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AUTHORS (423, 2021-09-13)
LICENSE (1515, 2021-09-13)
examples/ (0, 2021-09-13)
examples/adjacent-to-red.pl (681, 2021-09-13)
examples/constants1.pl (264, 2021-09-13)
examples/constants2.pl (381, 2021-09-13)
examples/constants3.pl (245, 2021-09-13)
examples/droplasts.pl (2468, 2021-09-13)
examples/droplasts2.pl (2151, 2021-09-13)
examples/find-duplicate.pl (941, 2021-09-13)
examples/grandparent.pl (632, 2021-09-13)
examples/graph-colouring.pl (520, 2021-09-13)
examples/graph-connectedness.pl (533, 2021-09-13)
examples/graph-reachability.pl (353, 2021-09-13)
examples/higher-order1.pl (570, 2021-09-13)
examples/higher-order2.pl (785, 2021-09-13)
examples/higher-order3.pl (2119, 2021-09-13)
examples/ibk1.pl (646, 2021-09-13)
examples/kinship1.pl (970, 2021-09-13)
examples/kinship2.pl (825, 2021-09-13)
examples/less-than.pl (612, 2021-09-13)
examples/member.pl (872, 2021-09-13)
examples/mutual-recursion.pl (457, 2021-09-13)
examples/predecessor.pl (628, 2021-09-13)
examples/relatedness.pl (571, 2021-09-13)
examples/robots.pl (2280, 2021-09-13)
examples/robots2.pl (2432, 2021-09-13)
examples/sequential.pl (863, 2021-09-13)
examples/sequential1.pl (850, 2021-09-13)
examples/son.pl (639, 2021-09-13)
examples/sorter.pl (9475, 2021-09-13)
examples/strings1.pl (682, 2021-09-13)
examples/strings2.pl (1289, 2021-09-13)
examples/strings3.pl (1203, 2021-09-13)
examples/tests.pl (10785, 2021-09-13)
examples/trains.pl (5299, 2021-09-13)
examples/undirected-edge.pl (359, 2021-09-13)
metagol.bib (222, 2021-09-13)
metagol.pl (10805, 2021-09-13)
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# THIS VERSION OF METAGOL IS NO LONGER UNDER DEVELOPMENT. IT HAS (MOSTLY) BEEN SUPERSEDED BY [POPPER](https://github.com/logic-and-learning-lab/Popper). Metagol is an inductive logic programming (ILP) system based on meta-interpretive learning. If you use Metagol for research, please use [this citation](https://raw.githubusercontent.com/metagol/metagol/master/metagol.bib) and cite the relevant paper. #### Using Metagol Metagol is written in Prolog and runs with SWI-Prolog. The following code demonstrates learning the grandparent relation given the mother and father relations as background knowledge: ```prolog :- use_module('metagol'). %% metagol settings body_pred(mother/2). body_pred(father/2). %% background knowledge mother(ann,amy). mother(ann,andy). mother(amy,amelia). mother(linda,gavin). father(steve,amy). father(steve,andy). father(gavin,amelia). father(andy,spongebob). %% metarules metarule([P,Q],[P,A,B],[[Q,A,B]]). metarule([P,Q,R],[P,A,B],[[Q,A,B],[R,A,B]]). metarule([P,Q,R],[P,A,B],[[Q,A,C],[R,C,B]]). %% learning task :- %% positive examples Pos = [ grandparent(ann,amelia), grandparent(steve,amelia), grandparent(ann,spongebob), grandparent(steve,spongebob), grandparent(linda,amelia) ], %% negative examples Neg = [ grandparent(amy,amelia) ], learn(Pos,Neg). ``` Running the above program will print the output: ```prolog % clauses: 1 % clauses: 2 % clauses: 3 grandparent(A,B):-grandparent_1(A,C),grandparent_1(C,B). grandparent_1(A,B):-mother(A,B). grandparent_1(A,B):-father(A,B). ``` In this program the predicate symbol `grandparent_1` is invented (i.e. does not appear in the background knowledge nor in the examples). #### Metarules Metagol requires metarules as input. Metarules define the form of clauses permitted in a hypothesis and thus the search space. Metarules are of the form `metarule(Name, Subs, Head, Body)`. An example metarule is: ```prolog metarule(chain, [P,Q,R], [P,A,B], [[Q,A,C],[R,C,B]]). ``` Here the symbols `P`, `Q`, and `R` denote second-order variables (i.e. can unify with predicate symbols). The symbols `A`, `B`, and `C` denote first-order variables (i.e. can unify with constant symbols). Metagol will search for appropriate substitutions for the variables in the second argument of a metarule (*Subs*). Users must supply metarules. Deciding which metarules to use is still an open (and hard!) problem. Some work in this area is detailed in the papers: * A. Cropper and S. Tourret. [Logical minimisation of metarules](http://andrewcropper.com/pubs/mlj19-reduce.pdf). Machine Learning 2019. * A. Cropper and S. Tourret: [Derivation reduction of metarules in meta-interpretive learning](http://andrewcropper.com/pubs/ilp18-dreduce.pdf). ILP 2018. * A. Cropper and S.H. Muggleton: [Logical minimisation of meta-rules within meta-interpretive learning](http://andrewcropper.com/pubs/ilp14-minmeta.pdf). ILP 2014. For learning dyadic programs without constant symbols, we recommend using these metarules: ```prolog metarule([P,Q], [P,A,B], [[Q,A,B]]). % identity metarule([P,Q], [P,A,B], [[Q,B,A]]). % inverse metarule([P,Q,R], [P,A,B], [[Q,A],[R,A,B]]). % precon metarule([P,Q,R], [P,A,B], [[Q,A,B],[R,B]]). % postcon metarule([P,Q,R], [P,A,B], [[Q,A,C],[R,C,B]]). % chain ``` Please look at the examples to see how metarules are used. #### Recursion The above metarules are all non-recursive. By contrast, this metarule is recursive: ```prolog metarule([P,Q], [P,A,B], [[Q,A,C],[P,C,B]]). ``` See the find-duplicate, sorter, member, and string examples. #### Interpreted background knowledge Metagol supports interpreted background knowledge (IBK), which was initially introduced in these papers: * A. Cropper, R. Morel, and S.H. Muggleton. [Learning higher-order logic programs](http://andrewcropper.com/pubs/mlj19-metaho.pdf). Machine Learning 2019. * A. Cropper and S.H. Muggleton: [Learning Higher-Order Logic Programs through Abstraction and Invention](http://andrewcropper.com/pubs/ijcai16-metafunc.pdf). IJCAI 2016. IBK is usually used to learn higher-order programs. For instance, one can define the `map/3` construct as follows: ```prolog ibk([map,[],[],_],[]). ibk([map,[A|As],[B|Bs],F],[[F,A,B],[map,As,Bs,F]]). ``` Given this IBK, Metagol will try to prove it through meta-interpretation, and will also try to learn a sub-program for the atom `[F,A,B]`. See the droplast, higher-order, and ibk examples. #### Metagol settings You can specify a maximum timeout (in seconds) for Metagol as follows: ```prolog metagol:timeout(600). % default 10 minutes ``` Metagol searches for a hypothesis using iterative deepening on the number of clauses in the solution. You can specify a maximum number of clauses: ```prolog metagol:max_clauses(Integer). % default 10 ``` The following flag denotes whether the learned theory should be functional: ```prolog metagol:functional. % default false ``` If the functional flag is enabled, then you must define a func_test predicate. An example func test is: ```prolog func_test(Atom1,Atom2,Condition):- Atom1 = [P,A,X], Atom2 = [P,A,Y], Condition = (X=Y). ``` This func test is used in the robot examples. This test checks that if Metagol can prove any two Atoms `Atom1` and `Atom2` from an induced program, then the condition `X=Y` always holds. For more examples of functional tests, see the robots.pl, sorter.pl, and strings2.pl files. ### Publications Here are some publications on MIL and Metagol. #### Key papers * A. Cropper and S. Tourret. [Logical minimisation of metarules](http://andrewcropper.com/pubs/mlj19-reduce.pdf). Machine Learning 2019. * A. Cropper, R. Morel, and S.H. Muggleton. [Learning higher-order logic programs](http://andrewcropper.com/pubs/mlj19-metaho.pdf). Machine Learning 2019. * S.H. Muggleton, D. Lin, and A. Tamaddoni-Nezhad: [Meta-interpretive learning of higher-order dyadic datalog: predicate invention revisited](https://link.springer.com/article/10.1007/s10994-014-5471-y). Machine