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A Metatheory of a Mechanized Object Theory
, 1994
"... In this paper we propose a metatheory, MT which represents the computation which implements its object theory, OT, and, in particular, the computation which implements deduction in OT. To emphasize this fact we say that MT is a metatheory of a mechanized object theory. MT has some "unusual&q ..."
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Cited by 21 (10 self)
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In this paper we propose a metatheory, MT which represents the computation which implements its object theory, OT, and, in particular, the computation which implements deduction in OT. To emphasize this fact we say that MT is a metatheory of a mechanized object theory. MT has some "unusual" properties, e.g. it explicitly represents failure in the application of inference rules, and the fact that large amounts of the code implementing OT are partial, i.e. they work only for a limited class of inputs. These properties allow us to use MT to express and prove tactics, i.e. expressions which specify how to compose possibly failing applications of inference rules, to interpret them procedurally to assert theorems in OT, to compile them into the system implementation code, and, finally, to generate MT automatically from the system code. The definition of MT is part of a larger project which aims at the implementation of selfreflective systems, i.e. systems which are able to intros...
Program Tactics and Logic Tactics
 IN PROCEEDINGS 5TH INTNL. CONFERENCE ON LOGIC PROGRAMMING AND AUTOMATED REASONING (LPAR'94
, 1994
"... In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theor ..."
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Cited by 19 (10 self)
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In this paper we present a first order classical metatheory, called MT, with the following properties: (1) tactics are terms of the language of MT (we call these tactics, Logic Tactics); (2) there exists a mapping between Logic Tactics and the tactics developed as programs within the GETFOL theorem prover (we call these tactics, Program Tactics). MT is expressive enough to represent the most interesting tacticals, i.e. then, orelse, try, progress and repeat. repeat allows us to express Logic Tactics which correspond to Program Tactics which may not terminate. This work is part of a larger project which aims at the development and mechanization of a metatheory which can be used to reason about, extend and, possibly, modify the code implementing Program Tactics and the GETFOL basic inference rules.
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 15 (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.
Using Reflection Techniques for Flexible Problem Solving (with Examples From Diagnosis)
, 1995
"... Flexible problem solving consists of the dynamic selection and configuration of problem solving methods for a particular problem type, depending on the particular problem and the goal of problem solving. In this paper, we propose an architecture that supports such flexible problem solving automatica ..."
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Cited by 9 (2 self)
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Flexible problem solving consists of the dynamic selection and configuration of problem solving methods for a particular problem type, depending on the particular problem and the goal of problem solving. In this paper, we propose an architecture that supports such flexible problem solving automatically. For this purpose, problem solving methods are described in a uniform way, by an abstract model of components, which together define the functionality of the methods. Such an abstract model is used for dynamic selection and configuration of the problem solving methods. The proposed architecture for flexible problem solving consists of well known reflection techniques: two objectmeta relations, a definable naming mechanism and the axiomhood and theoremhood reflection rules. We have succeeded in using standard metaarchitecture techniques to enable flexible problem solving. 1 Introduction The literature on Knowledge Engineering of the past decade has identified a number of different probl...
Metaprogramming with Theory Systems
, 1995
"... A theory system is a collection of interdependent theories, some if which stand in a meta/object relationship, forming an arbitrary number of metalevels. The main thesis of this chapter is that theory systems constitute a suitable formalism for constructing advanced applications in reasoning and so ..."
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A theory system is a collection of interdependent theories, some if which stand in a meta/object relationship, forming an arbitrary number of metalevels. The main thesis of this chapter is that theory systems constitute a suitable formalism for constructing advanced applications in reasoning and software engineering. The Alloy language for defining theory systems is introduced, its syntax is defined and a collection of inference rules is presented. A number of problems suitable for theory systems are discussed, with program examples given in Alloy. Some current implementation issues and future extensions are discussed. This paper appears as a chapter in Metalogics and Logic Programming, edited by K. Apt and F. Turini, and published by MIT Press in 1995. 1 Outline A conventional logic program can be seen as the nonlogical axioms of a single theory. This chapter presents a thesis that we obtain a more powerful tool for applications in artificial intelligence and software engineering...
Concurrent Metareasoning
"... Metaresoning is again under focus in the AI community. Here in this paper, a new classification for types of metareasoning has been proposed. In recent years, only the ones that are here named as premetareasoning and parametareasoning have been studied. The first one is for predicting the best com ..."
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Metaresoning is again under focus in the AI community. Here in this paper, a new classification for types of metareasoning has been proposed. In recent years, only the ones that are here named as premetareasoning and parametareasoning have been studied. The first one is for predicting the best computation path for having better performance programs. The second, mostly known as interruptible anytime algorithm, is to limit the computation time externally when the approximate answer is better than nothing. One other type of metareasoning (called here as postmetareasoning) is discussed in a case study. It has been shown as an effective method for reducing error in selflocalization. Based on the measurements in the case study, the postmetareasoning argued as useful when the effectiveness of reasoning methods are not known by the designer or when the system learns the reasoning methods and should evaluate and use the best one automatically. As the postmetareasoning is based on the results of different isolated reasoning methods, it is possible to be handled in parallel. The speed of postmetareasoning in such a case is determined by the time required by the slowest reasoning method and the postmetaresoning itself.
Building and Executing Proof Strategies in a Formal Metatheory
 Advances in Artifical Intelligence: Proceedings of the Third Congress of the Italian Association for Artificial Intelligence, IA*AI'93, Volume 728 of Lecture Notes in Computer Science
, 1993
"... This paper describes how "safe" proof strategies are represented and executed in the interactive theorem prover GETFOL. A formal metatheory (MT) describes and allows to reason about object level inference. A class of MT terms, called logic tactics, is used to represent proof strategies. ..."
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This paper describes how "safe" proof strategies are represented and executed in the interactive theorem prover GETFOL. A formal metatheory (MT) describes and allows to reason about object level inference. A class of MT terms, called logic tactics, is used to represent proof strategies. The semantic attachment facility and the evaluation mechanism of the GETFOL system have been used to provide the procedural interpretation of logic tactics. The execution of logic tactics is then proved to be "safe" under the termination condition. The implementation within the GETFOL system is described and the synthesis of a logic tactic implementing a normalizer in negative normal form is presented as a case study. 1 Introduction As pointed out in [GMMW77], interactive theorem proving [GMW79, CAB + 86, Pau89] has been growing up in the continuum existing between proof checking [deB70, Wey80] on one side and automated theorem proving [Rob65, And81, Bib81] on the other. Interactive theorem...