This paper is a reaction to Christopher Gauker's book Conditionals in Context. Gauker's semantics of assertibility and deniability will be reconstructed and one peculiar aspect of the semantics will be pointed to: connectives are sensitive to the syntactic structure of the formulas they connect. Even though this is a well motivated principle which can be supported by many examples from natural languages, one of its unwanted consequences is that the resulting formal semantics is not compositional. In this paper, Gauker's semantics will be modified and applied to Stalnaker's concept of context. In this framework, every sentential connective will be replaced with a pair of connectives one of which will be called extensional and the other intensional. This distinction enables us to have an adequate and compositional semantics of assertibility and deniability. We will provide also a syntactic characterization of the logic determined by this semantics.