Modal Logic for Evaluating Formulas in Incomplete Contexts

Authors:
Sergei A. Obiedkov
Affiliations:
-
Venue:
ICCS '02 Proceedings of the 10th International Conference on Conceptual Structures: Integration and Interfaces
Year:
2002

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Abstract

Formal contexts are used to represent objects as attribute sets. Incomplete contexts may be used to describe situations when it is not known whether an object has a particular attribute. In this paper, the notion of validity of implications in incomplete contexts is discussed. It is then extended to the case of an arbitrary propositional formula describing a certain dependency between attributes. Existing approaches to evaluating such formulas in incomplete contexts prove to be inadequate. A new three-valued modal logic with the third value of nonsense is introduced. Applied to incomplete contexts, this logic appears suitable for evaluating formulas.