Conditional Objects Revisited: Variants and Model Translations

The quality criteria of system P have been guiding qualitative uncertain reasoning now for more than two decades. Different semantical approaches have been presented to provide semantics for system P. The aim of the present paper is to investigate the semantical structures underlying system P in more detail, namely, on the level of the models. In particular, we focus on the approach via conditional objects which relies on Boolean intervals, without making any use of qualitative or quantitative information. Indeed, our studies confirm the singular position of conditional objects, but we are also able to establish semantical relationships via novel variants of model theories.