Inductive Logic Programming At 30: A New Introduction

In the paper

“which is considered essential for human-like AI (Lake et al., 2016).”

What the sources say

• Supported

  Section 4.2 treats transfer and learning-to-learn as important to making AI learn new tasks with human-like speed and flexibility. Sections 6.2 and 6.3 likewise describe learning new concepts as they are encountered and reusing knowledge across tasks as goals for human-like AI. Together, these support the paraphrase, although the authors do not use the phrase “lifelong and transfer learning” as a single requirement. (LLM, conf=0.85)

  cites Lake et al., 2016 source

In the paper

“Because of the expressivity of logic programs, ILP can learn complex relational theories, such as cellular automata (Inoue et al., 2014; Evans et al., 2021), event calculus theories (Katzouris et al., 2015), and Petri nets (Bain & Srinivasan, 2018), and various forms of non-monotonic programs (Bain & Muggleton, 1991; Inoue & Kudoh, 1997; Sakama, 2001).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Inoue et al., 2014
• Supported

  The Evans et al. citation is attached to the cellular-automata example, not the other examples in the sentence. In §5.1.2 (page unavailable), the paper reports that its symbolic Apperception Engine inferred dynamics from elementary cellular-automaton sequences and correctly predicted 249 of 256 trajectories. Section 5.2.4 distinguishes that system from ILASP, which could not solve the ECA tasks because of memory requirements; the paper therefore supports the example of learning cellular-automaton dynamics, not a claim that ILASP solved those tasks. (LLM, conf=0.87)

  cites Evans et al., 2021 source
• Supported

  The citation is attached specifically to “event calculus theories,” not to the sentence’s other examples. Section 2.2 states that ILP is used to learn event definitions in the form of domain-specific Event Calculus axioms. (LLM, conf=0.93)

  cites Katzouris et al., 2015 source

In the paper

“Prolog (Kowalski, 1988; Colmerauer & Roussel, 1993) is a logic programming language based on SLD-resolution and is therefore restricted to Horn clauses.”

What the sources say

• Partly supported

  In “The Edinburgh–Marseilles” (page unavailable), Kowalski identifies SLD-resolution as a procedure for Horn clauses and associates Prolog with logic programming using the Horn-clause subset. The passages do not explicitly say that Prolog is based on SLD-resolution or that it is restricted to Horn clauses; the latter is stronger than the source establishes. (LLM, conf=0.78)

  cites Kowalski, 1988 sourceExperimental — accuracy not yet measured
• Partly supported

  In “Colmerauer and Roussel” (p. 3), the authors describe choosing linear resolution and say the strategy is complete when only Horn clauses are used. “Part IV. The final Prolog” (p. 10) also describes Prolog as resolution-based. These passages do not establish that Prolog is restricted to Horn clauses; the copy calls the method SL-resolution rather than SLD-resolution. (LLM, conf=0.84)

  cites Colmerauer & Roussel, 1993 sourceExperimental — accuracy not yet measured

In the paper

“Quinlan's (1990) FOIL system is one of the most well-known ILP systems and is a natural extension of ID3 (Quinlan, 1986) from the propositional setting to the first-order setting.”

What the sources say

• Supported

  Section 4 identifies FOIL as Quinlan’s system, traces its ancestry to ID3, and says it uses an information-based search heuristic like ID3. The Abstract and Discussion describe its adaptation of attribute-value learning techniques to a first-order formalism. “One of the most well-known” is the citing authors’ characterization, not a finding attributed to the 1990 paper. (LLM, conf=0.88)

  cites Quinlan, 1990 source
• Supported

  The 1986 citation is attached to ID3, not to the claims about FOIL. The Introduction identifies ID3 as a Quinlan program, and Section 3 describes its decision-tree method using attributes of objects. This supports the citation’s identification of ID3 in the sentence. (LLM, conf=0.91)

  cites Quinlan, 1986 source

In the paper

“A third approach has recently emerged called meta-level ILP (Inoue et al., 2013; Muggleton et al., 2015; Inoue, 2016; Law et al., 2020; Cropper & Morel, 2021).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Inoue et al., 2013
• Supported

  The Introduction (p. 2) identifies meta-interpretive learning (MIL) as an ILP technique built around a meta-interpreter. Related Work (p. 4) contrasts it with earlier ILP approaches, supporting its citation as an example of the newer meta-level approach. (LLM, conf=0.88)

  cites Muggleton et al., 2015 source
• ?Not checked — no full text of the sourcecites Inoue, 2016

In the paper

“Other recent work focuses on learning from transitions (Inoue et al., 2014; Evans et al., 2021; Ribeiro et al., 2020) and learning from answer sets (Law et al., 2014).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Inoue et al., 2014
• Supported

  Evans et al. describe their own task as constructing rules and other model components from a sequence of observed states (§7.2, page not provided). That supports citing this paper as an example of work on learning from transitions. The separate claim about learning from answer sets is attached to Law et al., not Evans et al. (LLM, conf=0.90)

  cites Evans et al., 2021 source
• ?Not checked — no full text of the sourcecites Law et al., 2014 source

In the paper

“LFE is by far the most popular ILP setting (Shapiro, 1983; Muggleton, 1987; Muggleton & Buntine, 1988; Muggleton & Feng, 1990; Quinlan, 1990; Muggleton, 1995; Bratko, 1999; Srinivasan, 2001; Ray, 2009; Ahlgren & Yuen, 2013; Muggleton et al., 2015; Cropper & Muggleton, 2016; Kaminski et al., 2018; Cropper & Morel, 2021).”

