Formalizing Context (Expanded Notes)

Abstract

These notes discuss formalizing contexts as first class objects. The basic relationships are: ist(c,p) meaning that the proposition p is true in the context c, and value(c,p) designating the value of the term e in the context c Besides these, there are lifting formulas that relate the propositions and terms in subcontexts to possibly more general propositions and terms in the outer context. Subcontextx are often specialised with regard to time, place and terminology. 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, ie. beyond the nonmonotonic inference methods first invented in AI and now studied as a new domain of logic.