Logic and implementation in human reasoning: the psychology of syllogisms

Abstract

This thesis presents a novel account of syllogistic reasoning, based on data from a non-standard reasoning task called the Individuals Task. An abstract logical treatment of the system, based on a modalised Euler Circles system (Stenning & Oberlander 1994, 1995) is presented, and it is shown that this can be implemented in a diverse range of notationally distinct ways. The Individual Identification Algorithm, as this method is called, makes use of a logical distinction between the premisses of the syllogism; one has an existential, assertive role, and is called the source premiss, whereas the function of the other is to license inference, and so it is called the conditional premiss. This distinction is central to the way the IIA employs modal information to make the use of Euler Circles tractable.

The empirical parts of the thesis are concerned with relating the distinction between source and conditional premisses to the Figural Effect (Johnson-Laird & Steedman 1978). It is argued that the Figural Effect is reducible to a tendency for the terms from the source premiss to occur before the terms from the conditional premiss in Individual Conclusions. Since these are comprised of all three terms in the syllogism, it is possible to test new hypotheses concerning the role of the middle term in inference, and the results are shown to be incompatible with all existing theories of the Figural Effect.

Since the Individuals Task is non-standard, it is necessary to compare perfor¬ mance profiles on this task with those on the Standard Task; one result of this comparison is that a primary cause of error in the Standard Task is selection of an appropriate quantifier for the conclusion, a result which concurs with the con¬ clusions of Ford (1994) and Wetherick & Gilhooly (1990), but contradicts those of Mental Models theory (Johnson-Laird 1983).

Certain anomalies in the prediction of term order by the source/conditional distinction lead to the postulation of a second process for conclusion generation, called Minimal Linking. This logically unsound strategy has effects similar to the illicit conversion of A premisses (Chapman &; Chapman 1959, Revlis 1975).