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A knowledge representation based on the Belnap's four-valued logic

We treat knowledge from a computer-oriented point of view, considering it as a kind of data type. An axiomatic approach to the notion of data type undertaken by Dana Scott in [D.S.Scott, Outline of a Mathematical Theory of Computation, in: Proceedings of Princeton Conference on Information Science, 1971, pp. 169--176], is explored to find entities suitable for representation techniques. At the same time, we stay in Belnap''s paradigm of the toleration of inconsistency. We propose a representation of knowledge (possible with contradictions) in simple propositional language, and we show how such knowledge can be maintained and how it should be transformed on receipt of new information. In this transformation, the key role is played by Scott''s continuity rather than consistency.