SLD-Resolution Reduction of Second-Order Horn Fragments

Tourret, Sophie; Cropper, Andrew

doi:10.1007/978-3-030-19570-0_17

Cited by 3 publications

(10 citation statements)

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“…they considered the case where factorisation [51] was allowed when resolving two clauses, which is not implemented in practice in current MIL systems. For this reason, although Section 5 in [61] and Section 5.1 in the present paper seemingly consider the same problem, the results are opposite to one another. Third, in addition to entailment and derivation reduction, we also consider subsumption reduction.…”

Section: Clause Redundancymentioning

confidence: 52%

“…As mentioned in the introduction, entailment reduction can be too strong a form of reduction. We therefore describe a new form of reduction based on derivability [16,61]. Although our notion of derivation reduction can be defined for any proof system (such as unconstrained resolution as is done in [61]) we focus on SLD-resolution because we want to reduce sets of metarules, which are definite clauses.…”

Section: Derivation Reductionmentioning

confidence: 99%

“…They demonstrated on the Michalski trains dataset that the partially derivationally reduced set of metarules outperforms the entailment reduced set. In similar work Cropper and Tourret elaborated on their graph theoretic techniques and expanded the results to unconstrained resolution [61].…”

Section: Clause Redundancymentioning

confidence: 99%

“…In all cases we provide additional theoretical results showing whether certain fragments can be reduced, and, where possible, show the actual reductions. Second, Cropper and Tourret [61] focused on derivation reduction modulo first-order variable unification, i.e. they considered the case where factorisation [51] was allowed when resolving two clauses, which is not implemented in practice in current MIL systems.…”

Section: Clause Redundancymentioning

confidence: 99%

“…As mentioned in the introduction, entailment reduction can be too strong a form of reduction. We therefore describe a new form of reduction based on derivability [16,61].…”

Section: Derivation Reductionmentioning

confidence: 99%

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Logical reduction of metarules

Cropper

Tourret

2019

Mach Learn

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Many forms of inductive logic programming (ILP) use metarules, second-order Horn clauses, to define the structure of learnable programs and thus the hypothesis space. Deciding which metarules to use for a given learning task is a major open problem and is a trade-off between efficiency and expressivity: the hypothesis space grows given more metarules, so we wish to use fewer metarules, but if we use too few metarules then we lose expressivity. In this paper, we study whether fragments of metarules can be logically reduced to minimal finite subsets. We consider two traditional forms of logical reduction: subsumption and entailment. We also consider a new reduction technique called derivation reduction, which is based on SLD-resolution. We compute reduced sets of metarules for fragments relevant to ILP and theoretically show whether these reduced sets are reductions for more general infinite fragments. We experimentally compare learning with reduced sets of metarules on three domains: Michalski trains, string transformations, and game rules. In general, derivation reduced sets of metarules outperforms subsumption and entailment reduced sets, both in terms of predictive accuracies and learning times.

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Section: Clause Redundancymentioning

confidence: 52%

Section: Derivation Reductionmentioning

confidence: 99%

Section: Clause Redundancymentioning

confidence: 99%

Section: Clause Redundancymentioning

confidence: 99%

“…As mentioned in the introduction, entailment reduction can be too strong a form of reduction. We therefore describe a new form of reduction based on derivability [16,61].…”

Section: Derivation Reductionmentioning

confidence: 99%

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Logical reduction of metarules

Cropper

Tourret

2019

Mach Learn

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Inductive Logic Programming At 30: A New Introduction

Cropper

Dumančić

2022

jair

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Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a hypothesis (a set of logical rules) that generalises training examples. As ILP turns 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main learning settings; describe the building blocks of an ILP system; compare several systems on several dimensions; describe four systems (Aleph, TILDE, ASPAL, and Metagol); highlight key application areas; and, finally, summarise current limitations and directions for future research.

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Inductive logic programming at 30: a new introduction

Cropper¹,

Dumančić²

2020

Preprint

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Inductive logic programming (ILP) is a form of machine learning. The goal of ILP is to induce a logic program (a set of logical rules) that generalises training examples. As ILP approaches 30, we provide a new introduction to the field. We introduce the necessary logical notation and the main ILP learning settings. We describe the main building blocks of an ILP system. We compare several ILP systems on several dimensions. We detail four systems (Aleph, TILDE, ASPAL, and Metagol). We contrast ILP with other forms of machine learning. Finally, we summarise the current limitations and outline promising directions for future research. Scenario 1: concept learningSuppose you want to predict whether someone is happy. To do so, you ask four people (alice, bob, claire, and dave) whether they are happy. You also ask additional information, specifically their job, their company, and whether they like lego. Standard ML approaches would represent this data as a table, such as Table 1. Using standard ML terminology, each row represents a training example, the first three columns (name, job, and enjoys lego) represent features, and the final column (happy) represents the label or classification. Given this table, the goal of standard ML approaches is to induce a hypothesis to predict the label (the value for the column

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SLD-Resolution Reduction of Second-Order Horn Fragments

Cited by 3 publications

References 48 publications

Logical reduction of metarules

Logical reduction of metarules

Inductive Logic Programming At 30: A New Introduction

Inductive logic programming at 30: a new introduction

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