One way to ensure correctness of the inference performed by computer theorem provers is to force all proofs to be done step by step in a simple, more or less traditional, deductive system. Using techniques pioneered in Edinburgh LCF, this can be made palatable. However, some believe such an approach will never be efficient enough for large, complex proofs. One alternative, commonly called reflection, is to analyze proofs using a second layer of logic, a metalogic, and so justify abbreviating or simplifying proofs, making the kinds of shortcuts humans often do or appealing to specialized decision algorithms. In this paper we contrast the fully-expansive LCF approach with the use of reflection. We put forward arguments to suggest that the inadequacy of the LCF approach has not been adequately demonstrated, and neither has the practical utility of reflection (notwithstanding its undoubted intellectual interest). The LCF system with which we are most concerned is the HOL proof ...

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 formalismindependent way. This paper proposes metalogical axioms for reflective logics and declarative languages based on the theory of general logics [34]. 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. 1 Introduction Reflection is a fundamental idea. In logic it has been vigorously pursued by many researchers since the fundamental wor...

this paper I briefly sketch recent work on meta-logical foundations that seems promising as a conceptual basis on which to achieve the goal of formal interoperability. Specificaly, I will briefly discuss:

This paper is concerned with developing a reflective architecture for formalizing and reasoning about entities that occur in the process of software development, such as specifications, theorems, programs, and proofs. The starting point is a syntactic extension of the type theory ECC . An encoding of this object calculus within itself comprises the meta-level, and reflection principles are provided for switching between di#erent levels. These reflection principles are used to mix object- and meta-level reasoning, to generate "standard" units by executing meta-operators, and to apply formal tactics that allow for abstraction from the base logic. 1 Introduction Formalizing artifacts of software development and software engineering activities that produce these artifacts is, according to [2], a central issue of # Proc. of the IJCAI'95 Workshop "On Reflection and Meta Level Architecture and their Application in AI". Editors: M. Ibrahim, P. Cointe, F. Cummins, F. Giunchiglia, and J. Male...

this paper applications of reflection in rewriting logic and Maude to the following areas:

this paper is inspired by that notion, but focuses on a special aspect: zooming out in reflection works via the mechanism of coding. The 9 main thesis of Hofstadter is that `strange loops' are at the basis of selfconsciousness. I partly agree with this thesis and would like to add that mindfulness serves as the necessary zooming mechanism in the strange loop of self-consciousness. On the other hand, the thesis only explains the `self' aspect, the consciousness part still remains obscure. I disagree with the title of Dennet [1993]: `Consciousness explained'. No matter how many levels of cognition and feedback we place on top of sensory input in a model of the mind, it a prioiri seems not able to account for experiences. We always could simulated these processes on an oldfashioned computer consisting of relais, or even play it as a social game with cards. It is not that I object to base our consciousness on outer agents like the cardplayers (we depend on nature in a similar way). It is the claimed emergence of consciousness as a side e#ect of the cardgame that seems absurd