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A Logic-Based Framework Leveraging Neural Networks for Studying the Evolution of Neurological Disorders

Published online by Cambridge University Press:  02 December 2019

FRANCESCO CALIMERI
Affiliation:
DEMACS, University of Calabria, Italy, (e-mails: calimeri@mat.unical.it, cauteruccio@mat.unical.it, cinelli@mat.unical.it)
FRANCESCO CAUTERUCCIO
Affiliation:
DEMACS, University of Calabria, Italy, (e-mails: calimeri@mat.unical.it, cauteruccio@mat.unical.it, cinelli@mat.unical.it)
LUCA CINELLI
Affiliation:
DEMACS, University of Calabria, Italy, (e-mails: calimeri@mat.unical.it, cauteruccio@mat.unical.it, cinelli@mat.unical.it)
ALDO MARZULLO
Affiliation:
DEMACS, University of Calabria, Italy CREATIS; CNRS UMR5220; INSERM U1206; Université de Lyon, Université Lyon 1, INSA-Lyon, Villeurbanne, France, (e-mail: marzullo@mat.unical.it)
CLAUDIO STAMILE
Affiliation:
CREATIS; CNRS UMR5220; INSERM U1206; Université de Lyon, Université Lyon 1, INSA-Lyon, Villeurbanne, France, (e-mail: stamile@creatis.insa-lyon.fr)
GIORGIO TERRACINA
Affiliation:
DEMACS, University of Calabria, Italy, (e-mail: terracina@mat.unical.it)
FRANÇOISE DURAND-DUBIEF
Affiliation:
Hôpital Neurologique, Service de Neurologie A Hospices Civils de Lyon, Bron, France CREATIS; CNRS UMR5220; INSERM U1206; Université de Lyon, Université Lyon 1, INSA-Lyon, Villeurbanne, France, (e-mail: francoise.durand-dubief@chu-lyon.fr)
DOMINIQUE SAPPEY-MARINIER
Affiliation:
CERMEP - Imagerie du Vivant; Université de Lyon, Bron, France, and CREATIS; CNRS UMR5220; INSERM U1206; Université de Lyon, Université Lyon 1, INSA-Lyon, Villeurbanne, France, (e-mail: dominique.sappey-marinier@univ-lyon1.fr)

Abstract

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Type
Original Article
Copyright
Copyright © Cambridge University Press 2019

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References

Adrian, W. T., Alviano, M., Calimeri, F., Cuteri, B., Dodaro, C., Faber, W., Fuscà, D., Leone, N., Manna, M., Perri, S., Ricca, F., Veltri, P. and Zangari, J. 2018. The ASP system DLV: advancements and applications. KI 32, 2–3, 177179.Google Scholar
Alviano, M., Amendola, G., Dodaro, C., Leone, N., Maratea, M. and Ricca, F. 2019. Evaluation of disjunctive programs in WASP. In Logic Programming and Nonmonotonic Reasoning – 15th International Conference, LPNMR 2019, Philadelphia, PA, USA, June 3–7, 2019, Proceedings, Balduccini, M., Lierler, Y., and Woltran, S., Eds. Lecture Notes in Computer Science, vol. 11481. Springer, 241255.Google Scholar
Arias, J., Carro, M., Salazar, E., Marple, K. and Gupta, G. 2018. Constraint answer set programming without grounding. TPLP 18, 3–4, 337354.Google Scholar
Balduccini, M. and Lierler, Y. 2017. Constraint answer set solver EZCSP and why integration schemas matter. TPLP 17, 4, 462515.Google Scholar
Baral, C. 2003. Knowledge Representation, Reasoning, and Declarative Problem Solving. Cambridge University Press, New York, NY, USA.CrossRefGoogle Scholar
Bargmann, C. and Marder, E. 2013. From the connectome to brain function. Nature Methods 10, 483.Google Scholar
Barrett, C., Fontaine, P. and Tinelli, C. 2016. The Satisfiability Modulo Theories Library (SMT-LIB). URL: www.SMT-LIB.orgGoogle Scholar
Barrett, C. W., Deters, M., de Moura, L. M., Oliveras, A. and Stump, A. 2013. 6 years of SMT-COMP. J. Autom. Reasoning 50, 3, 243277.CrossRefGoogle Scholar
