S. Abiteboul and V. Vianu, Datalog extensions for database queries and updates, Journal of Computer and System Sciences, vol.43, issue.1
DOI : 10.1016/0022-0000(91)90032-Z

URL : https://hal.archives-ouvertes.fr/inria-00075656

H. Agli, Business Rules Uncertainty Management with Probabilistic Relational Models
DOI : 10.1016/S0019-9958(65)90241-X

URL : https://hal.archives-ouvertes.fr/hal-01345421

R. Agrawal and R. Srikant, Fast Algorithms for Mining Association Rules

D. O. Aihe and A. J. Gonzalez, Correcting flawed expert knowledge through reinforcement learning, Expert Systems with Applications, vol.42, issue.17-18
DOI : 10.1016/j.eswa.2015.04.015

E. M. Gold, Language identification in the limit, Information and Control, vol.10, issue.5
DOI : 10.1016/S0019-9958(67)91165-5

R. Misener and C. A. Floudas, ANTIGONE: Algorithms for coNTinuous / Integer Global Optimization of Nonlinear Equations, Journal of Global Optimization, vol.56, issue.2
DOI : 10.1021/ie800257x

G. Antoniou, Combining rules and ontologies: a survey, 2005.

Y. Anzai and H. A. Simon, The theory of learning by doing., Psychological Review, vol.86, issue.2
DOI : 10.1037/0033-295X.86.2.124

B. Kamsu-foguem, F. Rigal, and F. Mauget, Mining association rules for the quality improvement of the production process, Expert Systems with Applications, vol.40, issue.4
DOI : 10.1016/j.eswa.2012.08.039

URL : https://hal.archives-ouvertes.fr/hal-00767649

]. N. Sahinidis, BARON: A general purpose global optimization software package, Journal of Global Optimization, vol.19, issue.2
DOI : 10.1007/BF00138693

R. B. Gramacy, Modeling an Augmented Lagrangian for Blackbox Constrained Optimization, Technometrics, vol.65, issue.1, pp.1-11, 2016.
DOI : 10.1007/978-3-7908-2413-1_24

URL : http://arxiv.org/pdf/1403.4890

J. O. Berger, Statistical Decision Theory and Bayesian Analysis, 1985.
DOI : 10.1007/978-1-4757-4286-2

B. Berstel and -. Silva, Formalizing Both Refraction-Based and Sequential Executions of Production Rule Programs

B. Berstel and -. Silva, Operational Semantics of Rule Programs

A. Kolber, Defining Business Rules -What are They Really? Project Report 3. The Business Rules Group, 2000.

L. Rosa, A Comparative Study of Correlation Engines for Security Event Management, Proceedings of the 10th International Conference on Cyber Warfare and Security, 2015.

B. G. Buchanan and E. H. Shortliffe, Rule Based Expert Systems: The Mycin Experiments of the Stanford Heuristic Programming Project (The Addison-Wesley Series in Artificial Intelligence

R. M. Burstall, Proving Properties of Programs by Structural Induction, The Computer Journal, vol.12, issue.1
DOI : 10.1093/comjnl/12.1.41

M. Aps, Product Description. https://www.mosek.com/products/mosek

T. Frühwirth, Theory and practice of constraint handling rules, The Journal of Logic Programming, vol.37, issue.1-3
DOI : 10.1016/S0743-1066(98)10005-5

A. Church, An Unsolvable Problem of Elementary Number Theory, American Journal of Mathematics, vol.58, issue.2
DOI : 10.2307/2371045

W. J. Clancey, The epistemology of a rule-based expert system ???a framework for explanation, Artificial Intelligence, vol.20, issue.3
DOI : 10.1016/0004-3702(83)90008-5

