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.