Barrett, C. W. and Tinelli, C. 2018. Satisfiability modulo theories. In Handbook of Model Checking, Clarke, E. M., Henzinger, T. A., Veith, H. and Bloem, R., Eds. Springer, 305343.CrossRefGoogle Scholar
Baselice, S., Bonatti, P. A. and Gelfond, M. 2005. Towards an integration of answer set and constraint solving. In Logic Programming, 21st International Conference, ICLP 2005, Sitges, Spain, October 2–5, 2005, Proceedings, Gabbrielli, M. and Gupta, G., Eds. Lecture Notes in Computer Science, vol. 3668. Springer, 5266.CrossRefGoogle Scholar
Beck, H., Dao-Tran, M., Eiter, T. and Fink, M. 2015. LARS: A logic-based framework for analyzing reasoning over streams. In AAAI. AAAI Press, 14311438.Google Scholar
Brooks, D. R., Erdem, E., Erdogan, S. T., Minett, J. W. and Ringe, D. 2007. Inferring phylogenetic trees using answer set programming. J. Autom. Reasoning 39, 4, 471511.CrossRefGoogle Scholar
Calimeri, F., Cauteruccio, F., Marzullo, A., Stamile, C. and Terracina, G. 2018. Mixing logic programming and neural networks to support neurological disorders analysis. In RuleML+RR. Lecture Notes in Computer Science, vol. 11092. Springer, 3347.Google Scholar
Calimeri, F., Cozza, S. and Ianni, G. 2007. External sources of knowledge and value invention in logic programming. Ann. Math. Artif. Intell. 50, 3–4, 333361.CrossRefGoogle Scholar
Calimeri, F., Faber, W., Gebser, M., Ianni, G., Kaminski, R., Krennwallner, T., Leone, N., Ricca, F. and Schaub, T. 2012. ASP-Core-2: Input language format.Google Scholar
Calimeri, F., Fink, M., Germano, S., Humenberger, A., Ianni, G., Redl, C., Stepanova, D., Tucci, A. and Wimmer, A. 2016. Angry-hex: An artificial player for angry birds based on declarative knowledge bases. IEEE Trans. Comput. Intellig. and AI in Games 8, 2, 128139.CrossRefGoogle Scholar
Calimeri, F., Fuscà, D., Germano, S., Perri, S., and Zangari, J. 2019. Fostering the use of declarative formalisms for real-world applications: The embasp framework. New Generation Comput. 37, 1, 2965.CrossRefGoogle Scholar
Calimeri, F., Fuscà, D., Perri, S. and Zangari, J. 2017a. External computations and interoperability in the new DLV grounder. In AI*IA 2017 Advances in Artificial Intelligence – XVIth International Conference of the Italian Association for Artificial Intelligence, Bari, Italy, November 14–17, 2017, Proceedings, Esposito, F., Basili, R., Ferilli, S. and Lisi, F. A., Eds. Lecture Notes in Computer Science, vol. 10640. Springer, 172185.Google Scholar
Calimeri, F., Fuscà, D., Perri, S. and Zangari, J. 2017b. I-DLV: the new intelligent grounder of DLV. Intelligenza Artificiale 11, 1, 520.CrossRefGoogle Scholar
Calimeri, F., Ianni, G., Krennwallner, T. and Ricca, F. 2012. The answer set programming competition. AI Magazine 33, 4, 114118.CrossRefGoogle Scholar
Calimeri, F., Marzullo, A., Stamile, C. and Terracina, G. 2018. Graph based neural networks for automatic classification of multiple sclerosis clinical courses. In 26th European Symposium on Artificial Neural Networks, ESANN 2018, Bruges, Belgium, April 25–27, 2018.Google Scholar
Calimeri, F. and Ricca, F. 2013. On the application of the answer set programming system DLV in industry: a report from the field. Book Reviews 2013, 03, 116.Google Scholar
Cauteruccio, F., Lo Giudice, P., Terracina, G., Ursino, D., Mammone, N. and Morabito, F. 2019. A new network-based approach to investigating neurological disorders. International Journal of Data Mining, Modelling and Management 11, 315349.Google Scholar
