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Axiomatizing Reflective Logics and Languages
 by Manuel G. Clavel & Josť Meseguer.

Abstract
The very success and breadth of reflective techniques underscores the need for a general theory of reflection. at present what we have is a wide-ranging-variety of reflective systems, each explained in its own idiosyncratic terms. Metalogical foundations can allow us to capture the essential aspects of reflective systems in a formalism-independent way. This paper proposes metalogical axioms for reflective logics and declarative languages based on the theory of general logics. In this way, several strands of work in reflection, including functional, equational, Horn logic, and rewriting logic reflective languages, as well as a variety of reflective theorem proving systems are placed within a common theoretical framework. General axioms for computational strategies and for the internalization of those strategies in a reflective logic are also given.
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