What the sources say

• ?Not checked — no full text of the sourcecites Shapiro, 1983 source
• ?Not checked — no full text of the sourcecites Muggleton, 1987
• Partly supported

  Section 3.2 (p. 11) says the paper’s problem setting is based on ILP learning from entailment, so the source is an example of that setting. It does not say that learning from entailment is the most popular ILP setting, let alone by far. (LLM, conf=0.82)

  cites Cropper & Morel, 2021 sourceExperimental — accuracy not yet measured

In the paper

“The second most popular (De Raedt & Dehaspe, 1997; Blockeel & De Raedt, 1998; Law et al., 2014) learning setting is LFI where an example is an interpretation, i.e. a set of facts.”

What the sources say

• Partly supported

  Section 3.3.3 states that examples in the paper’s learning-from-interpretations setting are interpretations, and Section 2 describes a Herbrand interpretation as a set of ground facts. Section 3 calls normal inductive logic programming the setting used by the large majority of systems, but does not rank learning from interpretations as the second most popular; its numbered list is a list of formalisations, not a popularity ranking. Page numbers were not available in our copy. (LLM, conf=0.88)

  cites De Raedt & Dehaspe, 1997 sourceExperimental — accuracy not yet measured
• Partly supported

  The Introduction and Section 2 identify the setting as learning from interpretations and describe each example as a Prolog program encoding its properties, supporting the claim about LFI examples. Neither passage establishes that LFI is the second most popular learning setting. (LLM, conf=0.88)

  cites Blockeel & De Raedt, 1998 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites Law et al., 2014 source

In the paper

“Evans et al. (2021) use constraints to induce theories to explain sensory sequences.”

What the sources say

• Supported

  The Introduction describes a symbolic causal theory containing constraints that must explain the sensory sequence. It also says the Apperception Engine synthesizes such a theory from a sensory sequence. (LLM, conf=0.92)

  cites Evans et al., 2021 source

In the paper

“However, some systems (Shapiro, 1983; Bratko, 1999; Cropper & Morel, 2021) induce theories formed of multiple clauses and thus require generality orders over clausal theories .”

What the sources say

• ?Not checked — no full text of the sourcecites Shapiro, 1983 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Bratko, 1999
• Supported

  Section 3.1 (p. 10) defines a clausal theory as a set of clauses and uses “program” as a synonym for theory. Section 3.4 (pp. 14–15) extends subsumption to clausal theories and uses it to define generalisation and specialisation of hypotheses, supporting the claim about generality orders for multi-clause theories. (LLM, conf=0.92)

  cites Cropper & Morel, 2021 source

In the paper

“The above paragraph refers only to generality orders on single clauses, as many systems employ the covering algorithm whereby hypotheses are constructed iteratively clause by clause (Quinlan, 1990; De Raedt & Dehaspe, 1997; Muggleton, 1995; Blockeel & De Raedt, 1998; Srinivasan, 2001).”

What the sources say

• Supported

  Section 4, “FOIL, a system that constructs definitions” (page unavailable), says FOIL finds clauses one at a time, removing tuples explained by each clause before finding the next. Section 2.2 describes the same repeated covering procedure for the AQ family, supporting the statement that multiple systems use this approach. (LLM, conf=0.93)

  cites Quinlan, 1990 source
• Supported

  Section 5.3 says that other inductive logic programming approaches employ Michalski’s covering algorithm. The algorithm description in Section 4 shows a hypothesis being built by adding clauses one at a time, consistent with the citing sentence’s clause-by-clause description. The paper distinguishes those covering approaches from its own Claudien approach. (LLM, conf=0.86)

  cites De Raedt & Dehaspe, 1997 source
• ?Not checked — no full text of the sourcecites Muggleton, 1995 source

In the paper

“Top-down algorithms, (Quinlan, 1990; Blockeel & De Raedt, 1998; Bratko, 1999; Muggleton et al., 2008) start with a general hypothesis and then specialise it.”

What the sources say

• Supported

  Section 4.1 describes FOIL beginning a clause with only its left-hand side, then adding literals to the right-hand side one at a time. That is a top-down progression from a general clause to more specific ones. (LLM, conf=0.91)

  cites Quinlan, 1990 source
• Supported

  Section 4, “Top-down induction of logical decision trees” (page unavailable), describes TILDE refining a node’s query by adding literals to produce a more specific query. It also states that the refinement operator produces clauses subsumed by the original clause, supporting the general-to-specific description. (LLM, conf=0.88)

  cites Blockeel & De Raedt, 1998 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Bratko, 1999

In the paper

“∂ ILP (Evans & Grefenstette, 2018) uses neural networks to solve the problem.”

What the sources say

• Partly supported

  The Introduction and Experiments sections say ∂ILP was connected to a pretrained convolutional neural network to handle ambiguous digit images. Section 4 describes ∂ILP itself as differentiable deduction over weighted logic clauses, so the paper supports neural-network use in that experiment, not as the general mechanism by which ∂ILP solves problems. (LLM, conf=0.82)

  cites Evans & Grefenstette, 2018 sourceExperimental — accuracy not yet measured

In the paper

“For instance, Metagol (Muggleton et al., 2015; Cropper & Muggleton, 2016) uses a Prolog meta-interpreter to search for a proof of a meta-level Prolog program.”

What the sources say

• Supported

  The Implementation section (p. 8) says Metagol D is built around a Prolog meta-interpreter and uses Prolog backtracking search to find a satisfying solution. The Introduction (p. 2) describes the meta-interpreter proving examples while generating a program hypothesis, supporting the citing sentence’s description of its proof search. (LLM, conf=0.88)

  cites Muggleton et al., 2015 source
• ?Not checked — no full text of the sourcecites Cropper & Muggleton, 2016 source

In the paper

“Law et al. (2020) also provide an overview of conflict-driven ILP, which the systems ILASP3 (Law, 2018) and Popper (Cropper & Morel, 2021) adopt.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Law, 2018
• Supported

  The Abstract (p. 1) describes Popper as an ILP system that learns constraints from failed hypotheses. The Introduction (p. 4) says ILASP3 also uses a generate/test/constrain loop and compares how the two systems derive constraints from failures. This supports the characterization of both as adopting conflict-driven ILP. (LLM, conf=0.90)

  cites Cropper & Morel, 2021 source

In the paper

“Learning efficient logic programs has long been considered a difficult problem (Muggleton & De Raedt, 1994; Muggleton et al., 2012), mainly because there is no declarative difference between an efficient program, such as mergesort, and an inefficient program, such as bubble sort.”