Chabierski, P., Russo, A., Law, M. and Broda, K. 2017. Machine comprehension of text using combinatory categorial grammar and answer set programs. In COMMONSENSE. CEUR Workshop Proceedings, vol. 2052. CEUR-WS.org.Google Scholar
Cok, D. R., Stump, A. and Weber, T. 2015. The 2013 evaluation of SMT-COMP and SMT-LIB. J. Autom. Reasoning 55, 1, 6190.CrossRefGoogle Scholar
Dodaro, C. and Ricca, F. 2018. The external interface for extending WASP. Theory and Practice of Logic Programming [online] 124. doi: 10.1017/S1471068418000558.CrossRefGoogle Scholar
Duun-Henriksen, J., Madsen, R., Remvig, L., Thomsen, C., Sorensen, H. and Kjaer, T. 2012. Automatic detection of childhood absence epilepsy seizures: toward a monitoring device. Pediatric Neurology 46, 5, 287292.CrossRefGoogle Scholar
Eiter, T., Fink, M., Ianni, G., Krennwallner, T., Redl, C. and Schüller, P. 2016. A model building framework for answer set programming with external computations. TPLP 16, 4, 418464.Google Scholar
Eiter, T., Germano, S., Ianni, G., Kaminski, T., Redl, C., Schüller, P. and Weinzierl, A. 2018. The DLVHEX system. KI - Künstliche Intelligenz 32, 2–3, 187189.CrossRefGoogle Scholar
Eiter, T., Germano, S., Ianni, G., Kaminski, T., Redl, C., Schüller, P. and Weinzierl, A. 2018. The DLVHEX system. KI 32, 2–3, 187189.Google Scholar
Eiter, T., Redl, C. and Schüller, P. 2016. Problem solving using the HEX family. In Computational Models of Rationality, Essays Dedicated to Gabriele Kern-Isberner on the Occasion of her 60th Birthday, Beierle, C., Brewka, G., and Thimm, M., Eds. College Publications, 150174.Google Scholar
Erdem, E., Gelfond, M. and Leone, N. 2016. Applications of answer set programming. AI Magazine 37, 3, 5368.CrossRefGoogle Scholar
Faber, W., Leone, N. and Pfeifer, G. 2004. Recursive aggregates in disjunctive logic programs: Semantics and complexity. In Proceedings of the 9th European Conference on Artificial Intelligence (JELIA 2004), Alferes, J. J. and Leite, J., Eds. Lecture Notes on Artificial Intelligence (LNAI), vol. 3229. Springer Verlag, 200212.Google Scholar
Febbraro, O., Leone, N., Grasso, G. and Ricca, F. 2012. JASP: A framework for integrating answer set programming with Java. In Principles of Knowledge Representation and Reasoning: Proceedings of the Thirteenth International Conference, KR 2012, Rome, Italy, June 10–14, 2012, Brewka, G., Eiter, T., and McIlraith, S. A., Eds. AAAI Press.Google Scholar
Febbraro, O., Reale, K. and Ricca, F. 2011. Aspide: Integrated development environment for answer set programming. In Logic Programming and Nonmonotonic Reasoning – 11th International Conference, LPNMR 2011, Vancouver, Canada, May 16-19, 2011. Proceedings. Lecture Notes in Computer Science, vol. 6645, 317330.Google Scholar
Fuscà, D., Calimeri, F., Zangari, J. and Perri, S. 2017. I-DLV+MS: preliminary report on an automatic ASP solver selector. In RCRA@AI*IA. CEUR Workshop Proceedings, vol. 2011. CEUR-WS.org, 26–32.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2014. Clingo = ASP + control: Preliminary report. In Technical Communications of the Thirtieth International Conference on Logic Programming (ICLP’14), Leuschel, M. and Schrijvers, T., Eds. Vol. arXiv:1405.3694v1. Theory and Practice of Logic Programming, Online Supplement.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B. and Schaub, T. 2019. Multi-shot ASP solving with clingo. TPLP 19, 1, 2782.Google Scholar
Gebser, M., Kaminski, R., Kaufmann, B., Schaub, T., Schneider, M. T. and Ziller, S. 2011. A portfolio solver for answer set programming: Preliminary report. In LPNMR. LNCS, vol. 6645. Springer, 352357.Google Scholar
