The paper presents a formalization of the notion of locality in the local theories of inheritance which were introduced in T. Krishnaprasad [The semantics of inheritance networks, (Ph. D. Dissertation, SUNY at Stony Brook) (1989)]. It defines a framework for semantics specification, where the notion of local specificity is used to resolve inheritance conflicts. Next, the notion of local semantics, which states that the meaning of a node of an inheritance network is constrained only by the meaning assigned to the nodes in its immediate neighborhood, is generalized to ground local semantics, where the requirement for locality is weakened so as to allow two nodes with similar neighborhoods to have interchangeable, but not necessarily identical meaning. This helps clarify the relationship between local theories of inheritance and path- based theories, and explains some counter-intuitive interpretations of certain network topologies of the latter. It is shown that the semantics introduced in the above citation are local, while Touretzky’s semantics is not local, and examples are given to illustrate its nonlocality. It is also proven that the path-based theory described in J. Horty, R. Thomason and D. Touretzky [A skeptical theory of inheritance in nonmonotonic semantic networks, (Artificial Intelligence, 42, 311-348, Elsevier, Amsterdam) (1990)] is ground local. The notions of local specificity and ground local specificity are noted to be similar to Horty’s notions of general subsumption and off-path preemption. The practical significance of locality in different areas of Knowledge Representation is also discussed.