What the sources say

• Partly supported

  Section 11.2.1 (p. 668) says that inducing a correct sorting program does not guarantee an efficient one, supporting the difficulty of learning efficient logic programs. It does not say that this difficulty is mainly due to the absence of a declarative difference between efficient and inefficient programs, or use mergesort and bubble sort as examples. (LLM, conf=0.82)

  cites Muggleton & De Raedt, 1994 sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Muggleton et al., 2012

In the paper

“The most common interpretation of an Occamist bias is that amongst all hypotheses consistent with the data, the simplest is the most likely 28 .”

What the sources say

• Partly supported

  Section 8.1.1 (page unavailable) says Occam’s statement has sometimes been construed to mean that, other things being equal, simple hypotheses are more likely to be predictive. It does not call this the most common interpretation, and it discusses predictive performance rather than the likelihood that the simplest data-consistent hypothesis is true. (LLM, conf=0.84)

  cites Schaffer, 1993 sourceExperimental — accuracy not yet measured
• ?Not checked — no full text of the sourcecites Domingos (1999) source

In the paper

“For instance, TILDE extends a decision tree learner (Quinlan, 1986, 1993) to the first-order setting and uses the same information gain methods to induce hypotheses.”

What the sources say

• Supported

  Quinlan describes ID3 as a decision-tree learner (Section 4, pp. 7–8) and explains its information-gain criterion for selecting attributes (Section 4, p. 10). The citation identifies the learner and method that the citing authors say TILDE extends; it does not attribute TILDE itself to Quinlan. (LLM, conf=0.90)

  cites Quinlan, 1986 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Quinlan, 1993

In the paper

“Although preliminary work attempts to tackle this issue (Cropper & Morel, 2021; Cropper, 2022), work is still needed for these approaches to scale to very large problems.”

What the sources say

• Supported

  The citation is attached to the statement that preliminary work attempts to tackle scalability. Section 5.4 (p. 42) explicitly evaluates how Popper scales with the number and size of examples, while §6.1 (p. 45) identifies limitations for future work. The sentence’s conclusion about very large problems is the citing authors’ framing, not a finding attributed specifically to this paper. (LLM, conf=0.88)

  cites Cropper & Morel, 2021 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Cropper, 2022

In the paper

“ASP systems (which combine a grounder and a solver), such as Clingo (Gebser et al., 2014), first take a first-order program as input, ground it using an ASP grounder, and then use an ASP solver to determine whether the ground problem is satisfiable.”

What the sources say

• Supported

  The Introduction (p. 1) describes standard ASP systems as grounding an input program into a propositional program and then using a solver to compute its stable models; it identifies clingo as combining the gringo grounder and clasp solver. Section 2 (p. 2) says clingo 4 retains this standard behavior by default, although it also permits more flexible control of grounding and solving. (LLM, conf=0.88)

  cites Gebser et al., 2014 source

In the paper

“Although this approach is shown to improve the grounding problem compared to not using context-dependent examples, the approach still needs a finite grounding for each example and still struggles as the domain size increases (Cropper & Morel, 2021).”

What the sources say

• Partly supported

  Section 5.1.1 (p. 33) says the authors used context-dependent examples with ILASP, while Section 2.6 (p. 9) describes finite grounding and difficulty with large domains as limitations of ASP-based approaches. The paper does not show that context-dependent examples improve grounding compared with not using them, or specifically establish a finite-grounding requirement for each such example. (LLM, conf=0.83)

  cites Cropper & Morel, 2021 sourceExperimental — accuracy not yet measured

In the paper

“More precisely, Metagol learns to solve more tasks when using the refactored BK, especially when BK is large.”

What the sources say

• Supported

  The Lego results (Section 5.1, p. 6) say refactoring improves Metagol’s ability to solve tasks when background knowledge (BK) is large (at least 1,000 background tasks). The figure captions (p. 6) also report that Metagol solves more Lego and string-transformation tasks with refactoring. The paper notes a slight degradation for small BK, consistent with the claim’s emphasis on large BK. (LLM, conf=0.92)

  cites Dumancic et al., 2021 source

In the paper

“Although inverse resolution approaches could support PI, they never demonstrated completeness, partly because of the lack of a declarative bias to delimit the hypothesis space (Muggleton et al., 2015).”

What the sources say

• Supported

  The Related work section (p. 4) identifies early predicate-invention approaches based on inverting resolution and says their completeness was never demonstrated, partly because they lacked a declarative bias to delimit the hypothesis space. This directly supports the attributed paraphrase. (LLM, conf=0.95)

  cites Muggleton et al., 2015 source

In the paper

“The refactored program is smaller in size and contains fewer redundant clauses.”

What the sources say

• Supported

  The Knowledge Refactoring Problem definition (p. 3) requires the refactored program to be smaller than the original. The Knorf sections (pp. 4–5) state that it minimises both program size and syntactic redundancy between clauses. (LLM, conf=0.92)

  cites Dumancic et al., 2021 source

In the paper

“TILDE is a first-order generalisation of decision trees and uses information gain to divide and conquer the training examples.”

What the sources say

• Partly supported

  The Introduction and Section 4 describe TILDE as a first-order upgrade of C4.5 that uses top-down, divide-and-conquer decision-tree induction. Section 4 specifies gain ratio, rather than information gain, as TILDE’s split criterion. Page numbers are unavailable in our copy. (LLM, conf=0.88)

  cites Blockeel & De Raedt, 1998 sourceExperimental — accuracy not yet measured

In the paper

“TILDE learns from interpretations, instead of entailment as Aleph, and is an instance of top-down methodology.”

