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== History ==
Building on earlier work on [[Inductive inference]], [[Gordon Plotkin]] was the first to formalise induction in a [[Horn clause|clausal]] setting around 1970, adopting an approach of generalising from examples.<ref name=":0">{{Cite book |lastlast1=Nienhuys-Cheng |firstfirst1=Shan-hwei |title=Foundations of inductive logic programming |last2=Wolf |first2=Ronald de |date=1997 |publisher=Spinger |isbn=978-3-540-62927-6 |series=Lecture notes in computer science Lecture notes in artificial intelligence |___location=Berlin Heidelberg |pages=174–177}}</ref><ref>{{cite thesis |first=G.D. |last=Plotkin |title=Automatic Methods of Inductive Inference |date=1970 |type=PhD |publisher=University of Edinburgh |url=https://www.era.lib.ed.ac.uk/bitstream/handle/1842/6656/Plotkin1972.pdf |hdl=1842/6656}}</ref> In 1981, [[Ehud Shapiro]] introduced several ideas that would shape the field in his new approach of model inference, an algorithm employing refinement and backtracing to search for a complete axiomatisation of given examples.<ref name=":0" /><ref>{{cite tech report|first=Ehud Y.|last=Shapiro|title=Inductive inference of theories from facts|id=192|date=1981|publisher=Department of Computer Science, Yale University|url=http://ftp.cs.yale.edu/publications/techreports/tr192.pdf}} Reprinted in {{cite book |title=Computational logic : essays in honor of Alan Robinson |publisher=MIT Press |year=1991 |isbn=978-0-262-12156-9 |editor1-last=Lassez |editor1-first=J.-L. |pages=199–254 |editor2-last=Plotkin |editor2-first=G.}}</ref> His first implementation was the [[Model Inference System]] in 1981:<ref>{{cite book |last=Shapiro |first=Ehud Y. |url= |title=Proceedings of the 7th international joint conference on Artificial intelligence |date=1981 |publisher=Morgan Kaufmann |isbn= |volume=2 |___location= |pages=1064 |chapter=The model inference system |chapter-url=https://www.ijcai.org/Proceedings/81-2/Papers/100.pdf}}</ref><ref>{{cite book |last=Shapiro |first=Ehud Y. |url= |title=Algorithmic program debugging |date=1983 |publisher=MIT Press |isbn=0-262-19218-7 |___location= |pages=}}</ref> a [[Prolog]] program that inductively inferred [[Horn clause]] logic programs from positive and negative examples.<ref name=":0" /> The term ''Inductive Logic Programming'' was first introduced in a paper by [[Stephen Muggleton]] in 1990, defined as the intersection of machine learning and logic programming.<ref name=":0" /> Muggleton and Wray Buntine introduced predicate invention and [[inverse resolution]] in 1988.<ref name=":0" /><ref>{{cite book |last1=Muggleton |first1=S.H. |url= |title=Proceedings of the 5th International Conference on Machine Learning |last2=Buntine |first2=W. |date=1988 |isbn=978-0-934613-64-4 |pages=339–352 |chapter=Machine invention of first-order predicate by inverting resolution |doi=10.1016/B978-0-934613-64-4.50040-2}}</ref>
Several inductive logic programming systems that proved influential appeared in the early 1990s. [[First-order inductive learner|FOIL]], introduced by [[Ross Quinlan]] in 1990<ref>{{Cite journal |last=Quinlan |first=J. R. |date=August 1990 |title=Learning logical definitions from relations |url=http://dx.doi.org/10.1007/bf00117105 |journal=Machine Learning |volume=5 |issue=3 |pages=239–266 |doi=10.1007/bf00117105 |issn=0885-6125|doi-access=free }}</ref> was based on upgrading [[Propositional calculus|propositional]] learning algorithms [[AQ (machine learning)|AQ]] and [[ID3 algorithm|ID3]].