Towards a Theory of Access-Limited Logic for Knowledge Representation

One of the fundamental problems in the theory of knowledge representation is the dii-culty of achieving both logical coherence and computational tractability. We present steps toward a theory of access-limited logic, in which access to assertions in the knowledge-base is constrained by semantic network style locality relations. Where a classical de-ductive method or logic programming language would retrieve all assertions that satisfy a given pattern, an access-limited logic retrieves all assertions reachable by following an available access path. The complexity of inference is thus independent of the size of the knowledge-base and depends only on its local connectivity. Access-Limited Logic, though incomplete, still has a well deened semantics and a weakened form of completeness (`Socratic Completeness') and is complete in some important special cases.