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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 ...
Formalized mathematics
 TURKU CENTRE FOR COMPUTER SCIENCE
, 1996
"... It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In c ..."
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Cited by 23 (0 self)
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It is generally accepted that in principle it’s possible to formalize completely almost all of presentday mathematics. The practicability of actually doing so is widely doubted, as is the value of the result. But in the computer age we believe that such formalization is possible and desirable. In contrast to the QED Manifesto however, we do not offer polemics in support of such a project. We merely try to place the formalization of mathematics in its historical perspective, as well as looking at existing praxis and identifying what we regard as the most interesting issues, theoretical and practical.
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...
Reflection Principles in Computational Logic
 Journal of Logic and Computation
, 1997
"... We introduce the concept of reflection principle as a knowledge representation paradigm in a computational logic setting. Reflection principles are expressed as certain kinds of logic schemata intended to capture the basic properties of the domain knowledge to be modeled. Reflection is then used to ..."
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Cited by 10 (6 self)
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We introduce the concept of reflection principle as a knowledge representation paradigm in a computational logic setting. Reflection principles are expressed as certain kinds of logic schemata intended to capture the basic properties of the domain knowledge to be modeled. Reflection is then used to instantiate these schemata to answer specific queries about the domain. This differs from other approaches to reflection mainly in the following three ways. First, it uses logical instead of procedural reflection. Second, it aims at a cognitively adequate declarative representation of various forms of knowledge and reasoning, as opposed to reflection as a means for controlling computation or deduction. Third, it facilitates the building of a complex theory by allowing a simpler theory to be enhanced by a compact metatheory, contrary to the construction of metatheories that are only conservative extensions of the basic theory. A computational logic system for embedding reflection principles, called RCL (for Reflective Computational Logic), is presented in full detail. The system is an extension of Horn clause resolutionbased logic, and is devised in a way that makes important features of reflection parametric as much as possible, so that they can be tailored according to specific needs of different application domains. Declarative and procedural semantics of the logic are described and correctness and completeness of reflection as logical 1 inference are proved. Examples of reflection principles for three different application areas are shown. Relationship with a variety of distinct sources within the literature on relevant topics is discussed.
SLDResolution with Reflection
 Logic Programming  Proc. 1994 Intl. Symp., 554568
, 1995
"... We present a language containing names of ground expressions and a corresponding simple extension to SLDresolution which allows metalevel computation and interlevel communication through reflection. The extended language allows significant freedom in the choice of names and as an example of a possi ..."
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Cited by 5 (5 self)
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We present a language containing names of ground expressions and a corresponding simple extension to SLDresolution which allows metalevel computation and interlevel communication through reflection. The extended language allows significant freedom in the choice of names and as an example of a possible policy we discuss selfnaming expressions. We go on to present a language in which the choice of naming relation has been partly determined by specifying that names of compound expressions are compositional. This is a sensible design decision and we present in detail a rewrite system for extended unification for the language, having certain similarities with a constraint solving system over names. Comparisons are made with related languages and systems. This paper was presented at the 1994 International Symposium on Logic Programming, held in Ithaca, New York. P. Dell'Acqua has been supported by both Universit`a degli Studi di Milano and Uppsala Univ. 1 Introduction This paper prese...
SelfChecking Prover Study  Final Report
, 1995
"... this report includes an overview of the research and the final deliverables funded on the SRI project. Some of these build on results of the Computer Laboratory project and the contributions of Mr. John Harrison, Dr. Wai Wong and Dr. Joakim von Wright of the University of Cambridge Computer Laborato ..."
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Cited by 1 (0 self)
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this report includes an overview of the research and the final deliverables funded on the SRI project. Some of these build on results of the Computer Laboratory project and the contributions of Mr. John Harrison, Dr. Wai Wong and Dr. Joakim von Wright of the University of Cambridge Computer Laboratory are gratefully acknowledged. Research tasks
A Basis for a System Development Methodology
 Proceedings of the International and Interdisciplinary Conference on Modelling and Using Context, CONTEXT 97
, 1997
"... We propose a software architecture for usercooperative systems, like knowledge systems. This architecture incorporates important notions for building up a context, such as cooperation, explanations and incremental knowledge acquisition. Our main concern in this paper is representation methodology. ..."
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We propose a software architecture for usercooperative systems, like knowledge systems. This architecture incorporates important notions for building up a context, such as cooperation, explanations and incremental knowledge acquisition. Our main concern in this paper is representation methodology. We show that the architecture can be realized as a pure first order theory, which we argue constitutes a good basis for system development. A declarative relational language promotes modularity, clarity and maintainability. The system we outline is implemented in logic programming.
A Meta Constraint Logic Programming Scheme
, 1995
"... We present a Meta Constraint Logic Programming (MCLP) general scheme. The idea behind the work concerns the possibility of building meta CLP architectures by adding CLP solvers as meta level reasoners on the constraints of the underlying object systems. In this way, we are able not only to increase ..."
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We present a Meta Constraint Logic Programming (MCLP) general scheme. The idea behind the work concerns the possibility of building meta CLP architectures by adding CLP solvers as meta level reasoners on the constraints of the underlying object systems. In this way, we are able not only to increase the expressive power of CLP, but also to implement several constraint satisfaction techniques like arc, path and in general, kconsistency by using lower degrees of consistency algorithms in order to obtain higher degrees of consistency. T...
Integrating Reflection into SLDresolution (Extended Abstract)
, 1995
"... In this paper we present an extension of SLDresolution that allows us to model reflection rules in metalevel architectures. We employ an abstract language, introduce the concept of a name theory for such a language, and present an inference system that is parameterized with a name theory. The propo ..."
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In this paper we present an extension of SLDresolution that allows us to model reflection rules in metalevel architectures. We employ an abstract language, introduce the concept of a name theory for such a language, and present an inference system that is parameterized with a name theory. The proposed mechanism is completely general in such a way that for any metalevel architecture where the procedural semantics is independent of the specific device for unification and naming mechanism, a similar generalization is also possible.