1. Motivation

I Knowledge Graphs: huge collections of positive unaryand binary facts treated under Open World Assumption

isMarriedTo(alice, bob), researcher(mat)I Automatically constructed, thus

incomplete / inaccurateI Horn rule mining to complete / clean KGs

e.g., [Galárraga, et al., 2015]I But: exceptions are not captured by

Horn rules, thus erroneous predictions

I Our aim: mine rules with exceptions from KGsI Challenges: OWA, huge size of KGs

Motivation Nonmonotonic Rules Problem Statement

Mining Rules

NELL

2 / 9

conf(r, KG) =| |

| |+ | |=

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r : livesIn(X, Z)← isMarriedTo(Y, X), livesIn(Y, Z)I Contributions:I Quality-based Horn theory revision frameworkI Exception ranking method based on cross-talk among the rulesI Experiments on real-world Knowledge Graphs

3. Approach Overview

2. Quality-based Horn Theory Revision

Given:I Knowledge GraphI Set of Horn rules

Find:I Nonmonotonic rules revision, s.t.

I average conviction is maximized

conv(r, KG) =1− supp(r, KG)

1− conf(r, KG)I number of conflicting predictions is minimized

livesIn(X, Z)← isMarriedTo(Y, X), livesIn(Y, Z), not researcher(X)

not_livesIn(X, Z)← isMarriedTo(Y, X), livesIn(Y, Z), researcher(X)

livesIn(X, Z)← bornIn(X, Z), not moved(X)

not_livesIn(X, Z)← bornIn(X, Z), moved(X)

{livesIn(c, d), not_livesIn(c, d)}︸ ︷︷ ︸conflicting predictions

4. (Ab)normal Substitutions and Exception Candidates

r : livesIn(X, Z)← isMarriedTo(Y, X), livesIn(Y, Z) {not researcher(X)|not artist(Y)}︸ ︷︷ ︸exception candidates

5. Exception Ranking

rule1 . . . . . . . . .{ e1 | e2 | e3 | . . .}rule2 . . . . . . . . .{e1 | e2 | e3 | . . .}rule3 . . . . . . . . .{ e1 | e2 | e3 | . . .}

Globally best revision is infeasible: exponentially many candidates!

I Naive: pick a rule exception that results in the highest conviction

I Partial materialization (PM): apply all rules apart from a given one with theirexceptions to KG, then pick an exception for the given rule that results in thehighest average conviction of it and its rewriting

I Ordered partial materialization (OPM): same as PM, but apply only rulesordered higher than a given one

I Weighted ordered partial materialization (WOPM): same as OPM, but takesweights of predicted facts into account

6. Experiments

I Approximated ideal KG: originalI Available KG: randomly remove 20%

of facts for every relation from available KGI Rules: h(X, Y)← p(X, Z), q(Z, Y)I Exceptions: e1(X), e2(Y), e3(X, Y)I OPM ranker, predictions computed by an answer set solver

Examples of mined rules:r1 : writtenBy(X, Z)← hasPredecessor(X, Y), writtenBy(Y, Z), not american_film(X)

r2 : actedIn(X, Z)← isMarriedTo(X, Y), directed(Y, Z), not silent_film_actor(X)

References

I D. H. Tran., D. Stepanova, M. G. Elrab, Francesca A. Lisi, G. Weikum. Towards Nonmonotonic RuleLearning from Knowledge Graphs. In proc. Inductive Logic Programming, 2016.

I M. Gad-elrab, D.Stepanova, J.Urbani, G.Weikum. Exception-enriched Rule Learning from KnowledgeGraphs. In proc. International Semantic Web Conference, 2016.

I L. Galárraga, C. Teflioudi, K. Hose, F. M. Suchanek. Fast Rule Mining in Ontological Knowledge Baseswith AMIE+. VLBD journal, 2015.

I S. Wrobel. First Order Theory Refinement. In proc. Inductive Logic Programming, 1996.

7. Further Work

I Cardinality meta-data in rule learning: John has 5 children, 3 people won award

I Learn cardinality rules: “If X has≤ 2 siblings, then his parents have≤ 3 children”

Combining Rule Learning and Nonmonotonic Reasoningfor Link Prediction in Knowledge Graph

Francesca A. Lisi1, Daria Stepanova2

francesca.lisi@uniba.it, dstepano@mpi-inf.mpg.de,1Università degli Studi di Bari “Aldo Moro", Bari, Italy

2Max Planck Institute for Informatics, Saarbrücken, Germany