Model theory of deduction: a unified computational approach.(Statistical Data Included)

1. Introduction

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.

But, human deductions are not always valid Indeed, the inferential process can be affected by several semantic factors like, for instance, the problem's content or the reasoner's beliefs. For this reason, logic is not an account of human deductive reasoning (see, e.g., Harman, 1986). Further, logic is a wrong normative theory because it permits inferences that naive individuals are not liable to draw (Devlin, 1997). A psychological theory of deduction has to account for plausible cognitive procedures, and to predict both the valid and the invalid deductions that humans draw.

In this paper we deal with three types of deduction: syllogistic, relational and propositional reasoning. They involve, respectively, reasoning from quantified assertions (e.g., `All of the artists are beekeepers; All of the beekeepers are chemists'), premises containing relations (e.g., `The bicycle is bigger than the doll; The doll is bigger than the pen'), and propositions involving connectives (e.g., `If Ann is at the party, then Ben is there; Ann is at the party'). Mental Model Theory (MMT: Johnson-Laird, 1983; Johnson-Laird & Byrne, 1991) can explain human performance in all these three reasoning domains. As a matter of fact, the theory extends further over different areas, and most of them are currently covered by specific computational models independently developed.

Although earlier work (reviewed later) suggests that MMT can explain human performance in each reasoning domain separately, we show that one unified computational model can be at work in all the three domains. Such a model enhances the coherence of the theory, which is intended to account for any sort of deduction. Moreover, in formulating such a unified model, we do not sacrifice the explanatory adequacy for any of the individual reasoning domains; our unified model is as good as other MMT models developed specifically for each single area. The existence of such a computational model and its experimental performance demonstrate that a unified deductive mechanism is a viable hypothesis. There is no need to postulate specific mental processes associated with different deductive domains.

Our model assumes -- in accordance with MMT -- that any kind of reasoning consists of five main processes: construction of mental models of the premises, integration of mental models, formulation of conclusions consistent with the integrated models, falsification of conclusions, and production of (linguistic or motor) responses. To accomplish this, we assume that there exist a set of procedures which is common to any kind of deduction, and which is part of the competence of the human system. The implementation of such procedures on a computer requires the definition of an ontology of mental model objects, together with the definition of the basic abilities underlying deductive reasoning. Our ontology provides the first formal foundation for MMT. Hitherto it has never been made explicit within the mental model framework.

The unified theory we propose gains strength by virtue of wide scope and explanative parsimony along three dimensions: it applies across reasoning domains, it accounts for both competence and performance, it has a relevance from a developmental perspective. The cross-domain validity of the model relies on the fact that predictions of subjects' responses are grounded on a single basic mechanism, whose functioning can be affected by cognitive constraints.