Simulation of the Negative Conclusion Bias with INFERNET

Modeling human conditional reasoning of the type “if p then q” containing negations poses a challenge for connectionism. An integrate-and-fire pulsed network (INFERNET) was used to model this type of conditional reasoning. This model also provides an insight on certain human limitations. The model is compared to empirical data, and classical explanations. Statistical analysis shows that the model performance not only surpasses classical explanations but also is the best fitting model. INFERNET simulator results are also compared to human performance. Computational simulator performance compare well with human performance and limitations. Introduction INFERNET (Sougné, 1996, 1998a, 1998b, Sougné & French, 1997) achieves variable binding through temporal synchrony of node firing. In short, when one node fires in synchrony with another, they are temporarily bound together. It has a limited Working Memory (WM) span and the content of WM is maintained by oscillations. Once a node is activated, it tends to fire rhythmically at a particular frequency. This technique is successfully able to represent n-ary predicates (Sougné, 1996), relational reasoning with multiple instantiation (Sougné, 1998a; Sougné, 1998b), working memory (Sougné & French, 1997) and conditional reasoning (Sougné, 1996). This paper shows how the model can deal with negated conditionals. Many psychological studies in the area of deductive reasoning have focused on conditional reasoning of the type “if p then q”. Of course, some logicians would deny that material implication “ ⊃” is really what human mean by “if ...then”. Nonetheless, here are transcribed rules related to material implication: modus ponens (MP) p ⊃ q, p q , and modus tollens (MT) p ⊃ q,~ q ~ p . While most humans follow modus ponens, it is different for modus tollens. People also use two inappropriate rules related to material equivalence: Denial of the antecedent (DA) p ⊃ q,~ p ~ q × , and Affirmation of the consequent (AC) p ⊃ q,q p × . Throughout this paper the “if p then q” form will be called the “major premise”, p the antecedent, q the consequent. What happens when negations are introduced into the major premise? Negation can affect the antecedent or the consequent. It produces four forms of major premises. Table 1 shows these four forms and the inferences resulting from the application of the four rules (MT, DA, AC, MT).