The notion of context is indispensable in discussions of meaning, but the word context has often been used in conflicting senses. In logic, the first representation of context as a formal object was by the philosopher C. S. Peirce; but for nearly eighty years, his treatment was unknown outside a small group of Peirce aficionados. In the early 1980s, three new theories included related notions of context: Kamp’s discourse representation theory; Barwise and Perry’s situation semantics; and Sowa’s conceptual graphs, which explicitly introduced Peirce’s approach to the AI community. More recently, John McCarthy and his students have begun to use a closely related notion of context as a basis for organizing and partitioning knowledge bases. Each of the theories has distinctive, but complementary ideas that can enrich the others, but the relationships between them are far from clear. This paper analyzes the semantic foundations of these theories and shows how McCarthy’s ist(c,p) predicate can be interpreted in terms of the semantic notions underlying the others.