Generating Random Logic Programs Using Constraint Programming

Dilkas, Paulius; Belle, Vaishak

doi:10.1007/978-3-030-58475-7_48

“…Both exact solvers, based on knowledge compilation [23], as well as approximate solvers [19] have emerged in the recent years, as have lifted techniques [95] that exploit the relational syntax during inference (but in a finite domain setting). For ideas on generating such representations randomly to assess scalability and compare inference algorithms, see [29], for example.…”

Section: Logic Vs Machine Learningmentioning

confidence: 99%

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Belle

¹

2020

Lecture Notes in Computer Science

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The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains.

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“…Both exact solvers, based on knowledge compilation [23], as well as approximate solvers [19] have emerged in the recent years, as have lifted techniques [95] that exploit the relational syntax during inference (but in a finite domain setting). For ideas on generating such representations randomly to assess scalability and compare inference algorithms, see [29], for example.…”

Section: Logic Vs Machine Learningmentioning

confidence: 99%

Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains

Belle¹

2020

Preprint

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The tension between deduction and induction is perhaps the most fundamental issue in areas such as philosophy, cognition and artificial intelligence (AI). The deduction camp concerns itself with questions about the expressiveness of formal languages for capturing knowledge about the world, together with proof systems for reasoning from such knowledge bases. The learning camp attempts to generalize from examples about partial descriptions about the world. In AI, historically, these camps have loosely divided the development of the field, but advances in cross-over areas such as statistical relational learning, neuro-symbolic systems, and high-level control have illustrated that the dichotomy is not very constructive, and perhaps even ill-formed. In this article, we survey work that provides further evidence for the connections between logic and learning. Our narrative is structured in terms of three strands: logic versus learning, machine learning for logic, and logic for machine learning, but naturally, there is considerable overlap. We place an emphasis on the following "sore" point: there is a common misconception that logic is for discrete properties, whereas probability theory and machine learning, more generally, is for continuous properties. We report on results that challenge this view on the limitations of logic, and expose the role that logic can play for learning in infinite domains.

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“…a new parameter called solution density. There is also a recent attempt [33] to compare WMC algorithms on random instances of a particular application of WMC, i.e., probabilistic logic programs. However, it finds no meaningful differences among the algorithms in that context.…”

Section: Introductionmentioning

confidence: 99%

Generating Random Instances of Weighted Model Counting

Dilkas

¹

2023

Lecture Notes in Computer Science

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Weighted model counting (WMC) is an extension of propositional model counting with applications to probabilistic inference and other areas of artificial intelligence. In recent experiments, WMC algorithms perform similarly overall but with significant differences on specific subsets of benchmarks. A good understanding of the differences in the performance of algorithms requires identifying key characteristics that favour some algorithms over others. In this paper, we introduce a random model for WMC instances with a parameter that influences primal treewidth-the parameter most commonly used to characterise the difficulty of an instance. We then use this model to experimentally compare the performance of WMC algorithms c2d, Cachet, d4, DPMC, and miniC2D. Using these random instances, we show that the easy-hard-easy pattern is different for algorithms based on dynamic programming and algebraic decision diagrams than for all other solvers. We also show how all WMC algorithms scale exponentially with respect to primal treewidth and how this scalability varies across algorithms and densities. Finally, we combine insights from experiments involving both random and competition instances to determine how the best-performing WMC algorithm varies depending on clause density and primal treewidth.

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Generating Random Logic Programs Using Constraint Programming

Cited by 3 publications

References 27 publications

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Symbolic Logic Meets Machine Learning: A Brief Survey in Infinite Domains

Symbolic Logic meets Machine Learning: A Brief Survey in Infinite Domains

Generating Random Instances of Weighted Model Counting

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