What the sources say

• Supported

  The Introduction (Section 1) says the authors’ framework learns from interpretations and identifies TILDE as its implementation. Section 4 explicitly presents TILDE as a system in the learning-from-interpretations setting that uses a top-down decision-tree algorithm. (LLM, conf=0.94)

  cites Blockeel & De Raedt, 1998 source

In the paper

“TILDE learns from interpretations, instead of entailment as Aleph, and is an instance of top-down methodology.”

What the sources say

• Supported

  The Abstract describes a framework for top-down induction of logical decision trees and identifies TILDE as its implementation. Section 4 further states that TILDE employs the basic top-down decision-tree induction algorithm. (LLM, conf=0.94)

  cites Blockeel & De Raedt, 1998 source

In the paper

“For instance, Bohan et al. (2011) use ILP to generate plausible and testable hypotheses for trophic relations ('who eats whom') from ecological data.”

What the sources say

• Supported

  The Introduction explicitly says the authors use ILP to derive trophic hypotheses and that A/ILP generates plausible, testable hypotheses about ‘who eats whom’ from ecological data. The Results also describe the generated ‘eats’ relations as links that could be tested against literature or by experimentation. Page numbers are not supplied in our copy. (LLM, conf=0.95)

  cites Bohan et al., 2011 source

In the paper

“There has been much recent work on applying ILP in ecology (Bohan et al., 2011; Tamaddoni-Nezhad et al., 2014; Bohan et al., 2017).”

What the sources say

• Supported

  The Introduction describes this paper's application of abductive ILP to ecological data to discover trophic links. As one of several citations, it supports the sentence by providing an example of ILP applied in ecology. (LLM, conf=0.91)

  cites Bohan et al., 2011 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Tamaddoni-Nezhad et al., 2014
• Supported

  The “New Tools to Accelerate Network Characterisation” section says logic-based machine learning has recently been applied in ecology. Box 1 describes its use in ecological network reconstruction, and the References list several ecological applications, supporting the broad statement about recent ILP work. (LLM, conf=0.87)

  cites Bohan et al., 2017 source

In the paper

“ASPAL builds on TAL (Corapi et al., 2010),”

What the sources say

• ?Could not verify

  The Introduction and Section 5 describe TAL and its implementation, but do not mention ASPAL or say that it builds on TAL. Searches for “ASPAL” and for a successor relationship found no passage addressing the claim. (LLM, conf=0.76)

  cites Corapi et al., 2010 sourceExperimental — accuracy not yet measured

In the paper

“learning protein folding signatures (Turcotte et al., 2001)”

What the sources say

• Supported

  In “Molecular biology motivation,” the authors explicitly present an ILP application to learn rules identifying structural signatures of protein folds. Section 4.1 describes a fold rule generated by the ILP system Progol. This supports the citing phrase “learning protein folding signatures.” (LLM, conf=0.94)

  cites Turcotte et al., 2001 source

In the paper

“ILP systems have proven effective in learning SQL queries (Albarghouthi et al., 2017; Sivaraman et al., 2019)”

What the sources say

• ?Not checked — no full text of the sourcecites Albarghouthi et al., 2017 source
• Partly supported

  The Approach section says ALICE uses ILP to learn logical Prolog queries for code search, and the Introduction reports strong code-search results. Neither establishes that ILP systems have proven effective at learning SQL queries; the only SQL-query work found appears in the References. (LLM, conf=0.83)

  cites Sivaraman et al., 2019 sourceExperimental — accuracy not yet measured

In the paper

“modelling inhibition in metabolic networks (Tamaddoni-Nezhad et al., 2006)”

What the sources say

• Supported

  The Introduction states that the authors use Inductive Logic Programming (ILP), alongside abduction, to model inhibition in metabolic networks. This directly supports the citation’s identification of an ILP application. (LLM, conf=0.95)

  cites Tamaddoni-Nezhad et al., 2006 source

In the paper

“Other applications include code search (Sivaraman et al., 2019), in which an ILP system interactively learns a search query from examples”

What the sources say

• Supported

  The Introduction describes ALICE as an interactive code-search technique that infers a search pattern from user feedback and refines it using labeled positive and negative examples. Section III.A says ALICE uses inductive logic programming to construct a logical query for the code the user seeks. (LLM, conf=0.94)

  cites Sivaraman et al., 2019 source

In the paper

“The main advantages of neural approaches are that they can handle noisy BK, as illustrated by ∂ ILP, and can harness tremendous computational power (Ellis et al., 2019).”

What the sources say

• Partly supported

  The Discussion (p. 8) reports that the neural search framework scales to programs with very large branching factors, lending some support to the computational-capability point. Neither that passage nor the passages found by searching for noisy background knowledge and ∂ILP says that neural approaches handle noisy BK or identifies ∂ILP as an example. (LLM, conf=0.73)

  cites Ellis et al., 2019 sourceExperimental — accuracy not yet measured

In the paper

“Evans et al. (2021) apply the Apperception Engine to explain sequential data, such as rhythms and simple nursery tunes, image occlusion tasks, and sequence induction intelligence tests.”

What the sources say

• Supported

  The Introduction lists rhythms and nursery tunes, sequence-induction intelligence tests, and occlusion problems among the domains tested with the Apperception Engine. Section 5.1.6 describes the occlusion tasks as visual scenes in which moving objects become hidden from view. (LLM, conf=0.93)

  cites Evans et al., 2021 source

In the paper

“PI shares the goal with feature or representation learning (Bengio et al., 2013) stream of research originating in the deep learning community (LeCun et al., 2015).”