Gebser, M., Leone, N., Maratea, M., Perri, S., Ricca, F. and Schaub, T. 2018. Evaluation techniques and systems for answer set programming: a survey. In Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence, IJCAI 2018, July 13–19, 2018, Stockholm, Sweden., J. Lang, Ed. ijcai.org, 54505456.Google Scholar
Gebser, M., Maratea, M. and Ricca, F. 2016. What’s hot in the answer set programming competition. In Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, February 12–17, 2016, Phoenix, Arizona, USA., Schuurmans, D. and Wellman, M. P., Eds. AAAI Press, 43274329.Google Scholar
Gebser, M., Maratea, M. and Ricca, F. 2017. The sixth answer set programming competition. Journal of Artificial Intelligence Research 60, 4195.Google Scholar
Gebser, M., Maratea, M. and Ricca, F. 2019. The seventh answer set programming competition: Design and results. CoRR abs/1904.09134.CrossRefGoogle Scholar
Gebser, M., Schaub, T., Thiele, S. and Veber, P. 2011. Detecting inconsistencies in large biological networks with answer set programming. Theory and Practice of Logic Programming 11, 2–3, 323360.CrossRefGoogle Scholar
Gelfond, M. 2010. Knowledge representation language p-log – A short introduction. In Datalog, de Moor, O., Gottlob, G., Furche, T., and Sellers, A., Eds. LNCS, vol. 6702. Springer, 369383.CrossRefGoogle Scholar
Gelfond, M. and Leone, N. 2002. Logic Programming and Knowledge Representation – the A-Prolog perspective. Artificial Intelligence 138, 1–2, 338.CrossRefGoogle Scholar
Gelfond, M. and Lifschitz, V. 1991. Classical Negation in Logic Programs and Disjunctive Databases. New Gen. Comput. 9, 365385.Google Scholar
Goodfellow, I. J., Bengio, Y. and Courville, A. C. 2016. Deep Learning. Adaptive Computation and Machine Learning. MIT Press.Google Scholar
Haykin, S. 1998. Neural Networks: A Comprehensive Foundation, 2nd ed. Prentice Hall PTR, Upper Saddle River, NJ, USA.Google Scholar
Hornero, R., Abásolo, D., Escudero, J. and Gómez, C. 2009. Nonlinear analysis of electroencephalogram and magnetoencephalogram recordings in patients with Alzheimer’s disease. Philosophical Transactions of the Royal Society of London A: Mathematical, Physical and Engineering Sciences 367, 1887, 317336.Google Scholar
Hu, Z., Ma, X., Liu, Z., Hovy, E. H. and Xing, E. P. 2016. Harnessing deep neural networks with logic rules. In Proceedings of the 54th Annual Meeting of the Association for Computational Linguistics, ACL 2016, August 7–12, 2016, Berlin, Germany, Volume 1: Long Papers.CrossRefGoogle Scholar
Ion-Margineanu, A., Kocevar, G., Stamile, C., Sima, D. M., Durand-Dubief, F., Huffel, S. V. and Sappey-Marinier, D. 2017. A comparison of machine learning approaches for classifying multiple sclerosis courses using MRSI and brain segmentations. In ICANN (2). LNCS, vol. 10614. Springer, 643651.Google Scholar
Jenkinson, M., Beckmann, C. F., Behrens, T. E. J., Woolrich, M. W. and Smith, S. M. 2012. FSL. NeuroImage 62, 2, 782790.CrossRefGoogle ScholarPubMed
Jeong, J. 2004. EEG dynamics in patients with Alzheimer’s disease. Clinical Neurophysiology 115, 7, 14901505.CrossRefGoogle Scholar
Kaminski, R., Schaub, T. and Wanko, P. 2017. A tutorial on hybrid answer set solving with clingo. In Reasoning Web. Semantic Interoperability on the Web – 13th International Summer School 2017, London, UK, July 7–11, 2017, Tutorial Lectures, Ianni, G., Lembo, D., Bertossi, L. E., Faber, W., Glimm, B., Gottlob, G. and Staab, S., Eds. Lecture Notes in Computer Science, vol. 10370. Springer, 167203.Google Scholar