<ref name=":1">{{Cite book |lastlast1=Nienhuys-Cheng |firstfirst1=Shan-hwei |title=Foundations of inductive logic programming |last2=Wolf |first2=Ronald de |date=1997 |publisher=Spinger |isbn=978-3-540-62927-6 |series=Lecture notes in computer science Lecture notes in artificial intelligence |___location=Berlin Heidelberg |pages=354–358}}</ref> [[Golem (ILP)|Golem]], introduced by Muggleton and Feng in 1990, went back to a restricted form of Plotkin's least generalisation algorithm.<ref name=":1" /><ref>{{Cite journal |lastlast1=Muggleton |firstfirst1=Stephen H. |last2=Feng |first2=Cao |date=1990 |editor-last=Arikawa |editor-first=Setsuo |editor2-last=Goto |editor2-first=Shigeki |editor3-last=Ohsuga |editor3-first=Setsuo |editor4-last=Yokomori |editor4-first=Takashi |title=Efficient Induction of Logic Programs |url=https://dblp.org/rec/conf/alt/MuggletonF90.bib |journal=Algorithmic Learning Theory, First International Workshop, ALT '90, Tokyo, Japan, October 8-10, 1990, Proceedings |publisher=Springer/Ohmsha |pages=368–381}}</ref> The [[Progol]] system, introduced by Muggleton in 1995, first implemented inverse entailment, and inspired many later systems.<ref name=":1" /><ref name=":3">{{Cite journal |lastlast1=Cropper |firstfirst1=Andrew |last2=Dumančić |first2=Sebastijan |date=2022-06-15 |title=Inductive Logic Programming At 30: A New Introduction |url=http://dx.doi.org/10.1613/jair.1.13507 |journal=Journal of Artificial Intelligence Research |volume=74 |page=808 |pages= |doi=10.1613/jair.1.13507 |issn=1076-9757|doi-access=free }}</ref><ref name=":2">{{cite journal |last1=Muggleton |first1=S.H. |year=1995 |title=Inverting entailment and Progol |journal=New Generation Computing |volume=13 |issue=3–4 |pages=245–286 |citeseerx=10.1.1.31.1630 |doi=10.1007/bf03037227 |s2cid=12643399}}</ref> [[Aleph (ILP)|Aleph]], a descendant of Progol introduced by Ashwin Srinivasan in 2001, is still one of the most widely used systems {{As of|2022|lc=y|bare=}}.<ref name=":3" />
At around the same time, the first practical applications emerged, particularly in [[bioinformatics]], where by 2000 inductive logic programming had been successfully applied to drug design, carcinogenicity and mutagenicity prediction, and elucidation of the structure and function of proteins.<ref>{{Citation |last=Džeroski |first=Sašo |title=Relational Data Mining Applications: An Overview |date=2001 |url=http://link.springer.com/10.1007/978-3-662-04599-2_14 |work=Relational Data Mining |pages=339–364 |editor-last=Džeroski |editor-first=Sašo |access-date=2023-11-27 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |language=en |doi=10.1007/978-3-662-04599-2_14 |isbn=978-3-642-07604-6 |editor2-last=Lavrač |editor2-first=Nada}}</ref> Unlike the focus on [[automatic programming]] inherent in the early work, these fields used inductive logic programming techniques from a viewpoint of [[relational data mining]]. The success of those initial applications and the lack of progress in recovering larger traditional logic programs shaped the focus of the field.<ref>{{Citation |last=De Raedt |first=Luc |editor-first1=<!-- Deny Citation Bot--> |editor-last1=<!-- Deny Citation Bot--> |url=http://dx.doi.org/10.1007/978-3-540-68856-3 |title=Logical and Relational Learning |series=Cognitive Technologies |page=14|place=Berlin, Heidelberg |publisher=Springer |year=2008 |doi=10.1007/978-3-540-68856-3 |bibcode=2008lrl..book.....D |isbn=978-3-540-20040-6}}</ref>
