For the entire Islamic tradition, the crowning glory of Aristotelian logic is the syllogistic theory outlined in the Prior and Posterior Analytics, especially the latter. The purpose of logic is to provide the means whereby knowledge is to be acquired, and the most valuable type of knowledge is that which is certain and necessary, that is, knowledge gained according to the paradigm of demonstra...

We elaborate on the approach to syllogistic reasoning based on "case identification" (Stenning & Oberlander, 1995; Stenning & Yule, 1997). It is shown that this can be viewed as the formalisation of a method of proof that dates back to Aristotle, namely proof by exposition (ecthesis), and that there are traces of this method in the strategies described by a number of psychologists, from Störrin...

This paper is about syllogistic reasoning, i.e., reasoning from such pairs of premises as, All the chefs are musicians; some of the musicians are painters. We present a computer model that implements the latest account of syllogisms, which is based on the theory of mental models. We also report four experiments that were designed to test this account. Experiments 1 and 2 examined the strategies...

This paper continues the development of complete fragments of natural language by adding a noun-level complement operator to the basic syllogistic language of All X are Y and Some X are Y : in the fragment of this paper we can also say, for example, Some non-X are Y . We axiomatize this logic of this fragment in two ways: in a direct fashion, allowing the inference of an arbitrary sentence from...