Kawahara, J., Brown, C. J., Miller, S. P., Booth, B. G., Chau, V., Grunau, R. E., Zwicker, J. G. and Hamarneh, G. 2017. Brainnetcnn: Convolutional neural networks for brain networks; towards predicting neurodevelopment. NeuroImage 146, 10381049.CrossRefGoogle Scholar
Kingma, D. P. and Ba, J. 2014. Adam: A method for stochastic optimization. CoRR abs/1412.6980.Google Scholar
Kocevar, G., Stamile, C., Hannoun, S., Cotton, F., Vukusic, S., Durand-Dubief, F. and Sappey-Marinier, D. 2016. Graph theory-based brain connectivity for automatic classification of multiple sclerosis clinical courses. Frontiers in Neuroscience 10, 478.Google Scholar
Kouvaros, P. and Lomuscio, A. 2018. Formal verification of CNN-based perception systems. CoRR abs/1811.11373.Google Scholar
Law, M., Russo, A. and Broda, K. 2015. Learning weak constraints in answer set programming. TPLP 15, 4–5, 511525.Google Scholar
Law, M., Russo, A. and Broda, K. 2016. Iterative learning of answer set programs from context dependent examples. TPLP 16, 5–6, 834848.Google Scholar
Lenka, A., Naduthota, R., Jha, M., R, R. P., Prajapati, A., Jhunjhunwala, K., Saini, J., Yadav, R., Bharath, R. and Pal, P. 2015. Freezing of gait in parkinsons disease is associated with altered functional brain connectivity. Parkinsonism & Related Disorders 24, 100106.CrossRefGoogle ScholarPubMed
Leofante, F., Narodytska, N., Pulina, L. and Tacchella, A. 2018. Automated verification of neural networks: Advances, challenges and perspectives. CoRR abs/1805.09938.Google Scholar
Leone, N. and Ricca, F. 2015. Answer set programming: A tour from the basics to advanced development tools and industrial applications. In Web Reasoning and Rule Systems – 9th International Conference, RR 2015, Berlin, Germany, August 4–5, 2015, Proceedings. Lecture Notes in Computer Science (LNCS). Springer Verlag, 308326.Google Scholar
Lierler, Y. and Susman, B. 2017. On relation between constraint answer set programming and satisfiability modulo theories. TPLP 17, 4, 559590.Google Scholar
Lifschitz, V. 1999. Answer Set Planning. In Proceedings of the 16th International Conference on Logic Programming (ICLP’99), Schreye, D. D., Ed. The, MIT Press, Cruces, Las, New Mexico, USA, 2337.Google Scholar
Lonc, Z. and Truszczyński, M. 2006. Computing minimal models, stable models and answer sets. TPLP 6, 4, 395449.Google Scholar
Lublin, F. D., Reingold, S. C., Cohen, J. A., Cutter, G. R., Sørensen, P. S., Thompson, A. J., Wolinsky, J. S., Balcer, L. J., Banwell, B., Barkhof, F., Bebo, B. J., Calabresi, P. A., Clanet, M., Comi, G., Fox, R. J., Freedman, M. S., Goodman, A. D., Inglese, M., Kappos, L., Kieseier, B. C., Lincoln, J. A., Lubetzki, C., Miller, A. E., Montalban, X., O’Connor, P. W., Petkau, J., Pozzilli, C., Rudick, R. A., Sormani, M. P., Stüve, O., Waubant, E. and Polman, C. H. 2014. Defining the clinical course of multiple sclerosis: the 2013 revisions. Neurology 83, 3, 278286.CrossRefGoogle Scholar
Manna, M., Ricca, F. and Terracina, G. 2015. Taming primary key violations to query large inconsistent data via ASP. Theory and Practice of Logic Programming (TPLP). Cambridge University Press, UK. 15 (4–5), 696710.Google Scholar
Maratea, M., Pulina, L. and Ricca, F. 2014. A multi-engine approach to answer-set programming. Theory and Practice of Logic Programming 14, 6, 841868.CrossRefGoogle Scholar
