LINGUISTIC CONTEXT SPACES: NECESSARY FRAMES FOR CORRECT APPROXIMATE REASONING

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Abstract
Effective inference under uncertainty in Artificial Intelligence depends on context. Inferences based on Bayesian conditional probabilities use context effectively. However, newer approaches, such as fuzzy reasoning (and others—e.g., Dempster-Shafer, rough sets, etc.) cannot take context appropriately into account without further development of linguistic context. We develop the new concept of “context space” for fuzzy sets theory. Many-valued fuzzy sets were introduced by Nakanishi [1989]. We use them in this paper to describe context (context space) as an analog of probability space. Such a description of context space allows one to usefully construct fuzzy sets for specific applications, and thus improves the foundation for fuzzy sets theory. In addition, the problem of establishing membership functions (MFs) is considered for context spaces. It is shown that semantic operational procedures [Hisdal, 1984] and modal logic [Resconi, et al., 1992] are preferable when used jointly with a complete and exactly defined context space as introduced in the paper. Finally, the theory of fuzzy sets is compared with probability theory in connection with the problem of MF acquisition.

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