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The Semantics of Reflected Proof
 IN PROC. OF FIFTH SYMP. ON LOGIC IN COMP. SCI
, 1990
"... We begin to lay the foundations for reasoning about proofs whose steps include both invocations of programs to build subproofs (tactics) and references to representations of proofs themselves (reflected proofs). The main result is the definition of a single type of proof which can mention itself, ..."
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Cited by 90 (11 self)
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We begin to lay the foundations for reasoning about proofs whose steps include both invocations of programs to build subproofs (tactics) and references to representations of proofs themselves (reflected proofs). The main result is the definition of a single type of proof which can mention itself, using a new technique which finds a fixed point of a mapping between metalanguage and object language. This single type contrasts with hierarchies of types used in other approaches to accomplish the same classification. We show that these proofs are valid, and that every proof can be reduced to a proof involving only primitive inference rules. We also show how to extend the results to proofs from which programs (such as tactics) can be derived, and to proofs that can refer to a library of definitions and previously proven theorems. We believe that the mechanism of reflection is fundamental in building proof development systems, and we illustrate its power with applications to automating reasoning and describing modes of computation.
MetaLevel Inference Systems
, 1991
"... 1.1 Goals of this book................................ 13 ..."
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Cited by 16 (4 self)
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1.1 Goals of this book................................ 13
Metacognition in computation: A selected history
 In Proceedings of the AAAI Spring Symposium on Metacognition in Computation (pp
, 2005
"... This paper takes a cursory examination of some of the research roots concerning the topic of metacognition in computation. Various disciplines have examined the many phenomena of metacognition and have produced numerous results, both positive and negative. I discuss some of these aspects of cognitio ..."
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Cited by 2 (0 self)
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This paper takes a cursory examination of some of the research roots concerning the topic of metacognition in computation. Various disciplines have examined the many phenomena of metacognition and have produced numerous results, both positive and negative. I discuss some of these aspects of cognition about cognition and the results concerning them from the point of view of the psychologist and the computer scientist, and I attempt to place them in the context of computational theories. I examine metacognition with respect to both problem solving and to comprehension processes of cognition. The history is limited to the 20th century.