Logical AI develops computer programs that represent what they know about the world primarily by logical formulas and decide what to do primarily by logical reasoning---including nonmonotonic logical reasoning. It is convenient to use logical sentences and terms whose meaning depends on context. The reasons for this are similar to what causes human language to use context dependent meanings. This note gives elements of some of the formalisms to which we have been led. Fuller treatments are in \cite{McC93}, \cite{guha-thesis} and \cite{McCBuvac94} and the references cited in the Web page \cite{Buvac95}. The first main idea is to make contexts first class objects in the logic and use the formula $ist(c,p)$ to assert that the \emph{proposition} $p$ is true in the \emph{context} $c$. A second idea is to formalize how propositions true in one context transform when they are moved to different but related contexts. An ability to transcend the outermost context is needed to give computer programs the ability to reason about the totality of all they have thought about so far \cite{McC96}.

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