Contradictions, objects, and belief

We show how some model-theoretical devices (local reasoning, modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize the consequence relation that includes de dicto and de re contradictory beliefs. Instead of special " sense objects " , appearances of objects in an agent's belief are introduced and presented as ordered pairs consisting of an object and an individual constant. A non-classical identity relation is applied. A relation S on the set of possible worlds is introduced, which models possible distortions in an agent's picture of a (real) world. The application of such models in deontic logic is illustrated by a characteristic example. As is well known, a rational agent can have beliefs that contain contradictions, including disturbances of the identity of objects. Contradictions can arise not only in the de re sense of a belief (cf. the Hesperus—Phosphorus puzzle), but also, as Kripke has shown, in the de dicto sense. The aim of the logic of belief is, among other things, to formalize such " non-classical " states of affairs. This paper attempts to show how some model-theoretical devices (local reasoning , modes of presentation, an additional accessibility relation) can be combined in first-order modal logic to formalize de dicto contradictory beliefs, as well as de dicto non-contradictory beliefs that have de re contradictory consequences.