What the sources say

• Supported

  The Introduction (p. 1) identifies feature learning with representation learning and describes its goal as learning data transformations that make useful information easier to extract. The citation supports the identification and goal of that research stream; the comparison with PI is the citing authors’ framing. (LLM, conf=0.86)

  cites Bengio et al., 2013 source
• ?Not checked — no full text of the sourcecites LeCun et al., 2015 source

In the paper

“Although early work in ILP explored this form of learning (Sammut, 1981; Quinlan, 1990), it has been under-explored until recently (Lin et al., 2014; Cropper, 2019, 2020; Hocquette & Muggleton, 2020; Dumancic et al., 2021), mostly because of new techniques for PI.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Sammut, 1981
• Partly supported

  Section 4 describes FOIL learning definitions for one target relation at a time, and Section 7 says it uses other relations as background knowledge. That supports early work on multiple relational learning tasks, but the cited passages do not show FOIL retaining or transferring what it learned between tasks. The later claim about why the area was under-explored is attached to other citations, not Quinlan (1990). (LLM, conf=0.78)

  cites Quinlan, 1990 sourceExperimental — accuracy not yet measured
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Lin et al., 2014

In the paper

“Problog (De Raedt et al., 2007), a prominent member of this family, represents a minimal extension of Prolog that supports such stochastic execution.”

What the sources say

• Supported

  The Introduction describes ProbLog as essentially Prolog with probabilities attached to clauses. It explains that queries succeed or fail in randomly sampled programs, supporting the characterization of a minimal probabilistic extension with stochastic execution. (LLM, conf=0.90)

  cites De Raedt et al., 2007 source

In the paper

“For this reason, ILP naturally supports lifelong (Silver et al., 2013), multi-task (Caruana, 1997), and transfer learning (Torrey & Shavlik, 2009), which are considered essential for human-like AI (Lake et al., 2016).”

What the sources say

• ?Not checked — no full text of the sourcecites Silver et al., 2013
• Supported

  Caruana is cited specifically for multi-task learning, not for the sentence’s separate claims about lifelong learning, transfer learning, or human-like AI. The paper’s Overview (§1.1) defines and describes multitask learning, so it supports that identification. (LLM, conf=0.93)

  cites Caruana, 1997 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Torrey & Shavlik, 2009

In the paper

“While StarAI is a growing field, inducing probabilistic logic programs has received little attention, with few notable exceptions (Bellodi & Riguzzi, 2015; De Raedt et al., 2015), as inference remains the main challenge.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Bellodi & Riguzzi, 2015
• Supported

  The citation is attached to “few notable exceptions,” and this paper is one: its Abstract describes a method for inducing logic programs in a probabilistic setting. The claim about inference being the main challenge appears after the citation and is not attributed to this source. (LLM, conf=0.91)

  cites De Raedt et al., 2015

In the paper

“This program is semantically equivalent 33 to the previous one, but is shorter both in terms of the number of literals and clauses.”

In the paper

“For instance, grounding the permutation relation over the ASCII characters would require 128! facts.”

In the paper

“Although correct, this program is large and has 4 clauses and 12 literals.”

In the paper

“Most early attempts at PI were unsuccessful, and, as Table 4 shows, most systems do not support it.”

In the paper

“Moreover, it is a single Prolog file, which makes it easy to download and use 40 .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites [40]

In the paper

“it has a stable and easily available implementation with many options”

In the paper

“TILDE learns from interpretations, instead of entailment as Aleph, and is an instance of top-down methodology.”

In the paper

“Although TILDE learns normal programs, it requires them to be in the shape of a tree and does not support recursion.”

In the paper

“Although TILDE learns normal programs, it requires them to be in the shape of a tree and does not support recursion.”

In the paper

“Inductive logic programming (ILP) is a form of machine learning.”

• Also stated in: § 1. Introduction · p. 1 · plain

  “Inductive logic programming (ILP) (Muggleton, 1991) is a form of ML.”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1991 source

In the paper

“whereas most forms of ML use tables 1 to represent data (examples and hypotheses), ILP uses logic programs (sets of logical rules).”

What the sources say

• ?Not checked — no full text of the sourcecites De Raedt, 2008 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Rockt¨ aschel and Riedel, 2017

In the paper

“For instance, King et al. (1992) use ILP to model structure-activity relationships for drug design.”

What the sources say

• ?Not checked — no full text of the sourcecites King et al., 1992 source

In the paper

“ILP usually follows the closed world assumption (Reiter, 1977), so if anything is not explicitly true we assume it is false.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Reiter, 1977

In the paper

“Most ML algorithms are single-task learners and cannot reuse learned knowledge.”

In the paper

“Whilst researching yeast-based functional genomics, the Robot Scientist became the first machine to independently discover new scientific knowledge (King et al., 2009).”

• Also stated in: § 7. Applications · p. 58 · plain

  “Whilst researching yeast-based functional genomics, the Robot Scientist became the first machine to independently discover new scientific knowledge (King et al., 2009).”

What the sources say

• ?Not checked — no full text of the sourcecites King et al., 2009 source

In the paper

“This hypothesis corresponds to the quicksort algorithm (Hoare, 1961) and generalises to lists of arbitrary length and elements not seen in the training examples.”

What the sources say

• ?Not checked — no full text of the sourcecites Hoare, 1961 source

In the paper

“This scenario shows that ILP is a form of program synthesis (Shapiro, 1983), where the goal is to automatically build executable programs.”

What the sources say

• ?Not checked — no full text of the sourcecites Shapiro, 1983 source

In the paper

“Because they are closely related to relational databases, logic programs naturally support relational data such as graphs.”

In the paper

“Because of the symbolic nature of logic programs, ILP can reason about hypotheses, which allows it to learn optimal programs, such as minimal time-complexity programs (Cropper & Muggleton, 2019) and secure access control policies (Law et al., 2020).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Cropper & Muggleton, 2019
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Law et al., 2020

In the paper

“Unrestricted, the hypothesis space is infinite, so it is vital to restrict it to make the search feasible.”

