ABSTRACT
The most efficient, accurate, and fruitful way to communicate reasoning's is in natural languages. This chapter introduces a way which contributes to showing how "natural language can be viewed as a Knowledge Representation system with its own representation and inferential machinery" The Aristotelian rules of quality and distribution rules of quantity being superfluous are sound and complete methods for filtering out the 24 correct reasoning, valid syllogisms, from the 256 logical possibilities of Aristotelian syllogistic reasoning's. The way in which the syllogism could actually be considered fundamental reasoning-wise is not often remembered. Two models illustrate what are at issue— the "polysyllogism" and the "enthymeme." Basic to the Aristotelian approach is the breaking down of negation and denial into two fundamental types— that labeled "contradictory" and that labeled "contrary". The infinite-quantity (IQ) syllogistic is modeled on the traditional quantity and the higher-quantity fractional systems. The intermediate quantities in IQ are rational fractions that are intermediate proportions between universal and particular.
