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To date, most association rule mining algorithms have assumed that the domains of items are either discrete or, in a limited number of cases, hierarchical, categorical or linear. This constrains the search for interesting rules to those that satisfy the specified quality metrics as independent values or as higher level concepts of those values. However, in many cases the determination of a single hierarchy is not practicable and, for many datasets, an item's value may be taken from a domain that is more conveniently structured as a graph with weights indicating semantic (or conceptual) distance. Research in the development of algorithms that generate disjunctive association rules has allowed the production of rules such as Radios ∨ TVs → Cables. In many cases there is little semantic relationship between the disjunctive terms and arguably less readable rules such as Radios ∨ Tuesday → Cables can result. This paper describes two association rule mining algorithms, SemGrAMG and SemGrAMP, that accommodate conceptual distance information contained in a semantic graph. The SemGrAM algorithms permit the discovery of rules that include an association between sets of cognate groups of item values. The paper discusses the algorithms, the design decisions made during their development and some experimental results.