Definable naming relations in meta-level systems
Meta-level architectures are always, implicitly or explicitly, equipped with a component that establishes a relation between their object- and meta-level layers. This so-called naming relation has been a neglected part of the architecture of meta-level systems. This paper argues that the naming relation can be employed to increase the expressiveness and efficiency of meta-level architectures, while preserving known logical properties. We argue that the naming relation should not be a fixed part of a meta-level architecture, but that it should be definable to allow suitable encoding of syntactic information. Once the naming relation is definable, we can also make it meaningful. That is, it can also be used to encode pragmatic and semantic information, allowing for more compact and efficient meta-theories. We explore the formal constraints that such a definable naming relation must satisfy, and we describe a definition mechanism for naming relations which is based on term rewriting systems.