A Basis for a Multi-Level Meta-Logic Programming Language

We are developing a multilevel metalogic programming language that we call Alloy. It is based on rst-order predicate calculus extended with metalogical constructs. An Alloy program consists of a collection of theories, all in the same language, and a representation relation over these theories. The whole language is self-representable, including names for expressions with variables. A signiicant diierence, as compared with many previous approaches, is that an arbitrary number of metalevels can be employed and that the object-meta relationship between theories need not be circular. The language is primarily intended for representation of knowledge and metaknowledge and is currently being used in research on hierarchical representation of legal knowledge. We believe that the language allows sophisticated expression and eecient automatic deduction of interesting sets of beliefs of agents. This paper aims to give a preliminary and largely informal deeni-tion of the core of the language, a simple but incomplete and ineecient proof system for the language and a sketch of an alternative, more ef-cient, proof system. The latter is intended to be used as a procedural semantics for the language. It is being implemented by an extension of an abstract machine for Prolog. 1 Introduction We are interested in the representation of complex formalized knowledge,