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Metatheory and Reflection in Theorem Proving: A Survey and Critique
, 1995
"... 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 appro ..."
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Cited by 53 (2 self)
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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 fullyexpansive 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 ...
Experience with FS 0 as a framework theory
, 1993
"... Feferman has proposed a system, FS 0 , as an alternative framework for encoding logics and also for reasoning about those encodings. We have implemented a version of this framework and performed experiments that show that it is practical. Specifically, we describe a formalisation of predicate calcul ..."
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Cited by 16 (4 self)
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Feferman has proposed a system, FS 0 , as an alternative framework for encoding logics and also for reasoning about those encodings. We have implemented a version of this framework and performed experiments that show that it is practical. Specifically, we describe a formalisation of predicate calculus and the development of an admissible rule that manipulates formulae with bound variables. This application will be of interest to researchers working with frameworks that use mechanisms based on substitution in the lambda calculus to implement variable binding and substitution in the declared logic directly. We suggest that metatheoretic reasoning, even for a theory using bound variables, is not as difficult as is often supposed, and leads to more powerful ways of reasoning about the encoded theory. x 1 Introduction: why metamathematics? A logical framework is a formal theory that is designed for the purpose of describing other formal theories in a uniform way, and for making the work ...
Metareasoning: a Survey
 Computational Logic: Logic Programming and Beyond – Essays in Honour of Robert A. Kowalski (LNAI Volumes 2408
, 2002
"... We present the basic principles and possible applications of systems capable of metareasoning and reflection. After a discussion of the seminal approaches, we outline our own perception of the state of the art, mainly but not only in computational logic and logic programming. We review relevat succ ..."
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Cited by 10 (2 self)
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We present the basic principles and possible applications of systems capable of metareasoning and reflection. After a discussion of the seminal approaches, we outline our own perception of the state of the art, mainly but not only in computational logic and logic programming. We review relevat successful...
Construction and Deduction Methods for the Formal Development of Software
 In Broy and Jahnichen [2
, 1995
"... . In this paper we present an approach towards a framework based on the type theory ECC (Extended Calculus of Constructions) in which specifications, programs and operators for modular development by stepwise refinement can be formally described and reasoned about. We demonstrate how generic sof ..."
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Cited by 1 (0 self)
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. In this paper we present an approach towards a framework based on the type theory ECC (Extended Calculus of Constructions) in which specifications, programs and operators for modular development by stepwise refinement can be formally described and reasoned about. We demonstrate how generic software development steps can be expressed as higherorder functions and how proofs about their asserted effects can be carried out in the underlying logical calculus. For formalizing transformations that require syntactic manipulation of objects, we introduce a twolevel system combining a metalevel and an object level and show how to express and reason about transformations that faithfully represent objectlevel operators. 1 Introduction Modern software engineering regards software development as an evolutionary process [Wir95, BP81]. One view of this process is that, starting from abstract, highlevel requirement specifications, a series of refinement or implementation steps is app...
Towards a theory of mechanizable theories: I
"... this paper. We call these structures contexts. We claim that contexts are the appropriate building blocks for giving a general explanation of both reasoning and cognition ..."
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this paper. We call these structures contexts. We claim that contexts are the appropriate building blocks for giving a general explanation of both reasoning and cognition