In this paper I introduce the notion of bilogics, namely logics interpreted over a pair of structures, in contrast to classical logic and many of its variations, the formulae of which are interpreted over one structure. In particular, I introduce and study Contrastive Logic, suitable for expressing contrast and conformity between the two structures involved.A major reason for this study is striving towards an extension of truth-conditional semantics to cover several natural-language particles, which have been hitherto considered not to be (...) amenable to such an extensional treatment, and were delegated to the level of non-extensional pragmatics. Examples of such particles are but and already. (shrink)