C. Culbert and G. Riley, CLIPS Basic Programming Guide, 2003.

P. M. Murphy and M. J. Pazzani, Revision of Production System Rule-Bases
DOI : 10.1016/B978-1-55860-335-6.50032-5

J. Hiriart-urruty and C. Lemaréchal, Fundamentals of Convex Analysis, 2001.
DOI : 10.1007/978-3-642-56468-0

P. Belotti, Branching and bounds tightening techniques for non-convex MINLP
DOI : 10.1080/10556780903087124

A. Cohen, S. Goldwasser, and V. Vaikuntanathan, Aggregate Pseudorandom Functions and Connections to Learning
DOI : 10.1007/978-3-662-46497-7_3

URL : http://eprint.iacr.org/2015/038.pdf

M. W. Curtis, A Turing Machine Simulator, Journal of the ACM, vol.12, issue.1, pp.1-13, 1965.
DOI : 10.1145/321250.321251

H. Gallaire and J. Minker, Logic and Data Bases, 1978.
DOI : 10.1007/978-1-4684-3384-5

R. Davis, B. Buchanan, and E. Shortliffe, Production Rules as a Representation for a Knowledge-Based Consultation Program

L. M. Rios and N. V. Sahinidis, Derivative-free optimization: a review of algorithms and comparison of software implementations, Journal of Global Optimization, vol.18, issue.3
DOI : 10.1088/0953-8984/18/39/002

M. A. Duran and I. G. Grossmann, An Outer-approximation Algorithm for a Class of Mixed-Integer Nonlinear Programs

A. C. Scott, J. S. Bennett, and M. Peairs, The EMYCIN Manual, 1981.

D. Angluin, Queries and concept learning, Machine Learning, vol.27, issue.4
DOI : 10.1007/BF00116828

C. L. Forgy, Rete: A fast algorithm for the many pattern/many object pattern match problem, Artificial Intelligence, vol.19, issue.1, pp.17-37, 1982.
DOI : 10.1016/0004-3702(82)90020-0

T. Westerlund and K. Lundqvist, Alpha-ECP, Version 5.101: An Interactive MINLP-Solver Based on the Extended Cutting Plane Method

R. Gandy, Church's Thesis and Principles for Mechanisms
DOI : 10.1016/S0049-237X(08)71257-6

R. L. Sallam and G. Herschel, Automating Decisions With Intelligent Decision Automation, Market Analysis. Gartner, 2009.

A. Likas, N. Vlassis, and J. J. Verbeek, The global k-means clustering algorithm, Pattern Recognition, vol.36, issue.2
DOI : 10.1016/S0031-3203(02)00060-2

URL : https://hal.archives-ouvertes.fr/inria-00321493

G. The and . Kit, Product Description

O. Goldreich, S. Goldwasser, and S. Micali, How to construct random functions, Journal of the ACM, vol.33, issue.4
DOI : 10.1145/6490.6503

URL : http://dl.acm.org/ft_gateway.cfm?id=6503&type=pdf

R. Greinier, The complexity of theory revision, Artificial Intelligence, vol.107, issue.2
DOI : 10.1016/S0004-3702(98)00107-6

G. Optimizer, Product Description. http://www.gurobi.com/products/gurobi-optimizer

B. Von-halle, Business Rules Applied: Building Better Systems Using the Business Rules Approach, 2001.

J. R. Quinlan, Induction of decision trees, Machine Learning, vol.1, issue.1
DOI : 10.1037/13135-000

P. Albert, ILOG Rules, embedding rules in C++: Results and limits

R. Hat-jboss and B. 6. Datasheet, http://www.redhat.com/cms/managed-files/mi-brms-6-datasheet -11436837-inc0357730lw-201603-en, 2016.

