DIPARTIMENTO   DI   INFORMATICA
Università di Torino

Challenging Relational Learning

The following table contains a set of 451 artificial relational problems designed in order to test the ability of a relational learner at learning in the so called "mushy region", i.e the phase transition in matching complexity which occurs for critical values of the number L of constants occurring in an example and the number m of literals occurring in an inductive hypothesis.
Every problem consists of a triple: <Target concept, Learning set, Test set>

  • Target Concept is a first order formula of m binary literals over 4 variables,
  • Learning Set and Test Set contains 100 positive and 100 negative examples, each.
  • Every example consists of exactly L objects (constants).
Problem distribution in (m,L)-plane
Figure 1: Distribution of the Learning problems in (m, L)-plane.
Symbol (+) denotes problems solved by FOIL, i.e. for which FOIL found the correct solution or an approximation of it (Error rate < 20% on test set).

Symbol (.) denotes problems where FOIL failed (Error rate > 20% on test set).

Here is a list of the files in every archive that are useful and have meaning (all problems contain the same set of files), all other files being garbage.
p.mMM.lLL/f0the true concept (R?? --> brel??)
p.mMM.lLL/brel???.pl.gzthe tuples satisfying relation brel???
p.mMM.lLL/yes.f.gzlist of all positive instance in the dataset
p.mMM.lLL/no.f.gzlist of all negative instance in the dataset
p.mMM.lLL/no.learn.gzlist of negative instances used for learning
p.mMM.lLL/no.test.gzlist of negative instances used for testing
p.mMM.lLL/yes.learn.gzlist of positive instances used for learning
p.mMM.lLL/yes.test.gzlist of positive instances used for testing

The signature of the predicates defined in the files is the following:

  • brel???(Instance,Element1,Element2) Element1 and Element2 are in relation brel???
  • yes(Instance) Instance is positive
  • no(Instance) Instance is negative

Each target concept is a unique conjunction of predicates. So, a file f0 that contains the following lines:
	R0(x0, x1)
	R1(x1, x2)
	R2(x2, x3), R3(x1, x3), R4(x2, x3)
is to be intepreted as the following 1-clause logic program:
	yes(X):- brel0(X,X0,X1), brel1(X,X1,X2), brel2(X,X2,X3),
		 brel3(X,X1,X3), brel4(X,X2,X3).

Problem List: the numbers following m and l indicate the number m of literals in the target concept and the number L of constants in the examples. You can downloads the whole dataset here.

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