Objectives: The article proposed a new type of dependency on blocks and slices. Then found and proved the properties of this new dependency. Method: Logical inference methods were used. Findings: A new type of data relationship has been proposed: Multivalued positive Boolean dependencies on block and slice in the database model of block form. From this new concept, the article stated and demonstrated the equivalence of the three types of deduction, namely: m-deduction by logic, m-deduction by block, m-deduction by block has no more than two elements. Next are the necessary and sufficient criteria of the tight m-expression for the set of multivalued positive Boolean dependencies on block and slice, the sufficient properties for a set of functions {I, ∧, ∨}. The properties related to this new concept when the block degenerated into relation. Novelty: The proposed new dependency with their properties on the block and on the slice are completely new.

The article proposed the concept of multivalue positive Boolean dependencies by groups in the database model of block form, proved the equivalence of three types derived: m-deduction by logic, m-deduction in groups by block, m-deduction in groups by block not exceeding p elements,, necessary and sufficient conditions for a block to be a m-tight representation by groups of a set of multivalue positive Boolean dependencies by groups on the block ... In addition, some properties multivalue positive Boolean dependencies by groups have been stated and proved here.

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The report proposes the concept of positive boolean dependency in the database model of block form, proving equivalent theorem of three derived types, necessary and sufficient criteria of the derived type, the member problem... In addition, some properties related to this concept in the case of block r degenerated into relation are also expressed and demonstrated here.