Syllogistics reduces to only two rules of inference: monotonicity and symmetry, plus a third if one wants to take existential import into account. We give an implementation that uses only the monotonicity and symmetry rules, with an addendum for the treatment of existential import. Soundness follows from the monotonicity properties and symmetry properties of the Aristotelean quantifiers, while ...

Computational cognitive models can embody the structures and processes proposed in a cognitive theory. However, they do not necessarily reveal the theory’s underlying assumptions and specifications. This study aims to bridge the gap between cognitive theory and its computational implementation, focusing on a case of mental model theory on human reasoning. Using a mathematics-based and staticall...

Non-Axiomatic Reasoning System is an adaptive system that works with insu cient knowledge and resources. At the beginning of the paper, three binary term logics are de ned. The rst is based only on an inheritance relation. The second and the third suggest a novel way to process extension and intension, and they also have interesting relations with Aristotle's syllogistic logic. Based on the thr...

Recent neuroimaging studies have increasingly focused on the neural mechanisms of human deductive reasoning (see Goel, 2006 for recent review). Deductive reasoning is the cognitive process of drawing valid conclusions from a given set of premises. Although it should be performed independently of prior knowledge and intuitive beliefs, actual human reasoning often relies on them. Sometimes such b...

Two experiments were carried out in which subjects had to draw conclusions from syllogistic premises. The nature of their responses showed that the figure of the syllogisms exerted a strong effect on the accuracy of performance and on the nature of the conclusions that were drawn. For example, premises such as “Some of the parents are scientists; All of the scientists are drivers” tend to elici...

Logic as a philosophical discipline originated in ancient Greece, at about the same time as mathematics was constituted as a deductive science. From ancient times two logical systems have survived – the Aristotelian syllogistic logic and the Stoic propositional logic. It took almost two thousand years, until in the works of Boole, Frege and Peano logic was turned into a formal discipline. The r...