Logic Programs as Declarative and Procedural Bias in Inductive Logic Programming

Machine Learning is necessary for the development of Artificial Intelligence, as pointed out by Turing in his 1950 article ``Computing Machinery and Intelligence''. It is in the same article that Turing suggested the use of computational logic and background knowledge for learning. This thesis follows a logic-based machine learning approach called Inductive Logic Programming (ILP), which is advantageous over other machine learning approaches in terms of relational learning and utilising background knowledge. ILP uses logic programs as a uniform representation for hypothesis, background knowledge and examples, but its declarative bias is usually encoded using metalogical statements. This thesis advocates the use of logic programs to represent declarative and procedural bias, which results in a framework of single-language representation. We show in this thesis that using a logic program called the top theory as declarative bias leads to a sound and complete multi-clause learning system MC-TopLog. It overcomes the entailment-incompleteness of Progol, thus outperforms Progol in terms of predictive accuracies on learning grammars and strategies for playing Nim game. MC-TopLog has been applied to two real-world applications funded by Syngenta, which is an agriculture company. A higher-order extension on top theories results in meta-interpreters, which allow the introduction of new predicate symbols. Thus the resulting ILP system Metagol can do predicate invention, which is an intrinsically higher-order logic operation. Metagol also leverages the procedural semantic of Prolog to encode procedural bias, so that it can outperform both its ASP version and ILP systems without an equivalent procedural bias in terms of efficiency and accuracy. This is demonstrated by the experiments on learning Regular, Context-free and Natural grammars. Metagol is also applied to non-grammar learning tasks involving recursion and predicate invention, such as learning a definition of staircases and robot strategy learning. Both MC-TopLog and Metagol are based on a $\top$-directed framework, which is different from other multi-clause learning systems based on Inverse Entailment, such as CF-Induction, XHAIL and IMPARO. Compared to another $\top$-directed multi-clause learning system TAL, Metagol allows the explicit form of higher-order assumption to be encoded in the form of meta-rules.Open Acces

