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aAb^a Air Force Office algebra of open algebra of regular American Documentation Institute analysis of relevance assertions assignment of neighborhoods binary operations Boolean algebra Boolean model Boolean proposltional calculus Chain closed set descriptor number direct file Document Collections document corpus document number EMPIRICAL TESTING formal objects formed formula forming the double free distributive lattice Gave a public genus graph G implicative lattice Information Science interpretation Inverted file entries logical Algebras Models of Information National Science Foundation negation Office of Scientific open set partially ordered positive model Problem of Relevance propositions relation of matching represent a correct request retrieval operations Retrieval System Design retrieval theory reverse polish Science Foundation Grant Scientific Research search-retrieval system set of documents smaller matrix Study of Theories subtractive lattice system based system of partial tape Term-document connections term-term theorems Theories and Models Theories of Relevance Theories of Retrieval topological space variables various genera