Johan van Benthem asked for the following in soliciting this essay and John Perry's.
My proposal is the following. I would like to invite the two Johns to send me a rough outline of their contribution. It would be good if you could bring out (1) what the notion of context is and what it does according to you: in both cases, I think you want it to achieve 'efficiency' and 'portability' of information, (2) what is involved in the dynamics of changing contexts, perhaps with attendant changes in linguistic formulation (add or drop variables, etcetera). I would then like to comment on this, adding some thoughts on possible logical formalizations, emphasizing the interplay between what is said in a formula and what remains implicit in the models where it gets evaluated.
I have rejected the idea of defining what a context is, but I hope I have given some idea of what they do. The example relating the three argument on and the two argument on should provide a basis for comments. In the formulation of the ideas, the ability to combine formulas arising in different contexts has been more important than computational efficiency.
[McC93] and [MB94] have additional references. Also Sasa Buvac has several other papers on context on his Web page http://www-formal.stanford.edu/buvac/.