R. M. Karp, Reducibility Among Combinatorial Problems
DOI : 10.1007/978-3-540-68279-0_8

H. Kelbassa, Optimal refinement of rule bases

H. Kelbassa and R. Knauf, A Process Approach to Rule Base Validation and Refinement

S. C. Kleene, Introduction to Metamathematics

T. Cover and P. Hart, Nearest neighbor pattern classification, IEEE Transactions on Information Theory, vol.13, issue.1
DOI : 10.1109/TIT.1967.1053964

URL : http://ssg.mit.edu/cal/abs/2000_spring/np_dens/classification/cover67.pdf

A. Church, A Set of Postulates for the Foundation of Logic

M. Palmirani, LegalRuleML: XML-Based Rules and Norms
DOI : 10.1007/s10506-009-9079-7

A. Johnsen and A. J. Berre, A Bridge between Legislator and Technologist-Formalization in SBVR for Improved Quality and Understanding of Legal Rules

Y. Lin and L. Schrage, The global solver in the LINDO API, Optimization Methods and Software, vol.24, issue.4-5
DOI : 10.1080/10556780902753221

Y. Matiyasevich, Hilbert's Tenth Problem, 1993.

M. Minsky, Computation: Finite and Infinite Machines, 1972.

T. Hastie, R. Tibshirani, and J. Friedman, The Elements of Statistical Learning, 2013.

R. Caruana and A. Niculescu, An empirical comparison of supervised learning algorithms, Proceedings of the 23rd international conference on Machine learning , ICML '06
DOI : 10.1145/1143844.1143865

B. Zadrozny and C. Elkan, Transforming classifier scores into accurate multiclass probability estimates, Proceedings of the eighth ACM SIGKDD international conference on Knowledge discovery and data mining , KDD '02
DOI : 10.1145/775047.775151

URL : http://www.cse.unsw.edu.au/~qzhang/papers/p44.pdf

M. , Z. Muehlen, and M. Indulska, Modeling languages for business processes and business rules: A representational analysis

E. H. Shortcliffe, Computer-Based Medical Consultations: MYCIN, 1976.

R. Lippmann, An Introduction to Computing with Neural Nets
DOI : 10.1109/massp.1987.1165576

DOI : 10.1016/B978-0-12-170150-5.50016-0

A. Newell and H. A. Simon, Human Problem Solving, 1972.

A. Niculescu-mizil and R. Caruana, Predicting good probabilities with supervised learning, Proceedings of the 22nd international conference on Machine learning , ICML '05
DOI : 10.1145/1102351.1102430

URL : http://www.cs.cornell.edu/~alexn/calibration.icml05.crc.rev3.pdf

J. Nocedal and S. Wright, Numerical Optimization, 2006.
DOI : 10.1007/b98874

P. Paumelle, Proven practices for enhancing performance: A Q&A for, 2010.

B. Stineman, Why WebSphere Operational Decision Management? White Paper Executive Summary, 2011.

O. Project, ONTOlogies meet Business RULEs, 2009.

L. Brownston, Programming Expert Systems in OPS5: An Introduction to Rule-based Programming

C. L. Forgy, OPS5 User's Manual, 1981.
DOI : 10.21236/ADA106558

J. C. Platt, Probabilistic Outputs for Support Vector Machines and Comparisons to Regularized Likelihood Methods

G. Plotkin, A Structural Approach to Operational Semantics, p.19, 1981.

W. F. Clocksin and C. S. Mellish, Programming in Prolog, 1987.
DOI : 10.1007/978-3-642-96873-0

L. Sterling and E. Shapiro, Programming in Pure Prolog In: The Art of Prolog, pp.129-148, 1999.

]. K. Apt and D. Pedreschi, Reasoning about Termination of Pure Prolog Programs, Information and Computation, vol.106, issue.1
DOI : 10.1006/inco.1993.1051

J. R. Quinlan, Generating Production Rules from Decision Trees

W. N. Venables and D. M. , Smith, and the R Core Team. An Introduction to R. United Kingdom: Network Theory, 2016.

L. Breiman, Random Forests

]. L. Raschid, A semantics for a class of stratified production system programs, The Journal of Logic Programming, vol.21, issue.1
DOI : 10.1016/0743-1066(94)90005-1

A. Y. Ng and M. I. Jordan, On Discriminative vs Generative Classifiers: A Comparison of Logistic Regression and Naive Bayes, Advances in Neural Information Processing Systems, pp.841-848, 2001.

R. G. Ross, The Business Rule Book

. Houston, TX: Business Rule Solutions LLC, 1994.