Recently, classical tasks from automated programming have moved back into focus, as the introduction of meta-interpretative learning makes predicate invention and learning recursive programs more feasible. This technique was pioneered with the [[Metagol]] system introduced by Muggleton, Dianhuan Lin, Niels Pahlavi and Alireza Tamaddoni-Nezhad in 2014.<ref>{{Cite journal |lastlast1=Muggleton |firstfirst1=Stephen H. |last2=Lin |first2=Dianhuan |last3=Pahlavi |first3=Niels |last4=Tamaddoni-Nezhad |first4=Alireza |date=2013-05-01 |title=Meta-interpretive learning: application to grammatical inference |url=http://dx.doi.org/10.1007/s10994-013-5358-3 |journal=Machine Learning |volume=94 |issue=1 |pages=25–49 |doi=10.1007/s10994-013-5358-3 |s2cid=254738603 |issn=0885-6125}}</ref> This allows ILP systems to work with fewer examples, and brought successes in learning string transformation programs, answer set grammars and general algorithms.<ref>{{Cite journal |lastlast1=Cropper |firstfirst1=Andrew |last2=Dumančić |first2=Sebastijan |last3=Evans |first3=Richard |last4=Muggleton |first4=Stephen |date=2022 |title=Inductive logic programming at 30 |url=https://link.springer.com/10.1007/s10994-021-06089-1 |journal=Machine Learning |language=en |volume=111 |issue=1 |pages=147–172 |doi=10.1007/s10994-021-06089-1 |issn=0885-6125|doi-access=free }}</ref>
== Setting ==
Inductive logic programming has adopted several different learning settings, the most common of which are learning from [[entailment]] and learning from interpretations.<ref name="setting">{{Cite journal |lastlast1=Cropper |firstfirst1=Andrew |last2=Dumančić |first2=Sebastijan |date=2022-06-15 |title=Inductive Logic Programming At 30: A New Introduction |url=http://dx.doi.org/10.1613/jair.1.13507 |journal=Journal of Artificial Intelligence Research |volume=74 |pages=779{{endash}}782 |doi=10.1613/jair.1.13507 |issn=1076-9757 |doi-access=free}}</ref> In both cases, the input is provided in the form of ''background knowledge {{mvar|B}}'', a logical theory (commonly in the form of [[Clause (logic)|clauses]] used in [[logic programming]]), as well as positive and negative examples, denoted <math display="inline">E^+</math> and <math display="inline">E^{-}</math> respectively. The output is given as a ''hypothesis'' ''{{mvar|H}}'', itself a logical theory that typically consists of one or more clauses.
The two settings differ in the format of examples presented.
== Probabilistic inductive logic programming ==
Probabilistic inductive logic programming adapts the setting of inductive logic programming to learning [[Probabilistic logic programming|probabilistic logic programs]]. It can be considered as [[statistical relational learning]] within the formalism of probabilistic logic programming.<ref>{{Citation |lastlast1=De Raedt |firstfirst1=Luc |title=Probabilistic Inductive Logic Programming |date=2008 |url=http://dx.doi.org/10.1007/978-3-540-78652-8_1 |work=Probabilistic Inductive Logic Programming |pages=1–27 |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-540-78651-1 |last2=Kersting |first2=Kristian|doi=10.1007/978-3-540-78652-8_1 }}</ref><ref name="pilp">{{Cite journal |lastlast1=Riguzzi |firstfirst1=Fabrizio |last2=Bellodi |first2=Elena |last3=Zese |first3=Riccardo |date=2014-09-18 |title=A History of Probabilistic Inductive Logic Programming |url=http://journal.frontiersin.org/article/10.3389/frobt.2014.00006/ |journal=Frontiers in Robotics and AI |volume=1 |doi=10.3389/frobt.2014.00006 |issn=2296-9144 |doi-access=free }}</ref>
Given
=== Structure Learning ===
Structure learning was pioneered by [[Daphne Koller]] and Avi Pfeffer in 1997,<ref>{{Cite conference |lastlast1=Koller |firstfirst1=Daphne |last2=Pfeffer |first2=Avi |date=August 1997 |title=Learning probabilities for noisy first-order rules |url=http://www.robotics.stanford.edu/~koller/Papers/Koller+Pfeffer:IJCAI97.pdf |conference=[[IJCAI]]}}</ref> where the authors learn the structure of [[First-order logic|first-order]] rules with associated probabilistic uncertainty parameters. Their approach involves generating the underlying [[graphical model]] in a preliminary step and then applying expectation-maximisation.<ref name="pilp" />