Learning 2015. * S.H. Muggleton, D. Lin, N. Pahlavi, and A. Tamaddoni-Nezhad: [Meta-interpretive learning: application to grammatical inference](https://link.springer.com/article/10.1007/s10994-013-5358-3). Machine Learning 2014. #### Theory and Implementation * A. Cropper and S. Tourret. [Logical minimisation of metarules](http://andrewcropper.com/pubs/mlj19-reduce.pdf). Machine Learning 2019. * A. Cropper, R. Morel, and S.H. Muggleton. [Learning higher-order logic programs](http://andrewcropper.com/pubs/mlj19-metaho.pdf). Machine Learning 2019. * A. Cropper and S.H. Muggleton: [Learning efficient logic programs](http://andrewcropper.com/pubs/mlj18-metaopt.pdf). Machine learning 2018. * R. Morel, A. Cropper, and L. Ong. [Typed meta-interpretive learning of logic programs](http://andrewcropper.com/pubs/jelia19-typed.pdf). JELIA 2019. * A. Cropper and S. Tourret: [Derivation Reduction of Metarules in Meta-interpretive Learning](http://andrewcropper.com/pubs/ilp18-dreduce.pdf). ILP 2018. * A. Cropper and S.H. Muggleton: [Learning Higher-Order Logic Programs through Abstraction and Invention](http://andrewcropper.com/pubs/ijcai16-metafunc.pdf). IJCAI 2016. * A. Cropper and S.H. Muggleton: [Learning Efficient Logical Robot Strategies Involving Composable Objects](http://andrewcropper.com/pubs/ijcai15-metagolo.pdf). IJCAI 2015. * S.H. Muggleton, D. Lin, and A. Tamaddoni-Nezhad: [Meta-interpretive learning of higher-order dyadic datalog: predicate invention revisited](https://link.springer.com/article/10.1007/s10994-014-5471-y). Machine Learning 2015. * S.H. Muggleton, D. Lin, N. Pahlavi, and A. Tamaddoni-Nezhad: [Meta-interpretive learning: application to grammatical inference](https://link.springer.com/article/10.1007/s10994-013-5358-3). Machine Learning 2014. * A. Cropper and S.H. Muggleton: [Logical Minimisation of Meta-Rules Within Meta-Interpretive Learning](http://andrewcropper.com/pubs/ilp14-minmeta.pdf). ILP 2014. * S.H. Muggleton, D. Lin, Jianzhong Chen, and A. Tamaddoni-Nezhad: MetaBayes: Bayesian Meta-Interpretative Learning Using Higher-Order Stochastic Refinement. ILP 2013. #### Applications / other * A.Cropper: [Forgetting to learn logic programs](http://andrewcropper.com/pubs/aaai20-forgetgol.pdf). AAAI 2020. * A.Cropper: [Playgol: learning programs through play](http://andrewcropper.com/pubs/ijcai19-playgol.pdf). IJCAI 2019. * S.H. Muggleton, U. Schmid, C. Zeller, A. Tamaddoni-Nezhad, and T.R. Besold: Ultra-Strong Machine Learning: comprehensibility of programs learned with ILP. Machine Learning 2018. * S. Muggleton, W-Z. Dai, C. Sammut, A. Tamaddoni-Nezhad, J. Wen, and Z-H. Zhou: Meta-Interpretive Learning from noisy images. Machine Learning 2018. * M. Siebers and U. Schmid: [Was the Year 2000 a Leap Year? Step-Wise Narrowing Theories with Metagol](https://link.springer.com/chapter/10.1007/978-3-319-99960-9_9). ILP 2018. * A. Cropper, A. Tamaddoni-Nezhad, and S.H. Muggleton: [Meta-Interpretive Learning of Data Transformation Programs](http://andrewcropper.com/pubs/ilp15-datacurate.pdf). ILP 2015. * A. Cropper and S.H. Muggleton: [Can predicate invention compensate for incomplete background knowledge?](http://andrewcropper.com/pubs/scai15-incomplete.pdf) SCAI 2015. * D. Lin, E. Dechter, K. Ellis, J.B. Tenenbaum, and S.H. Muggleton: [Bias reformulation for one-shot function induction](https://www.doc.ic.ac.uk/~shm/Papers/ECAI-546.pdf). ECAI 2014. #### Theses * A. Cropper: [Efficiently learning efficient programs](http://andrewcropper.com/pubs/phd-thesis.pdf). Imperial College London, UK 2017 * D. Lin: Logic programs as declarative and procedural bias in inductive logic programming. Imperial College London, UK 2013

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