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Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization

Authors:

Scott Dietzen,

Frank PfenningAuthors Info & Claims

Machine Learning, Volume 9, Issue 1

Pages 23 - 55

https://doi.org/10.1023/A:1022676712939

Published: 01 June 1992 Publication History

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Abstract

Certain tasks, such as formal program development and theorem proving, fundamentally rely upon the manipulation of higher-order objects such as functions and predicates. Computing tools intended to assist in performing these tasks are at present inadequate in both the amount of ‘knowledge’ they contain (i.e., the level of support they provide) and in their ability to ‘learn’ (i.e., their capacity to enhance that support over time). The application of a relevant machine learning technique—explanation-based generalization (EBG)—has thus far been limited to first-order problem representations. We extend EBG to generalize higher-order values, thereby enabling its application to higher-order problem encodings.

Logic programming provides a uniform framework in which all aspects of explanation-based generalization and learning may be defined and carried out. First-order Horn logics (e.g., Prolog) are not, however, well suited to higher-order applications. Instead, we employ λProlog, a higher-order logic programming language, as our basic framework for realizing higher-order EBG. In order to capture the distinction between domain theory and training instance upon which EBG relies, we extend λProlog with the necessity operator □ of modal logic. We develop a meta-interpreter realizing EBG for the extended language, λ^□ Prolog, and provide examples of higher-order EBG.

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Tate RStepp MLerner S(2010)Generating compiler optimizations from proofsACM SIGPLAN Notices10.1145/1707801.170634545:1(389-402)Online publication date: 17-Jan-2010
https://dl.acm.org/doi/10.1145/1707801.1706345
Tate RStepp MLerner SHermenegildo MPalsberg J(2010)Generating compiler optimizations from proofsProceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages10.1145/1706299.1706345(389-402)Online publication date: 17-Jan-2010
https://dl.acm.org/doi/10.1145/1706299.1706345

Index Terms

Higher-Order and Modal Logic as a Framework for Explanation-Based Generalization
1. Computing methodologies
  1. Artificial intelligence
    1. Knowledge representation and reasoning
      1. Logic programming and answer set programming
  2. Machine learning
2. Theory of computation
  1. Logic
    1. Constraint and logic programming

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Published In

Machine Language Volume 9, Issue 1

June 1992

93 pages

ISSN:0885-6125

Editors:
Jaime G. Carbonell
Carnegie Mellon Univ., Pittsburgh, PA
,
Thomas Dietterich
Oregon State Univ., Corvallis

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Kluwer Academic Publishers

United States

Publication History

Published: 01 June 1992

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Tate RStepp MLerner S(2010)Generating compiler optimizations from proofsACM SIGPLAN Notices10.1145/1707801.170634545:1(389-402)Online publication date: 17-Jan-2010
https://dl.acm.org/doi/10.1145/1707801.1706345
Tate RStepp MLerner SHermenegildo MPalsberg J(2010)Generating compiler optimizations from proofsProceedings of the 37th annual ACM SIGPLAN-SIGACT symposium on Principles of programming languages10.1145/1706299.1706345(389-402)Online publication date: 17-Jan-2010
https://dl.acm.org/doi/10.1145/1706299.1706345

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Recommendations

Modal Hyperdoctrine: Higher-Order and Non-normal Extensions

Self-Formalisation of Higher-Order Logic

Solving Modal Logic Problems by Translation to Higher-Order Logic

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