In the paper

“The representation determines the learning setting which in turn defines what it means for a program to solve the ILP problem.”

In the paper

“As Srinivasan et al. (1994) state, 'There is more to scientific theory formulation than data fitting. To be acceptable, a theory must be understandable and open to critical analysis' .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Srinivasan et al., 1994

In the paper

“Moreover, because induced hypotheses have the same language as the BK, they can be stored in the BK, making transfer learning trivial (Lin et al., 2014).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Lin et al., 2014

In the paper

“Some languages support non-monotonic reasoning, such as answer set programming (Gebser et al., 2012).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Gebser et al., 2012

In the paper

“ILP represents data as logic programs.”

In the paper

“For instance, it is trivial to define a summation relation over the infinite set of natural numbers ( add(A,B,C):C = A+B ).”

In the paper

“For instance, the Robot Scientist (King et al., 2004) is a system that uses ILP to generate hypotheses to explain data and can also automatically devise experiments to test the hypotheses, physically run the experiments, interpret the results, and then repeat the cycle.”

What the sources say

• ?Not checked — no full text of the sourcecites King et al., 2004 source

In the paper

“Using logic programs to represent data allows ILP to learn with complex relational information and for easy integration of expert knowledge.”

In the paper

“Because of logic's similarity to natural language, logic programs can be easily read by humans, which is crucial for explainable AI 5 .”

In the paper

“Building an ILP system (Figure 1) requires making several choices or assumptions.”

In the paper

“For instance, although AlphaGo (Silver et al., 2016) has super-human Go ability, it cannot reuse this knowledge to play other games, nor the same game with a slightly different board.”

What the sources say

• ?Not checked — no full text of the sourcecites Silver et al., 2016 source

In the paper

“By contrast, tabled-based ML approaches are mostly restricted to finite data and cannot represent this information.”

In the paper

“There are, however, many logic programming languages, each with strengths and weaknesses.”

In the paper

“if we train a neural system to add numbers with 10 digits, it can generalise to numbers with 20 digits, but when tested on numbers with 100 digits, the predictive accuracy drastically decreases (Reed & de Freitas, 2016; Kaiser & Sutskever, 2016).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Reed & de Freitas, 2016
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Kaiser & Sutskever, 2016

In the paper

“For instance, when inducing solutions to a set of string transformation tasks, such as those in Scenario 2, Lin et al. (2014) show that an ILP system can automatically identify easier problems to solve, learn programs for them, and then reuse the learned programs to help learn programs for more difficult problems.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Lin et al., 2014

In the paper

“Choosing a suitable representation language is crucial in determining which problems a system can solve.”

In the paper

“However, if we follow Mitchell's (1997) definition of ML 8 then ILP is no different from other ML approaches: it improves given more examples.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Mitchell, 1997

In the paper

“Choosing an appropriate language bias is necessary for efficient learning and is a major challenge.”

In the paper

“Datalog is, however, sufficient for the happy Scenario because structured terms are unnecessary.”

In the paper

“By contrast, definite programs with function symbols have the expressive power of Turing machines and are consequently undecidable (T¨ arnlund, 1977).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites T¨ arnlund, 1977

In the paper

“ILP is in the symbolic learning category.”

In the paper

“However, as Domingos (2015) points out, there are generally five areas of ML: symbolists, connectionists, Bayesian, analogisers, and evolutionists.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Domingos, 2015

In the paper

“Unlike Prolog, Datalog is purely declarative.”

In the paper

“For instance, the clause p ( a ) ∨ p ( b ) cannot be expressed in Horn logic because it has two positive literals.”

In the paper

“Most Prolog implementations (Wielemaker et al., 2012; Costa et al., 2012) allow extra-logical features, such as cuts.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Wielemaker et al., 2012
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Costa et al., 2012

In the paper

“Therefore, most work in ILP focuses on fragments of clausal logic, such as Horn programs: clauses with at most one positive literal.”

In the paper

“Turing can be seen as one of the first symbolist, as he proposed using a logical representation to build thinking machines (Turing, 1950; Muggleton, 1994a).”

What the sources say

• ?Not checked — no full text of the sourcecites Turing, 1950 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Muggleton, 1994a

In the paper

“Recognising the limitations of table-based representations, Banerji (1964) proposed using predicate logic as a representation language for learning.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Banerji, 1964

In the paper

“ILP as a field was founded by Muggleton (1991), who stated that it lies at the intersection of ML and knowledge”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1991 source

In the paper

“Prolog is not purely declarative because of constructs like cut, which means that a procedural reading of a Prolog program is needed to understand it.”

In the paper

“Other notable contributions include inverse resolution (Muggleton & Buntine, 1988), which was also one of the earliest approaches at predicate invention.”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton & Buntine, 1988 source

In the paper

“Meta-level approaches often delegate the search for a hypothesis to an off-the-shelf solver (Corapi et al., 2011; Muggleton et al., 2014; Law et al., 2014; Kaminski et al., 2018; Evans et al., 2021; Cropper & Morel, 2021) after which the meta-level solution is translated back to a standard solution for the ILP problem.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Corapi et al., 2011
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Muggleton et al., 2014
• ?Not checked — no full text of the sourcecites Law et al., 2014 source

In the paper

“In other words, the order of clauses in a Prolog program has a major influence on its execution and results.”

In the paper

“However, this decidability comes at the cost of expressivity as Datalog is not Turing complete.”

In the paper

“The traditional way to categorise approaches is whether they use a top-down or bottomup search, where generality orders the search space 7 .”

In the paper

“Other notable work includes Vera (1975) on induction algorithms for predicate calculus and Sammut's (1981) MARVIN system, one of the first to learn executable programs.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Vera, 1975

In the paper

“As with all ML techniques, ILP restricts the hypothesis space by enforcing an inductive bias (Mitchell, 1997).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Mitchell, 1997

In the paper

“Therefore, the list manipulation programs from previous sections cannot (easily) be expressed in Datalog 9 .”

