Propositional logic based on the dynamics of disbelief

Gärdenfors' (1984) epistemic modelling of intuitionistic propositional logic interprets propositions as functions from belief states to belief states. In this paper we generalise his approach by including also disbelief, or rejection, as a basic epistemic attitude. Propositions are here defined as ordered pairs of functions on belief states, representing the attitudes of acceptance and rejection, respectively. For this semantics we obtain strong completeness results wrt the constructive logics of Nelson (1949) and Almukdad and Nelson (1984).