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Learning formulas in finite variable logics

Authors:

Paul Krogmeier,

P. MadhusudanAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 6, Issue POPL

Article No.: 10, Pages 1 - 28

https://doi.org/10.1145/3498671

Published: 12 January 2022 Publication History

Abstract

We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that classify a set of positively- and negatively-labeled structures. We give algorithms for realizability and synthesis of such formulas along with upper and lower bounds. We also establish positive results using our technique for other logics and variants of the learning problem, including first-order logic with least fixed point definitions, higher-order logics, and synthesis of queries and terms with recursively-defined functions.

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Video advertisement for the talk "Learning Formulas in Finite Variable Logics" at POPL 2022. Abstract: We consider grammar-restricted exact learning of formulas and terms in finite variable logics. We propose a novel and versatile automata-theoretic technique for solving such problems. We first show results for learning formulas that classify a set of positively- and negatively-labeled structures. We give algorithms for realizability and synthesis of such formulas along with upper and lower bounds. We also establish positive results using our technique for other logics and variants of the learning problem, including first-order logic with least fixed point definitions, higher-order logics, and synthesis of queries and terms with recursively-defined functions.

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Cited By

Krogmeier PMadhusudan P(2023)Languages with Decidable Learning: A Meta-theoremProceedings of the ACM on Programming Languages10.1145/35860327:OOPSLA1(143-171)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586032
Murali APeña LBlanchard ELöding CMadhusudan P(2022)Model-guided synthesis of inductive lemmas for FOL with least fixpointsProceedings of the ACM on Programming Languages10.1145/35633546:OOPSLA2(1873-1902)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563354
Krogmeier PLin ZMurali AMadhusudan P(2022)Synthesizing axiomatizations using logic learningProceedings of the ACM on Programming Languages10.1145/35633486:OOPSLA2(1697-1725)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563348

Index Terms

Learning formulas in finite variable logics
1. Computing methodologies
  1. Machine learning
    1. Machine learning approaches
2. Theory of computation
  1. Formal languages and automata theory
    1. Tree languages

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cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 6, Issue POPL

January 2022

1886 pages

EISSN:2475-1421

DOI:10.1145/3511309

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Published: 12 January 2022

Published in PACMPL Volume 6, Issue POPL

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Krogmeier PMadhusudan P(2023)Languages with Decidable Learning: A Meta-theoremProceedings of the ACM on Programming Languages10.1145/35860327:OOPSLA1(143-171)Online publication date: 6-Apr-2023
https://dl.acm.org/doi/10.1145/3586032
Murali APeña LBlanchard ELöding CMadhusudan P(2022)Model-guided synthesis of inductive lemmas for FOL with least fixpointsProceedings of the ACM on Programming Languages10.1145/35633546:OOPSLA2(1873-1902)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563354
Krogmeier PLin ZMurali AMadhusudan P(2022)Synthesizing axiomatizations using logic learningProceedings of the ACM on Programming Languages10.1145/35633486:OOPSLA2(1697-1725)Online publication date: 31-Oct-2022
https://dl.acm.org/doi/10.1145/3563348

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