We give an approach to cognitive modelling, which allows for richer expression than the one based simply on the firing of sets of neurons. The object language of the approach is first-order logic augmented by operations of an algebra, PSEN. Some operations useful for this kind of modelling are postulated: combination, comparison, and inhibition of sets of sentences. Inhibition is realised using an algebraic version of AGM belief contraction (Gärdenfors, 1988). It is shown how these operations can be realised using PSEN. Algebraic modelling using PSEN is used to give an account of an explanation of some signs and symptoms of schizophrenia due to Frith (1992) as well as a proposal for the cognitive basis of autonomic computing. A brief discussion of the computability of the operations of PSEN is also given.
Cognitive Components And Neural Logic
We conceive of cognitive functioning being based upon a system of cognitive components, some of which are connected by neural pathways. This is an abstraction from the actual structure and function of the brain. Cognitive components are an abstraction of physical regions in the brain. Abstract pathways are taken to be channels, which convey information and each pathway corresponds to a bundle of neuronal chains linking one brain region to another. We assume that there is a resultant electrical flow of current in one direction only in a neuronal bundle. The correspondence of this abstraction to reality may not be perfect, but we take it as the basis for our cognitive modelling. Figure 1, based on Frith (1992), is an example of this kind of abstraction. It shows seven cognitive components. Some of them are connected by pathways, which are shown as arrows. For example, there is a pathway connecting the components action and monitor. The direction of the arrow indicates that activity in the action component induces activity in the monitor component.