Inductive programming meets the real world

© Gulwani, S. et al. | ACM 2015. This is the author's version of the work. It is posted here for your personal use. Not for redistribution. The definitive Version of Record was published in Communications of the ACM, http://dx.doi.org/10.1145/2736282[EN] Since most end users lack programming skills they often spend considerable time and effort performing tedious and repetitive tasks such as capitalizing a column of names manually. Inductive Programming has a long research tradition and recent developments demonstrate it can liberate users from many tasks of this kind.Gulwani, S.; Hernández-Orallo, J.; Kitzelmann, E.; Muggleton, SH.; Schmid, U.; Zorn, B. (2015). Inductive programming meets the real world. Communications of the ACM. 58(11):90-99. doi:10.1145/2736282S90995811Bengio, Y., Courville, A. and Vincent, P. Representation learning: A review and new perspectives.Pattern Analy. Machine Intell. 35, 8 (2013), 1798--1828.Bielawski, B. Using the convertfrom-string cmdlet to parse structured text.PowerShell Magazine, (Sept. 9, 2004); http://www.powershellmagazine.com/2014/09/09/using-the-convertfrom-string-cmdlet-to-parse-structured-text/Carlson, A., Betteridge, J., Kisiel, B., Settles, B., Hruschka-Jr, E.R. and T.M. Mitchell, T.M. Toward an architecture for never-ending language learning. InAAAI, 2010.Chandola, V., Banerjee, A. and V. Kumar, V. Anomaly detection: A survey.ACM Computing Surveys 41, 3 (2009), 15.Cypher, A. (Ed).Watch What I Do: Programming by Demonstration.MIT Press, Cambridge, MA, 1993.Ferri-Ramírez, C., Hernández-Orallo, J. and Ramírez-Quintana, M.J. Incremental learning of functional logic programs. InProceedings of FLOPS, 2001, 233--247.Flener, P. and Schmid, U. An introduction to inductive programming.AI Review 29, 1 (2009), 45--62.Gulwani, S. Dimensions in program synthesis. InProceedings of PPDP, 2010.Gulwani, S. Automating string processing in spreadsheets using input-output examples. InProceedings of POPL, 2011; http://research.microsoft.com/users/sumitg/flashfill.html.Gulwani, S. Example-based learning in computer-aided STEM education.Commun. ACM 57, 8 (Aug 2014), 70--80.Gulwani, S., Harris, W. and Singh, R. Spreadsheet data manipulation using examples.Commun. ACM 55, 8 (Aug. 2012), 97--105.Henderson, R.J. and Muggleton, S.H. Automatic invention of functional abstractions.Latest Advances in Inductive Logic Programming, 2012.Hernández-Orallo, J. Deep knowledge: Inductive programming as an answer, Dagstuhl TR 13502, 2013.Hofmann, M. and Kitzelmann, E. I/O guided detection of list catamorphisms---towards problem specific use of program templates in IP. InACM SIGPLAN PEPM, 2010.Jha, J., Gulwani, S., Seshia, S. and Tiwari, A. Oracle-guided component-based program synthesis. InProceedings of the ICSE, 2010.Katayama, S. Efficient exhaustive generation of functional programs using Monte-Carlo search with iterative deepening. InProceedings of PRICAI, 2008.Kitzelmann, E. Analytical inductive functional programming.LOPSTR 2008, LNCS 5438.Springer, 2009, 87--102.Kitzelmann, E. Inductive programming: A survey of program synthesis techniques. InAAIP, Springer, 2010, 50--73.Kitzelmann, E. and Schmid, U. Inductive synthesis of functional programs: An explanation based generalization approach.J. Machine Learning Research 7, (Feb. 2006), 429--454.Kotovsky, K., Hayes, J.R. and Simon, H.A. Why are some problems hard? Evidence from Tower of Hanoi.Cognitive Psychology 17, 2 (1985), 248--294.Lau, T.A. Why programming-by-demonstration systems fail: Lessons learned for usable AI.AI Mag. 30, 4, (2009), 65--67.Lau, T.A., Wolfman, S.A., Domingos, P. and Weld, D.S. Programming by demonstration using version space algebra.Machine Learning 53, 1-2 (2003), 111--156.Le, V. and Gulwani, S. FlashExtract: A framework for data extraction by examples. InProceedings of PLDI, 2014.Lieberman, H. (Ed).Your Wish is My Command: Programming by Example.Morgan Kaufmann, 2001.Lin, D., Dechter, E., Ellis, K., Tenenbaum, J.B. and Muggleton, S.H. Bias reformulation for one-shot function induction. InProceedings of ECAI, 2014.Marcus, G.F. The Algebraic Mind.Integrating Connectionism and Cognitive Science.Bradford, Cambridge, MA, 2001.Martìnez-Plumed, C. Ferri, Hernández-Orallo, J. and M.J. Ramírez-Quintana. On the definition of a general learning system with user-defined operators.arXiv preprint arXiv:1311.4235, 2013.Menon, A., Tamuz, O., Gulwani, S., Lampson, B. and Kalai, A. A machine learning framework for programming by example. InProceedings of the ICML, 2013.Miller, R.C. and Myers, B.A. Multiple selections in smart text editing. InProceedings of IUI, 2002, 103--110.Muggleton, S.H. Inductive Logic Programming.New Generation Computing 8, 4 (1991), 295--318.Muggleton, S.H. and Lin, D. Meta-interpretive learning of higher-order dyadic datalog: Predicate invention revisited.IJCAI 2013, 1551--1557.Muggleton, S.H., Lin, D., Pahlavi, N. and Tamaddoni-Nezhad, A. Meta-interpretive learning: application to grammatical inference.Machine Learning 94(2014), 25--49.Muggleton, S.H., De Raedt, L., Poole, D., Bratko, I., Flach, P. and Inoue, P. ILP turns 20: Biography and future challenges.Machine Learning 86, 1 (2011), 3--23.Olsson, R. Inductive functional programming using incremental program transformation.Artificial Intelligence 74, 1 (1995), 55--83.Perelman, D., Gulwani, S., Grossman, D. and Provost, P. Test-driven synthesis.PLDI, 2014.Raza, M., Gulwani, S. and Milic-Frayling, N. Programming by example using least general generalizations.AAAI, 2014.Schmid, U. and Kitzelmann, E. Inductive rule learning on the knowledge level.Cognitive Systems Research 12, 3 (2011), 237--248.Schmid, U. and Wysotzki, F. Induction of recursive program schemes.ECML 1398 LNAI(1998), 214--225.Shapiro, E.Y. An algorithm that infers theories from facts.IJCAI(1981), 446--451.Solar-Lezama, A.Program Synthesis by Sketching.Ph.D thesis, UC Berkeley, 2008.Summers, P.D. A methodology for LISP program construction from examples.JACM 24, 1 (1977), 162--175.Tenenbaum, J.B., Griffiths, T.L. and Kemp, C. Theory-based Bayesian models of inductive learning and reasoning.Trends in Cognitive Sciences 10, 7 (2006), 309--318.Young, S. Cognitive user interfaces.IEEE Signal Processing 27, 3 (2010), 128--140

Pac-Learning Recursive Logic Programs: Efficient Algorithms

We present algorithms that learn certain classes of function-free recursive logic programs in polynomial time from equivalence queries. In particular, we show that a single k-ary recursive constant-depth determinate clause is learnable. Two-clause programs consisting of one learnable recursive clause and one constant-depth determinate non-recursive clause are also learnable, if an additional ``basecase'' oracle is assumed. These results immediately imply the pac-learnability of these classes. Although these classes of learnable recursive programs are very constrained, it is shown in a companion paper that they are maximally general, in that generalizing either class in any natural way leads to a computationally difficult learning problem. Thus, taken together with its companion paper, this paper establishes a boundary of efficient learnability for recursive logic programs.Comment: See http://www.jair.org/ for any accompanying file