Using Binary Decision Diagrams to Enumerate Inductive Logic Programming Solutions

We propose an efficient algorithm for enumerating solutions of Inductive Logic Programming problem with Binary Decision Diagrams. • Basic formalization of ILP allows many potential solutions, and we might miss important solutions. ⇒ Enumeration is fundamental technique to avoid such missing. • Key idea: We use Binary Decision Diagram for enumeration. • Binary Decision Diagram (BDD) is a directed acyclic graph representing compactly a Boolean function. • We show how to build recursively a Binary Decision Diagram that represents the set of solutions. 0

[1]  Luc De Raedt,et al.  Learning the Parameters of Probabilistic Logic Programs from Interpretations , 2011, ECML/PKDD.

[2]  Céline Rouveirol,et al.  Extensions of Inversion of Resolution Applied to Theory Completion , 1992 .

[3]  Luc De Raedt,et al.  ProbLog: A Probabilistic Prolog and its Application in Link Discovery , 2007, IJCAI.

[4]  Akihiro Yamamoto,et al.  Learning Elementary Formal Systems , 1992, Theor. Comput. Sci..

[5]  Akihiro Yamamoto,et al.  Hypothesis finding based on upward refinement of residue hypotheses , 2003, Theor. Comput. Sci..

[6]  Ehud Y. Shapiro.  An Algorithm that Infers Theories from Facts , 1981, IJCAI.

[7]  Stephen Muggleton,et al.  A Strategy for Constructing New Predicates in First-Order Logic , 1988, EWSL.

[8]  Luc De Raedt,et al.  Inference and learning in probabilistic logic programs using weighted Boolean formulas , 2013, Theory and Practice of Logic Programming.

[9]  Stephen Muggleton,et al.  Inverse entailment and progol , 1995, New Generation Computing.

[10]  Ronald L. Rivest,et al.  Inferring Decision Trees Using the Minimum Description Length Principle , 1989, Inf. Comput..

[11]  David Eppstein,et al.  Finding the k shortest paths , 1994, Proceedings 35th Annual Symposium on Foundations of Computer Science.

[12]  J. Rissanen,et al.  Modeling By Shortest Data Description* , 1978, Autom..

[13]  Ian H. Witten,et al.  Complexity-based induction , 2004, Machine Learning.

[14]  Ashwin Srinivasan,et al.  Compression, Significance, and Accuracy , 1992, ML.

[15]  Sheldon B. Akers,et al.  Binary Decision Diagrams , 1978, IEEE Transactions on Computers.

[16]  Sofia Cassel,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 2012 .

[17]  Shin-ichi Minato,et al.  Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems , 1993, 30th ACM/IEEE Design Automation Conference.

[18]  Gordon Plotkin,et al.  A Note on Inductive Generalization , 2008 .

[19]  Chen-Shang Lin,et al.  On the OBDD-Representation of General Boolean Functions , 1992, IEEE Trans. Computers.

[20]  Stephen Muggleton,et al.  Learning from Positive Data , 1996, Inductive Logic Programming Workshop.