In the paper

“Some approaches combine the two (Muggleton, 1995; Srinivasan, 2001; Cropper, 2022).”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1995 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Srinivasan, 2001
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Cropper, 2022

In the paper

“McCarthy (1959) made the first comprehensive proposal for the use of logic in AI with his advice seeker .”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites McCarthy, 1959

In the paper

“Shapiro's (1983) work on inducing Prolog programs made major contributions to ILP, including the concepts of backtracking and refinement operators.”

What the sources say

• ?Not checked — no full text of the sourcecites Shapiro, 1983 source

In the paper

“Other notable work includes Vera (1975) on induction algorithms for predicate calculus and Sammut's (1981) MARVIN system, one of the first to learn executable programs.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Sammut, 1981

In the paper

“Robinson (1965) showed that a single rule of inference (the resolution principle) is both sound and refutation complete for clausal logic.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Robinson (1965)

In the paper

“Plotkin's (1971) work on subsumption and least general generalisation has influenced nearly all of ILP, especially theory.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Plotkin, 1971

In the paper

“Michalski's (1969) work on the AQ algorithm, which induces rules using a set covering algorithm, has greatly influenced many ILP systems.”

What the sources say

• ?Not checked — no full text of the sourcecites Michalski, 1969 source

In the paper

“In addition, ASP programs support rules that are not available in Prolog, such as choice rules and weak and hard constraints.”

In the paper

“According to De Raedt (1997), there are three main ILP learning settings: learning from entailment (LFE), interpretations (LFI), and satisfiability (LFS).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites De Raedt (1997)

In the paper

“For instance, to learn a definition of a recursive concept, the hypothesis needs to capture at least the base and recursive case.”

In the paper

“An inductive bias is essential and all ML approaches impose an inductive bias (Mitchell, 1997).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Mitchell, 1997

In the paper

“Building an ILP system requires making several choices or assumptions, which are part of the inductive bias of a learner.”

In the paper

“ILP approaches that learn normal logic programs can further be characterised by their semantics, such as whether they are based on completion (Clark, 1977), well-founded (Gelder et al., 1991), or stable model (answer set) (Gelfond & Lifschitz, 1988) semantics.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Clark, 1977
• ?Not checked — no full text of the sourcecites Gelder et al., 1991 source
• ?Not checked — no full text of the sourcecites Gelfond & Lifschitz, 1988

In the paper

“As providing a complete interpretation might be unfeasible in many cases, many ILP systems focus on partial interpretations (De Raedt, 1997).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites De Raedt, 1997

In the paper

“Most ASP solvers (Gebser et al., 2012), in principle, always terminate (unlike Prolog query evaluation, which may lead to an infinite loop).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Gebser et al., 2012

In the paper

“A generality order helps structure the search over the hypothesis space by reasoning about the relative properties of two programs.”

In the paper

“When learning Prolog programs with NAF, the programs must be stratified; otherwise, the learned program may loop under certain queries (Law et al., 2018).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Law et al., 2018

In the paper

“There are many benefits to learning ASP programs (Otero, 2001; Law et al., 2014).”

What the sources say

• ?Not checked — no full text of the sourcecites Otero, 2001 source
• ?Not checked — no full text of the sourcecites Law et al., 2014 source

In the paper

“Some systems, such as Progol (Muggleton, 1995), allow for clauses as examples.”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1995 source

In the paper

“These relations are general and hold for arbitrary numbers and we do not need to precompute all the logical consequences of the definitions, which is impossible because there are infinitely many.”

In the paper

“Similar to Datalog, an answer set program is purely declarative.”

In the paper

“By contrast, table-based ML approaches are restricted to finite propositional data. For instance, it is impossible to use the greater than relation over the set of natural numbers in a decision tree learner because it would require an infinite feature table.”

In the paper

“Inoue et al. (2013) represent knowledge as a causal graph and use constraints to denote impossible connections between nodes.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Inoue et al., 2013

In the paper

“Most approaches reason about the generality of programs syntactically through θ -subsumption (or subsumption for short) (Plotkin, 1971).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Plotkin, 1971

In the paper

“The two main learning settings are LFE and LFI (Section 3).”

In the paper

“For instance, the default cost function in Aleph (Srinivasan, 2001) is coverage , defined as the number of positive examples entailed subtracted by the number of negative examples entailed by the hypothesis.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Srinivasan, 2001

In the paper

“Although some systems learn propositional programs, such as Duce (Muggleton, 1987), most learn first-order (or higher-order) programs.”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1987

In the paper

“These relations hold for lists of any length and any type.”

In the paper

“The logic of definite clauses with negation as failure (NAF) (Clark, 1977) is nonmonotonic, which brings us to the special class of normal logic programs , which take the following form:”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Clark, 1977

In the paper

“Most systems, however, learn from sets of facts, so this dimension of comparison is not useful.”

In the paper

“Systems that focus on program synthesis (Shapiro, 1983; Bratko, 1999; Ahlgren & Yuen, 2013; Cropper & Muggleton, 2016, 2019; Cropper & Morel, 2021) tend to induce definite programs, typically as Prolog programs.”

What the sources say

• ?Not checked — no full text of the sourcecites Shapiro, 1983 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Bratko, 1999
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Ahlgren & Yuen, 2013

In the paper

“Definite programs are monotonic because anything that could be deduced before a (definite) clause is added to it can still be deduced after it is added.”

In the paper

“Too many relations (assuming that they can appear in a hypothesis) is often a problem because the size of the hypothesis space is a function of the size of the BK.”

