John McCarthy
Computer Science Department
Stanford University
These notes discuss formalizing contexts as first class objects. The
basic relation is 
. It asserts that the proposition
is true in the context 
. The most important formulas
relate the propositions true in different contexts. Introducing
contexts as formal objects will permit axiomatizations in limited
contexts to be expanded to transcend the original limitations.
This seems necessary to provide AI programs using logic with certain
capabilities that human fact representation and human reasoning
possess. Fully implementing transcendence seems to require
further extensions to mathematical logic, i.e. beyond the nonmonotonic
inference methods first invented in AI and now studied
as a new domain of logic. Various notations are considered,
but these notes are tentative in not proposing a single language with
all the desired capabilities.