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.