In the paper

“For instance, HYPER (Bratko, 1999) searches a tree in which the nodes correspond to hypotheses. Each child of a hypothesis in the tree is more specific than or equal to its predecessor in terms of theta-subsumption, i.e. a hypothesis can only entail a subset of the examples entailed by its parent.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Bratko, 1999

In the paper

“In contrast to other forms of bias in ILP, such as modes or grammars, metarules are themselves logical statements, which allows us to reason about them.”

In the paper

“Unrestricted, the hypothesis space is infinite, so it is important to restrict it to make the search feasible.”

In the paper

“Likewise, if a clause entails a negative example, then there is no need to explore any of its generalisations because they will also entail the example.”

In the paper

“Providing a recall is a hint to a system to ignore certain hypotheses.”

In the paper

“A generality relation imposes an order over the hypothesis space.”

In the paper

“The Blumer bound (Blumer et al., 1987) (the bound is a reformulation of Lemma 2.1) helps explain this trade-off. This bound states that given two hypothesis spaces, searching the smaller space will result in fewer errors compared to the larger space, assuming that the target hypothesis is in both spaces.”

What the sources say

• ?Not checked — no full text of the sourcecites Blumer et al., 1987 source

In the paper

“Depending on the specific system, modes can also support the introduction of constant symbols.”

In the paper

“Bottom-up algorithms start with the examples and generalise them (Muggleton, 1987; Muggleton & Buntine, 1988; Muggleton & Feng, 1990; Muggleton et al., 2009; Inoue et al., 2014).”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton, 1987
• ?Not checked — no full text of the sourcecites Muggleton & Buntine, 1988 source
• ?Not checked — no full text of the sourcecites Muggleton & Feng, 1990

In the paper

“Different systems use mode declarations in slightly different ways.”

In the paper

“Metarules are second-order rules which define the structure of learnable programs which in turn defines the hypothesis space.”

In the paper

“There are two traditional search methods: bottom-up and top-down .”

In the paper

“Metarules 17 are a popular form of syntactic bias and are used by many systems (De Raedt & Bruynooghe, 1992; Flener, 1996; Kietz & Wrobel, 1992; Wang et al., 2014; Muggleton et al., 2015; Cropper & Muggleton, 2016; Kaminski et al., 2018; Evans & Grefenstette, 2018; Bain & Srinivasan, 2018).”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites De Raedt & Bruynooghe, 1992
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Flener, 1996
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Kietz & Wrobel, 1992

In the paper

“If a user does not have such knowledge, then it can be very difficult to determine suitable mode declarations.”

In the paper

“To introduce RLGG, we start by introducing Plotkin's (1971) notion of least-general generalisation (LGG), which tells us how to generalise two clauses.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Plotkin, 1971

In the paper

“Progol and Aleph use mode declarations with input/output argument types because they induce Prolog programs, where the order of literals in a rule matters.”

In the paper

“For instance, if a clause does not entail a positive example, then there is no need to explore any of its specialisations because it is logically impossible for them to entail the example.”

In the paper

“Mode declarations are expressive enough to enforce a strong bias to significantly prune the hypothesis space.”

In the paper

“A benefit of metarules is that they require little knowledge of the BK and a user does not need to provide recall values, types, or specify input/output arguments.”

In the paper

“The difficulty is finding the balance of having enough BK to solve a problem, but not too much that a system becomes overwhelmed.”

In the paper

“By contrast, ILASP induces ASP programs, where the order of literals in a rule does not matter, so ILASP does not use input/output arguments.”

In the paper

“If a hypothesis is considered that does not entail all the positive examples, it is immediately discarded because it can never be refined into a complete hypothesis.”

In the paper

“For instance, Golem (Muggleton & Feng, 1990) generalises pairs of examples based on relative least-general generalisation (RLGG) (Buntine, 1988).”

What the sources say

• ?Not checked — no full text of the sourcecites Muggleton & Feng, 1990
• ?Not checked — no full text of the sourcecites Buntine, 1988 source

In the paper

“These methods rely on notions of generality, where one program is more general or more specific than another (Section 2.4).”

In the paper

“Despite this preliminary work, deciding which metarules to use for a given problem is still a major challenge, which future work must address.”

• Also stated in: § 4.4.3 Discussion · p. 27 · plain

  “However, as previously mentioned, the major downside with metarules is determining which metarules to use for an arbitrary learning task.”

• Also stated in: § 4.4.3 Discussion · p. 27 · plain

  “Although there is some preliminary work in identifying universal sets of metarules (Cropper & Muggleton, 2014; Tourret & Cropper, 2019; Cropper & Tourret, 2020), deciding which metarules to use for a given problem is a major challenge, which future work must address.”

In the paper

“ASPAL (Corapi et al., 2011), ILASP (Law et al., 2014), HEXMIL (Kaminski et al., 2018), and the Apperception Engine (Evans et al., 2021) translate an ILP problem into an ASP problem and use powerful ASP solvers to find a model of the problem - note that these systems all employ very different algorithms.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Corapi et al., 2011
• ?Not checked — no full text of the sourcecites Law et al., 2014 source
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Kaminski et al., 2018

In the paper

“The main advantages of top-down approaches are that they can more easily learn recursive programs and textually minimal programs.”

In the paper

“Bottom-up approaches can be seen as being dataor example-driven .”

In the paper

“The main advantages of top-down approaches are that they can more easily learn recursive programs and textually minimal programs.”

In the paper

“Progol is one of the most important systems and has inspired many other approaches (Srinivasan, 2001; Ray, 2009; Ahlgren & Yuen, 2013), including Aleph, which we cover in detail in Section 6.1.”

What the sources say

• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Srinivasan, 2001
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Ray, 2009
• ?Not matched

  Couldn’t be matched to a paper in Crossref, so it can’t be checked.

  cites Ahlgren & Yuen, 2013

In the paper

“Law et al. (2020) also provide an overview of conflict-driven ILP, which the systems ILASP3 (Law, 2018) and Popper (Cropper & Morel, 2021) adopt.”