Notes on Formalizing Context

Abstract

These notes discuss formalizing contexts as first class objects. The basic relation is ist(c,p). It asserts that the proposition p is true in the context c. 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.