Formalizing Context
(Expanded Notes)

John McCarthy and Sasa Buvac

These notes discuss formalizing contexts   as first class objects.   The basic relations are

  meaning that the proposition p is true in the context c, and

  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. Subcontexts are often specialized 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, i.e. beyond the nonmonotonic inference   methods first invented in AI and now studied as a new domain of logic.

• Introduction
• Relations among Contexts
• Entering and Exiting Contexts
• Lifting Axioms
• Natural Deduction via Context
  • Postponing Preconditions via
• Integrating Databases
  • The GE, Navy, and Air Force Example
  • A Simple Formalization
  • Formalization for Bargaining
  • Treating as an Abbreviation
  • Existence as a Predicate
• Combining Planning Contexts
  • Combining Planning Languages
  • Discharging Kindness Assumptions
  • Combining Heterogeneous Objects
• Representing Discourse
  • The Logic of and
  • Example: Air Force-GE Discourse
  • Deriving Properties of the Air Force-GE Discourse
    • First Question: Propositional Case
    • Second Question: Qualitative Case
    • Third Question: Dealing with Ambiguity
• Transcending Contexts
• Relative Decontextualization
• Mental States as Outer Contexts
• Remarks
• Conclusion
• References
• About this document ...