Human reasoning and cognitive science

In the late summer of 1998, the authors, a cognitive scientist and a logician, started talking about the relevance of modern mathematical logic to the study of human reasoning, and we have been talking ever since. This book is an interim report of that conversation. It argues that results such as those on the Wason selection task, purportedly showing the irrelevance of formal logic to actual human reasoning, have been widely misinterpreted, mainly because the picture of logic current in psychology and cognitive science is completely mistaken. We aim to give the reader a more accurate picture of mathematical logic and, in doing so, hope to show that logic, properly conceived, is still a very helpful tool in cognitive science. The main thrust of the book is therefore constructive. We give a number of examples in which logical theorizing helps in understanding and modeling observed behavior in reasoning tasks, deviations of that behavior in a psychiatric disorder (autism), and even the roots of that behavior in the evolution of the brain

Logic in Cognitive Science: Bridging the Gap between Symbolic and Connectionist Paradigms

What can logic contribute to cognitive science? In the early days of cognitive science, logic was taken to play both a descriptive and a normative role in theories of intelligent behavior. Descriptively, human beings were taken to be fundamentally logical, or rational. Normatively, logic was taken t

Default reasoning and neural networks

In this dissertation a formalisation of nonmonotonic reasoning, namely Default logic, is discussed. A proof theory for default logic and a variant of Default logic - Prioritised Default logic - is presented. We also pursue an investigation into the relationship between default reasoning and making inferences in a neural network. The inference problem shifts from the logical problem in Default logic to the optimisation problem in neural networks, in which maximum consistency is aimed at The inference is realised as an adaptation process that identifies and resolves conflicts between existing knowledge about the relevant world and external information. Knowledge and data are transformed into constraint equations and the nodes in the network represent propositions and constraint equations. The violation of constraints is formulated in terms of an energy function. The Hopfield network is shown to be suitable for modelling optimisation problems and default reasoning.Computer ScienceM.Sc. (Computer Science