Premises and conclusions in classical syllogistic reasoning are formed using one of four quantifiers (All, Some, Some not, None). In everyday communication and reasoning, however, statements such as “most” and “few” are formed as well. So far only Chater and Oaksford’s (1999) Probability Heuristics Model (PHM) makes predictions for these so-called generalized quantifiers. In this article we (i)...

In 1883, while a student of C. S. Peirce at Johns Hopkins University, Christine Ladd-Franklin published a paper titled On the Algebra of Logic, in which she develops an elegant and powerful test for the validity of syllogisms that constitutes the most significant advance in syllogistic logic in two thousand years.1 Sadly, her work has been all but forgotten by logicians and historians of logic....

In the present article we attempt to show that Aristotie's syllogistic is an underlying logie which includes a natural deductive system and that it is not an axiomatic theoryas had previously been thought. We construct a mathematical model which reflects certain structural aspects of Aristotle's logic and we examine both the mathematical properties of the model and the relation of the model to ...

This paper presents an ongoing research project called “natural logic” and makes the case that it is relevant to AI, Computational Linguistics, and Cognitive Science. We propose to add some of the natural logic modules which have already been developed to existing NLP systems. We see our approach as complementing and augmenting data-driven approaches exemplified by IBM’s Watson. We give a brief...

We describe SYLLOG, a model of syllogistic inference, built with in the ACT-R framework. Its construction was guided by data obtained from 88 subjects performing the syllogistic inference task. The model’s inference engine uses the PC inference rule Hypothetical Syllogism (HS) and a set of modal logic transformation rules either to create a representation of the premises that allows an appropri...

A recent development in the cognitive science of reasoning has been the emergence of a probabilistic approach to the behaviour observed on ostensibly logical tasks. According to this approach the errors and biases documented on these tasks occur because people import their everyday uncertain reasoning strategies into the laboratory. Consequently participants' apparently irrational behaviour is ...

In this paper, a new approximate syllogistic reasoning schema is described that expands some of the approaches expounded in the literature into two ways: (i) a number of different types of quantifiers (logical, absolute, proportional, comparative and exception) taken from Theory of Generalized Quantifiers and similarity quantifiers, taken from statistics, are considered and (ii) any number of p...