds in all the models of the premises. A phenomenon predicted by this theory (and not by other current theories of reasoning) is that certain inferences should be illusory, i.e. they should have conclusions that are compelling, drawn by most people, but totally wrong. Dr. Fabien Savary, who is now a Web maestro, and I have confirmed their existence. Here is an example.
One of the following assertions is true about a particular hand of cards, and one of them is
false about the same hand of cards:
If there is a king in the hand, then there is an ace in the hand.
If there isn't a king in the hand, then there is an ace in the hand.
Subjects overwhelmingly infer that there is an ace in the hand. This phenomenon is predicted by the model theory, which postulates that reasoners normally represent only what is true, and not what is false, in their models of the premises. Notice, however, that if the first assertion is false then there is a king in the hand, but not an ace. And if the second assertion is false then there isn't a king in the hand and there isn't an ace in the hand. Hence, either way, there isn't an ace in the hand. Current theories of reasoning based on formal rules of inference, because they contain only valid rules of inference cannot explain such a systematic error. Dr. Yingrui Yang (Princeton) and I have recently shown that similar errors occur with quantified assertions, such as 'All the beads are red'.
3. A study of conditional reasoning
This study is being carried out in collaboration with Professor Juan Garcia Madruga (Madrid) and Profesor Carlos Santamaria (Tenerife). It shows that the transitivity of conditional assertions is influenced by their content.
4. A study of truth and falsity
Patricia Barres (Princeton) has investigated how individuals generate true instances of assertions and false instances of them. The model theory predicts that there is no direct route to false instances, but rather that they are generated by first considering what would be true. Barres's data corroborate this prediction.
5. Reasoning about probabilistic conclusions
Dr. Savary and I showed that illusory inferences occur in inferences about which is more likely of two events (see our paper in Acta Psychologica, 1996). More recently, we have developed a theory of probabilistic reasoning in collaboration with Professor Paolo Legrenzi (President of the University of Vita-Salute San Raffaele, Milan), Maria Legrenzi (Padova), Vittorio Girotto (CREPCO, University of Aix-en-Provence), and Jean-Paul Caverni (Director, CREPCO, University of Aix-en-Provence). The theory is based on the theory of mental models, and it postulates that in simple cases individuals assume by default that each model is equally probable, and that the probability of an event is accordingly proportional to the number of models in which it occurs. Experimental evidence has corroborated this prediction. Thus, given an assertion, such as:
In the box, there is a green marble or a red marble, or both.
people tend to estimate the probability that there is a red marble alone in the box as a third. This task also readily gives rise to illusory inferences.
6. Modal reasoning
The aim of this project is to test whether the model theory accounts for reasoning that yields conclusions about what is possible. Each model corresponds to a possibility, and so the theory predicts a key interaction: it should be easier to infer that an event is possible (one model) than that it is necessary (all models), whereas it should be easier to infer that an event is not necessary (one model) than that it is not possible (all models). Victoria Bell (Princeton) has confirmed this interaction in several experiments. Likewise, Yevgeniya Goldvarg (Princeton)has shown that illusory inferences occur in this domain. For example, consider the following problem.
Only one of the following assertions is true about a particular hand of cards:
There is a king in the hand, or an ace, or both.
There is a queen in the hand, or an ace, or both.
There is a jack in the hand, or a ten, or both.
Is is possible that there is an ace in the hand?
Nearly every participant in our experiment responded: 'yes'. But, it is an illusion. If there was an ace in the hand, then two of the premises would be true, contrary to the opening remark that only one of them is true. Various other colleagues, including Patrizia Tabossi (Trieste), Vittorio Girotto (Aix-en-Provence), Mary Newsome (Princeton), have examined experimentally conditions that reduce the propensity of reasoners to make illusory inferences.
7. Temporal reasoning
Walter Schaeken (Leuven, Belgium) and I have shown that the model theory gives a good account of temporal reasoning: premises that call for multiple models yield more difficult inferences than those that call only for a single model. The difficulty is apparent in both the participants' errors and latencies. And they take longer to read, and presumably to understand, the particular premise that calls for the construction of multiple models.
8. In collaboration with Bruno Bara and Monica Bucciarelli (University of Turin), the application of the mental model theory to the development of reasoning ability in children, and the study of how reasoners try to falsify conclusions.
9. In collaboration with Keith Oatley (OISE, University of Toronto), the study of how emotions affect reasoning.
10. In collaboration with Dr. Antonio Rizzo (Siena) and Victoria Bell (Princeton), a study of how diagrams can help people to reason.
Some recent publications
Human and Machine Thinking. Hillsdale, NJ: Lawrence Erlbaum Associates, 1992.
Mental models and probabilistic thinking. Cognition, 50, 1994.
Some computer programs implementing the mental model theory
PropAI -- a program that uses fully explicit models for propositional reasoning and that draws its own maximally parsimonious conclusions.
Syllog -- a program that makes syllogistic inferences based on mental models. The output shows both the predicted errors and the correct response.