In 2008, [[Luc De Raedt|De Raedt]] et al. presented an algorithm for performing [[theory compression]] on [[ProbLog]] programs, where theory compression means removing as many clauses as possible from the theory in order to maximize the probability. No new clause can be added to the theory.<ref name="pilp" />
In the same year, Meert, W. et al. introduced a method for learning parameters and structure of [[Ground term|ground]] probabilistic logic programs by considering the [[Bayesian network|Bayesian networks]] equivalent to them and applying techniques for learning Bayesian networks.<ref>{{Citation |lastlast1=Blockeel |firstfirst1=Hendrik |title=Towards Learning Non-recursive LPADs by Transforming Them into Bayesian Networks |url=http://dx.doi.org/10.1007/978-3-540-73847-3_16 |work=Inductive Logic Programming |pages=94–108 |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-540-73846-6 |last2=Meert |first2=Wannes|series=Lecture Notes in Computer Science |date=2007 |volume=4455 |doi=10.1007/978-3-540-73847-3_16 }}</ref><ref name="pilp" />
ProbFOIL, introduced by De Raedt and Ingo Thon in 2010, combined the inductive logic programming system [[First-order inductive learner|FOIL]] with [[ProbLog]]. Logical rules are learned from probabilistic data in the sense that both the examples themselves and their classifications can be probabilistic. The set of rules has to allow to predict the probability of the examples from their description. In this setting, the parameters (the probability values) are fixed and the structure has to be learned.<ref>{{Citation |lastlast1=De Raedt |firstfirst1=Luc |title=Probabilistic Rule Learning |date=2011 |url=http://link.springer.com/10.1007/978-3-642-21295-6_9 |work=Inductive Logic Programming |volume=6489 |pages=47–58 |editor-last=Frasconi |editor-first=Paolo |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |doi=10.1007/978-3-642-21295-6_9 |isbn=978-3-642-21294-9 |last2=Thon |first2=Ingo |s2cid=11727522 |editor2-last=Lisi |editor2-first=Francesca A.}}</ref><ref name="pilp" />
In 2011, Elena Bellodi and Fabrizio Riguzzi introduced SLIPCASE, which performs a beam search among probabilistic logic programs by iteratively refining probabilistic theories and optimizing the parameters of each theory using expectation-maximisation.<ref>{{Citation |lastlast1=Bellodi |firstfirst1=Elena |title=Learning the Structure of Probabilistic Logic Programs |date=2012 |url=http://dx.doi.org/10.1007/978-3-642-31951-8_10 |work=Inductive Logic Programming |pages=61–75 |access-date=2023-12-09 |place=Berlin, Heidelberg |publisher=Springer Berlin Heidelberg |isbn=978-3-642-31950-1 |last2=Riguzzi |first2=Fabrizio|doi=10.1007/978-3-642-31951-8_10 }}</ref>
Its extension SLIPCOVER, proposed in 2014, uses bottom clauses generated as in [[Progol]] to guide the refinement process, thus reducing the number of revisions and exploring more effectively the search space. Moreover, SLIPCOVER separates the search for promising clauses from that of the theory: the space of clauses is explored with a [[beam search]], while the space of theories is searched [[Greedy search|greedily]].<ref>{{Cite journal |lastlast1=Bellodi |firstfirst1=Elena |last2=Riguzzi |first2=Fabrizio |date=2014-01-15 |title=Structure learning of probabilistic logic programs by searching the clause space |url=http://dx.doi.org/10.1017/s1471068413000689 |journal=Theory and Practice of Logic Programming |volume=15 |issue=2 |pages=169–212 |doi=10.1017/s1471068413000689 |arxiv=1309.2080 |s2cid=17669522 |issn=1471-0684}}</ref><ref name="pilp" />
==See also==
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