An Algorithm for Inferring Multivalued Dependencies with an Application to Propositional Logic

An algorithm is given for deciding whether a functional or a multivalued dependency σ (with a right-hand side Y) is implied by a set of functional and multivalued dependencies Σ. The running time of the algorithm is O(| Y |‖Σ‖), where Y is the number of attributes in Y and ‖Σ‖ is the size of the description of Σ. The problem of constructing the dependency basis of a set of attributes X is also investigated. It is shown that the dependency basis can be found in O(S‖Σ‖) time, where S is the number of sets in the dependency basis. Since functional and multivalued dependencies correspond to a subclass of propositional logic (that can be viewed as a generalization of Horn clauses), the algorithm given is also an efficient inference procedure for this subclass of propositional logic.