T. Achterberg, SCIP: solving constraint integer programs, Mathematical Programming Computation, vol.29, issue.2
DOI : 10.1287/ijoc.6.4.445

C. Shannon, A Universal Turing Machine with Two Internal States
DOI : 10.1515/9781400882618-007

]. S. Amaran, Simulation optimization: a review of algorithms and applications

J. C. Nash, The (Dantzig) simplex method for linear programming, Computing in Science & Engineering, vol.2, issue.1, pp.29-31, 2000.
DOI : 10.1109/5992.814654

J. Sneyers, T. Schrijvers, and B. Demoen, The computational power and complexity of constraint handling rules, Proceedings of the 2nd Workshop on Constraint Handling Rules, pp.3-17, 2005.
DOI : 10.1145/1462166.1462169

I. Spss-modeler, . Spss-analytic, and . Server, Big data simplified. Data Sheet. https://public.dhe.ibm.com/common/ssi, 2016.

G. Lausen, B. Ludäscher, and W. May, On active deductive databases: The statelog approach
DOI : 10.1007/BFb0055496

URL : http://www.informatik.uni-freiburg.de/~dbis/Publications/98/moc98.pdf

M. A. Hearst, Support vector machines, IEEE Intelligent Systems and their Applications, pp.18-28, 1998.
DOI : 10.1109/5254.708428

J. Wielemaker, Abstract, Theory and Practice of Logic Programming, vol.37, issue.1-2
DOI : 10.1145/62959.62968

J. R. Quinlan, Simplifying decision trees, International Journal of Man-Machine Studies, vol.273, pp.221-234, 1987.

M. Triska, Correctness Considerations in CLP(FD) Systems, 2014.

A. Turing, On computable numbers, with an application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, pp.230-265, 1937.

A. Turing, On Computable Numbers, with an Application to the Entscheidungsproblem, Proceedings of the London Mathematical Society, pp.230-265, 1937.

J. E. Hopcroft and J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, 1979.
DOI : 10.1145/568438.568455

L. Liberti and F. Marinelli, Mathematical programming: Turing completeness and applications to software analysis, Journal of Combinatorial Optimization, vol.42, issue.1
DOI : 10.1112/plms/s2-42.1.230

URL : http://www.lix.polytechnique.fr/%7Eliberti/mpturing.pdf

T. Hastie, R. Tibshirani, and J. Friedman, Unsupervised Learning " . In: The Elements of Statistical Learning, pp.485-585, 2009.

L. G. Valiant, A Theory of the Learnable

A. Van-gelder, Efficient loop detection in prolog using the tortoise-and-hare technique, The Journal of Logic Programming, vol.4, issue.1
DOI : 10.1016/0743-1066(87)90020-3

V. N. Vapnik, The Nature of Statistical Learning Theory, 1995.

S. Verbaeten, K. Sagonas, and D. De-schreye, Modular Termination Proofs for Prolog with Tabling
DOI : 10.1007/10704567_21

URL : http://www.cs.kuleuven.ac.be/publicaties/rapporten/cw/CW279.ps.gz

V. Vianu, Rule-Based Languages, Annals of Mathematics and Artificial Intelligence, vol.191, issue.2, pp.215-259, 1997.

A. Paschke, G. Hallmark, and C. De-sainte-marie, RIF Production Rule Dialect (Second Edition). W3C Recommendation, 2013.

]. O. Wang, Controlling the Average Behavior of Business Rules Programs
DOI : 10.1007/978-3-319-51469-7_22

]. O. Wang and L. Liberti, Controlling Some Statistical Properties of Business Rules Programs
DOI : 10.1007/978-3-319-42019-6_6

O. Wang, The Learnability of Business Rules
DOI : 10.1007/978-3-319-42019-6_6

D. A. Waterman, Adaptive production systems
DOI : 10.21236/ADA013570

H. P. Williams, Model Building in Mathematical Programming. 4th, 1999.

J. Mcdermott, R1: An Expert in the Computer Systems Domain