There are many useful relations among contexts and also context valued functions. Here are some.
1. is a context related to in which the time is specialized to have the value . We may have the relation
Instead of using the function , it may be convenient to use a predicate and an axiom
There are also relations concerned with specializing places and with specializing speakers and hearers. Such relations permit lifting sentences containing pronouns to contexts not presuming specific places and persons.
2. If is a proposition and is a context, then is another context like in which is assumed, where ``assumed'' is taken in the natural deduction sense of section .
3. There is a general relation between contexts. We say when involves no more assumptions than and every proposition meaningful in is translatable into one meaningful in . We have nonmonotonic relations
4. A major set of relations that need to be expressed are those between the context of a particular conversation and a subsequent written report about the situation in which the conversation took place. References to persons and objects are decontextualized in the report, and sentences like those given above can be used to express their relations.
5. Consider a wire with a signal on it which may have the
value 0 or 1. We can associate a context with this wire
that depends on time. Call it
at time 331, the value of this signal is 0. We can write