Marek, V. W. and Truszczyński, M. 1999. Stable Models and an Alternative Logic Programming Paradigm. In The Logic Programming Paradigm – A 25-Year Perspective, Apt, K. R., Marek, V. W., Truszczyński, M. and Warren, D. S., Eds. Springer Verlag, 375398.CrossRefGoogle Scholar
Mcdonald, W. I., Compston, A., Edan, G., Goodkin, D., Hartung, H.-P., Lublin, F. D., Mcfarland, H. F., Paty, D. W., Polman, C. H., Reingold, S. C., Sandberg-Wollheim, M., Sibley, W., Thompson, A., van den Noort, S., Weinshenker, B. Y. and Wolinsky, J. S. 2001. Recommended diagnostic criteria for multiple sclerosis: guidelines from the international panel on the diagnosis of multiple sclerosis. Annals of Neurology: Official Journal of the American Neurological Association and the Child Neurology Society 50, 1, 121127.CrossRefGoogle Scholar
Mellarkod, V. S., Gelfond, M. and Zhang, Y. 2008. Integrating answer set programming and constraint logic programming. Ann. Math. Artif. Intell. 53, 1-4, 251287.CrossRefGoogle Scholar
Newman, M. E. J. 2002. Assortative mixing in networks. Physical Review Letters 89, 208701.CrossRefGoogle ScholarPubMed
Nickles, M. and Mileo, A. 2014. Web stream reasoning using probabilistic answer set programming. In RR. LNCS, vol. 8741. Springer, 197205.Google Scholar
Niemelä, I. 1999. Logic programming with stable model semantics as constraint programming paradigm. Annals of Mathematics and Artificial Intelligence 25, 3–4, 241273.CrossRefGoogle Scholar
Petersen, R. 2004. Mild cognitive impairment as a diagnostic entity. Journal of Internal Medicine 256, 3, 183194.CrossRefGoogle Scholar
Przymusinski, T. C. 1991. Stable semantics for disjunctive programs. New Generation Computing 9, 401424.Google Scholar
Pulina, L. and Tacchella, A. 2010. An abstraction-refinement approach to verification of artificial neural networks. In Computer Aided Verification, Touili, T., Cook, B. and Jackson, P., Eds. Springer, Berlin, Heidelberg, 243257.CrossRefGoogle Scholar
Qiu, J., Tang, J., Ma, H., Dong, Y., Wang, K. and Tang, J. 2018. Deepinf: Social influence prediction with deep learning. In Proc. of the 24th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, 21102119. ACM. New York, NY, USA.CrossRefGoogle Scholar
Rath, J. and Redl, C. 2017. Integrating answer set programming with object-oriented languages. In Practical Aspects of Declarative Languages – 19th International Symposium, PADL 2017, Paris, France, January 16–17, 2017, Proceedings, Lierler, Y. and Taha, W., Eds. Lecture Notes in Computer Science, vol. 10137. Springer, 5067.Google Scholar
Redl, C. 2016. The dlvhex system for knowledge representation: recent advances (system description). TPLP 16, 5–6, 866883.Google Scholar
Ricca, F. 2003. A Java wrapper for DLV. In Answer Set Programming, Advances in Theory and Implementation, Proceedings of the 2nd Intl. ASP’03 Workshop, Messina, Italy, September 26–28, 2003, Vos, M. D. and Provetti, A., Eds. CEUR Workshop Proceedings, vol. 78. CEUR-WS.org.Google Scholar
Rubinov, M. and Sporns, O. 2010. Complex network measures of brain connectivity: Uses and interpretations. NeuroImage 52, 3, 10591069.CrossRefGoogle Scholar
Schüller, P. and Weinzierl, A. 2015. Answer set application programming: A case study on tetris. In Proceedings of the Technical Communications of the 31st International Conference on Logic Programming (ICLP 2015), Cork, Ireland, August 31 – September 4, 2015, Vos, M. D., Eiter, T., Lierler, Y. and Toni, F., Eds. CEUR Workshop Proceedings, vol. 1433. CEUR-WS.org.Google Scholar
