"possible worlds'' and the possibility relation are both primitive notions. This has both technical and conceptual short-comings. From a technical point of view, the mathematics associated with Kripke semantics is often quite complicated. From a conceptual point of view, it is not clear how to use Kripke structures to model knowledge and belief, where one wants a clearer understanding of the notions that are primitive in Kripke semantics. We introduce "modal structures'' as models for logic. We use the idea of possible worlds,
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but by directly describing the "internal semantics'' of each possible world. It is much easier to study the standard logical questions, such as completeness, decid-ability, and compactness, using modal structures. Furthermore, modal structures offer a much more intuitive approach to modelling knowledge and belief.