Learning Concepts Definable in First-Order Logic with Counting

Bergerem, Steffen van

doi:10.1109/lics.2019.8785811

Cited by 5 publications

(4 citation statements)

References 19 publications

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“…Other recent work studies the parameterized complexity of learning queries in FO [van Bergerem et al 2022], algorithms for learning in FO with counting [van Bergerem 2019], and learning in description logics [Funk et al 2019]. Applications for FO learning have emerged, e.g., synthesizing invariants [Garg et al 2014Hance et al 2021;Koenig et al 2020Koenig et al , 2022Yao et al 2021] and learning program properties [Astorga et al 2019[Astorga et al , 2021Miltner et al 2020].…”

Section: Related Workmentioning

confidence: 99%

Languages with Decidable Learning: A Meta-theorem

Krogmeier¹,

Madhusudan²

2023

Preprint

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We study expression learning problems with syntactic restrictions and introduce the class of finite-aspect checkable languages to characterize symbolic languages that admit decidable learning. The semantics of such languages can be defined using a bounded amount of auxiliary information, which we call semantic aspects, that is independent of expression size but depends on a fixed structure over which evaluation occurs. We introduce a generic programming language for expressing model-checking programs that work over expression syntax trees, and we give a meta-theorem that connects such programs for finite-aspect checkable languages to finite tree automata, which allows us to derive new decidable learning results and decision procedures for several expression learning problems by writing model-checking programs in the programming language.

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Section: Related Workmentioning

confidence: 99%

Languages with Decidable Learning: A Meta-theorem

Krogmeier¹,

Madhusudan²

2023

Preprint

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“…FO, FOW 1 (P), FOWA 1 (P), FOWA(P)), let σ be a signature, and let Φ ⊆ L[σ, S, W] be a set of formulas ϕ(x, ȳ) with |x| = k and |ȳ| = . For a (σ, W)-structure A, we follow the same approach as [4,7,8,10,24] and consider the instance space X = A k and concepts from the concept class C(Φ, A, k,…”

Section: Learning Concepts On Weighted Structuresmentioning

confidence: 99%

“…To obtain a reasonable running time, we intend to find algorithms that compute a hypothesis in sublinear time, measured in the size of the background structure. This local access model has already been studied for relational structures in [8,24] for concepts definable in FO or in FOCN(P). Modifications of the local access model for strings and trees have been studied in [4,7].…”

Section: Learning Concepts On Weighted Structuresmentioning

confidence: 99%

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Learning Concepts Described by Weight Aggregation Logic

van Bergerem,

Schweikardt

2020

Preprint

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We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows to aggregate weights of tuples, compare such aggregates, and use them to build more complex formulas. We provide locality properties of fragments of this logic including Feferman-Vaught decompositions and a Gaifman normal form for a fragment called FOW 1 , as well as a localisation theorem for a larger fragment called FOWA 1 . This fragment can express concepts from various machine learning scenarios. Using the locality properties, we show that concepts definable in FOWA 1 over a weighted background structure of at most polylogarithmic degree are agnostically PAC-learnable in polylogarithmic time after pseudo-linear time preprocessing.

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Learning formulas in finite variable logics

Krogmeier

Madhusudan

2022

Proc. ACM Program. Lang.

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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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Learning Concepts Definable in First-Order Logic with Counting

Cited by 5 publications

References 19 publications

Languages with Decidable Learning: A Meta-theorem

Languages with Decidable Learning: A Meta-theorem

Learning Concepts Described by Weight Aggregation Logic

Learning formulas in finite variable logics

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