Shen, D. and Lierler, Y. 2018. SMT-based constraint answer set solver EZSMT+ for non-tight programs. In Principles of Knowledge Representation and Reasoning: Proceedings of the Sixteenth International Conference, KR 2018, Tempe, Arizona, 30 October – 2 November 2018, Thielscher, M., Toni, F., and Wolter, F., Eds. AAAI Press, 6771.Google Scholar
Shovon, M. H. I., Nandagopal, N., Vijayalakshmi, R., Du, J. T. and Cocks, B. 2017. Directed connectivity analysis of functional brain networks during cognitive activity using transfer entropy. Neural Processing Letters 45, 3, 807824.CrossRefGoogle Scholar
Simonyan, K., Vedaldi, A., and Zisserman, A. 2013. Deep inside convolutional networks: Visualising image classification models and saliency maps. CoRR abs/1312.6034.Google Scholar
Stamile, C., Kocevar, G., Cotton, F., Hannoun, S., Durand-Dubief, F., Frindel, C., Rousseau, D. and Sappey-Marinier, D. 2015. A longitudinal model for variations detection in white matter fiber-bundles. In 2015 International Conference on Systems, Signals and Image Processing (IWSSIP), 5760.Google Scholar
Stein, M., Simmons, A., Feinstein, J. and Paulus, M. 2007. Increased amygdala and insula activation during emotion processing in anxiety-prone subjects. The American Journal of Psychiatry 164, 2, 318327.CrossRefGoogle Scholar
Terracina, G., Leone, N., Lio, V. and Panetta, C. 2008. Experimenting with recursive queries in database and logic programming systems. Theory and Practice of Logic Programming (TPLP) 8(2), 129165. URL: http://arxiv.org/abs/0704.3157.Google Scholar
Thimm, M. 2014. Tweety – A comprehensive collection of Java libraries for logical aspects of artificial intelligence and knowledge representation. In Proceedings of the 14th International Conference on Principles of Knowledge Representation and Reasoning (KR 2014).Google Scholar
Tournier, J., Calamante, F. and Connelly, A. 2012. Mrtrix: Diffusion tractography in crossing fiber regions. The International Journal of Imaging Systems and Technology 22, 1, 5366.CrossRefGoogle Scholar
Towell, G. G. and Shavlik, J. W. 1993. Extracting refined rules from knowledge-based neural networks. Machine Learning 13, 71101.Google Scholar
Vos, T., Allen, C., Arora, M., Barber, R., Bhutta, Z. and Brown, A. 2016. Gbd 2015 disease and injury incidence and prevalence collaborators. global, regional, and national incidence, prevalence, and years lived with disability for 310 diseases and injuries, 1990–2015: A systematic analysis for the global burden of disease study 2015. Lancet 388, 10053, 15451602.Google Scholar
Wieser, H., Schindler, K. and Zumsteg, D. 2006. EEG in Creutzfeldt–Jakob disease. Clinical Neurophysiology 117, 5, 935951.CrossRefGoogle Scholar
Wu, Z., Pan, S., Chen, F., Long, G., Zhang, C. and Yu, P. 2019. A comprehensive survey on graph neural networks. CoRR abs/1901.00596.Google Scholar
Zhang, Q., Cao, R., Zhang, S., Edmonds, M., Wu, Y. N. and Zhu, S. 2017. Interactively transferring CNN patterns for part localization. CoRR abs/1708.01783.Google Scholar
Zhang, Q., Wu, Y. N. and Zhu, S. 2018. Interpretable convolutional neural networks. In 2018 IEEE Conference on Computer Vision and Pattern Recognition, CVPR 2018, Salt Lake City, UT, USA, June 18–22, 2018. IEEE Computer Society, 88278836.Google Scholar
Zhang, Q., Yang, Y., Wu, Y. N. and Zhu, S. 2018. Interpreting CNNs via decision trees. CoRR abs/1802.00121.CrossRefGoogle Scholar
Zhang, Q. and Zhu, S. 2018. Visual interpretability for deep learning: A survey. Frontiers of IT & EE 19, 1, 2739.Google Scholar