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A monotonicity-based proof-theoretic account of syllogistic reasoning

In this paper, we will develop a proof-theoretic account of syllogistic reasoning based on the inference rules of monotonicity, symmetry and existential import. Monotonicity, however, will have a special status since it will be argued that this rule provides the very mechanism of quantified reasoning. We will implement this account in the framework of a natural logic for a fragment of natural language; this language extends in some respects the language of traditional syllogistic reasoning. This implementation will provide us with a competence model of human reasoning from premises built from our fragment of language; i.e., it explains how an ideal reasoner could perform any reasoning task from these premises in a complete and sound way. We will assess the psychological plausibility of this competence model, and argue that, among the proof-theoretic approaches to reasoning, the monotonicity account is the most plausible. We will then address issues surrounding performance, i.e., the actual way people do perform syllogistic tasks. In particular, we will focus our attention on three phenomena: (1) The relative difficulty of some syllogistic tasks, in particular when the syllogisms at stake are invalid; (2) the pragmatic nature of some processes; and (3) the figural effect, namely the fact that people have a tendency to produce a conclusion whose terms (subject and predicate) reproduce the role which they have in the premises. We will mainly address these three performance matters in discussing Geurts’ (2003a) stance about them.