Algebraic modelling of some cognitive neuropsychology of schizophrenia

Frith (1992) gives an account of signs and symptoms of schizophrenia using a cognitive neuropsychological model. We show how Frith's account can be modelled using an algebra, PSEN, whose elements are sets of first-order formulas. These correspond to cognitive components of Frith's model, while cognitive pathways correspond to PSEN's partial order relation: restricted entailment. We use an algebraic formulation of belief contraction, constructed using operations of PSEN, to model inhibitory pathways in Frith's model. Our formulation of belief contraction is equivalent to the AGM approach in Gardenfors (1988) and Gardenfors and Rott (1995). We give conditions under which PSEN's operations, and belief contraction are computable.