Steps Toward Formalizing Context

The issue of context arises in various areas of AI, including knowledge representation, natural language processing, and intelligent information retrieval. Although the word context is frequently used in descriptions, explanations, and analyses of computer programs in these areas, its meaning is frequently left to the reader’s understanding; that is, it is used in an implicit and intuitive manner.1 An example of how contexts may help in AI is found in McCarthy’s (constructive) criticism (McCarthy 1984) of MYCIN (Shortliffe 1976), a program for advising physicians on treating bacterial infections of the blood and meningitis. When MYCIN is told that the patient has Chlorae Vibrio in his intestines, it would immediately recommend two weeks of tetracycline treatment and nothing else. While this would indeed do away with the bacteria, the patient would perish long before that due to diarrhea. A “contextual” version of mycin should know about the context of a treatment and would realize that any prescription must be made in the light of the fact that there is alarming dehydration. Thus, in the contextual MYCIN, the circumstances surrounding a patient would have to be made explicit using a formal approach and would be used as such by the program. The main motivation for studying formal contexts is to resolve the problem of generality in AI, as introduced by McCarthy (1987). McCarthy believes that AI programs suffer from a lack of generality. A seemingly minor addition (as in the MYCIN example) to the particular, predetermined possibilities that a program is required to handle often necessitates a partial redesign and rewrite of the program. Explicitly represented contexts would help because a program would then make its assertion about a certain context. A more general objection to the implicit representation of context—unless the representation is part of a program that is not mission critical (in a broad sense of the term)—can be given as follows: Assume that we write longer (more involved in terms of complexity) or shorter (simpler in terms of complexity) axioms depending on which implicit context we are in. The problem is that long axioms are often longer than is convenient in daily situations. Thus, we find it handy to utter “this is clever,” leaving any explanation about whether we are talking about a horse or a mathematical argument to the context of talk. However, shorter axioms might invite just the opposite of a principle of charity from an adversary. To quote McCarthy (1987, p. 1034):