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We consider Russell’s theory of negative facts and construct a suitable theoretical model that provides an ontological basis for this theory. Proceeding from the hypothesis that negative facts cannot be eliminated and cannot be reduced to any sort of positive facts, we argue that negative (atomic) facts should be logically expressed by means of a special type of predication – a negative predication. The introduction of negative properties enables us to justify the essential discrimination between positive and negative predications. In the final section, we present a model-theoretical semantics for negative facts.