Set theory is the common language of mathematics. Therefore, set theory plays an important rôle in many important applications of automated deduction. In this paper, we present an improved tableau calculus for the decidable fragment of set theory called multi-level syllogistic with singleton (MLSS). Furthermore, we describe an extension of our calculus for the bigger fragment consisting of MLSS...

A recent meta-study shows that the conclusions driven by human reasoners in psychological experiments about syllogistic reasoning are not the conclusions predicted by classical first-order logic. Moreover, current cognitive theories deviate significantly from the empirical data. In the following, three important cognitive approaches are presented and compared to predictions made by a new approa...

It has long been known that conversion of the quantifiers can explain syllogistic reasoning errors (Newstead, 1989; Revlis, 1975; Wilkins, 1928). Geurts is more concerned with explaining how people solve valid syllogisms, and an integral part of his model is the (entirely legal) conversion of ‘no’ and ‘some’. This part of Geurts’ theory seems unexceptionable, but more problematic is his assumpt...

A neural net system called "Conposi t " is described. Conposit performs rule-based manipulation of very short term, complex symbolic data structures. This paper concentrates on a simulated version of Conposit that embodies core aspects of JohnsonLaird's mental model theory of syllogistic reasoning. This Conposit version is not intended to be a psychological theory, but rather to act as a test a...

10% 29%18%33% 11%Concrete 12% 20%26%32% 10% Syllogisms 10% 25%24%31% 11%Conditionals 14% 24%23%33% 6% Wason 14% 36%21%20% 8%Non-Wason 12% 22%22%36% 8% Morris & SchunnLogical Reasoning Skills 37 Figure 1. Solution times associated with self-reported strategies for conditional and syllogisticreasoning problems.

It seems widely accepted that human reasoning cannot be modeled by means of Classical Logic. Psychological experiments have repeatedly shown that participants’ answers systematically deviate from the classical logically correct answers. Recently a new approach on modeling human syllogistic reasoning has been developed which seems to perform the best compared to other state-of-the-art cognitive ...

Natural language contains an abundance of reasoning patterns. Historically, there have been many attempts to capture their rational usage in normative systems of logical rules. However, empirical studies have repeatedly shown that human inference differs from what is characterized by logical validity. In order to better characterize the patterns of human reasoning, psychologists have proposed a...