{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,3,24]],"date-time":"2025-03-24T06:35:54Z","timestamp":1742798154095},"reference-count":36,"publisher":"Elsevier BV","issue":"2","license":[{"start":{"date-parts":[[2002,6,1]],"date-time":"2002-06-01T00:00:00Z","timestamp":1022889600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Cognitive Systems Research"],"published-print":{"date-parts":[[2002,6]]},"DOI":"10.1016\/s1389-0417(01)00057-2","type":"journal-article","created":{"date-parts":[[2002,10,10]],"date-time":"2002-10-10T19:00:31Z","timestamp":1034276431000},"page":"167-201","source":"Crossref","is-referenced-by-count":11,"title":["From synapses to rules"],"prefix":"10.1016","volume":"3","author":[{"given":"B.","family":"Apolloni","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"D.","family":"Malchiodi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"C.","family":"Orovas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"G.","family":"Palmas","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"78","reference":[{"key":"10.1016\/S1389-0417(01)00057-2_BIB1","doi-asserted-by":"crossref","first-page":"716","DOI":"10.1109\/TAC.1974.1100705","article-title":"A new look at the statistical model identification","volume":"19","author":"Akaike","year":"1985","journal-title":"IEEE Transactions on Automatic Control"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB2","first-page":"9","article-title":"Rule extraction from constrained error backpropagation mlp","author":"Andrews","year":"1994"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB3","first-page":"29","article-title":"Inserting and extracting knowledge from constrained backpropagation network","author":"Andrews","year":"1995"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB4","unstructured":"Apolloni, B., Baraghini, F., & Palmas, G. (2000a). PAC meditation on boolean formulas. Technical report, Universit\u00e0 degli Studi di Milano."},{"key":"10.1016\/S1389-0417(01)00057-2_BIB5","doi-asserted-by":"crossref","first-page":"91","DOI":"10.1016\/S0304-3975(95)00240-5","article-title":"Pac learning of concept classes through the boundaries of their items","volume":"172","author":"Apolloni","year":"1997","journal-title":"Theoretical Computer Science"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB6","doi-asserted-by":"crossref","first-page":"295","DOI":"10.1016\/S0304-3975(99)00289-3","article-title":"Gaining degrees of freedom in subsymbolic learning","volume":"255","author":"Apolloni","year":"2001","journal-title":"Theoretical Computer Science"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB7","article-title":"From synapses to rules","author":"Apolloni","year":"2000"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB8","doi-asserted-by":"crossref","unstructured":"Apolloni, B., Orovas, C., Taylor, J. G., Fellenz, W., Gielen, S., & Westerdijk, M. (2000c) A general framework for symbol and rule extraction in neural networks. In Amari, S., Lee Giles, C., Gori, M., & Piari, V., editors, Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks \u2013 IJCNN 2000, pp. II-87, II-92, Los Alamitos. IEEE Computer Society. IEEE Transactions on Neural Networks, submitted.","DOI":"10.1109\/IJCNN.2000.857879"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB9","doi-asserted-by":"crossref","first-page":"49","DOI":"10.1007\/BF00198911","article-title":"Dynamic sizing of multilayer perceptrons","volume":"71","author":"Apolloni","year":"1994","journal-title":"Biological Cybernetics"},{"issue":"5","key":"10.1016\/S1389-0417(01)00057-2_BIB10","doi-asserted-by":"crossref","first-page":"1099","DOI":"10.1109\/72.788650","article-title":"Subsymbolically managing pieces of symbolical functions for sorting","volume":"10","author":"Apolloni","year":"1999","journal-title":"IEEE Transactions on Neural Networks"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB11","doi-asserted-by":"crossref","unstructured":"Bishop, C. M. (1995). Neural networks for pattern recognition. Oxford: Clarendon Press.","DOI":"10.1093\/oso\/9780198538493.001.0001"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB12","doi-asserted-by":"crossref","first-page":"929","DOI":"10.1145\/76359.76371","article-title":"Learnability and the Vapnik-Chervonenkis dimension","volume":"36","author":"Blumer","year":"1989","journal-title":"Journal of the ACM"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB13","doi-asserted-by":"crossref","unstructured":"Cover, T. & Thomas, J. (1991). Elements of Information Theory. New York: Wiley.","DOI":"10.1002\/0471200611"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB14","unstructured":"Cox, E., (1998). The Fuzzy Systems Handbook. San Diego, CA: AP Professional."},{"key":"10.1016\/S1389-0417(01)00057-2_BIB15","series-title":"Advances in Neural Information Processing Systems","article-title":"Extracting tree-structured representations of trained networks","author":"Craven","year":"1996"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB16","unstructured":"Doffner, G., & Prem, E. (1993). Connectionism, symbol grounding, and autonomous agents. In Proc. 19th ACM Symp. Theory of Computing. Boulder, CO, pp. 144\u2013148."},{"issue":"2","key":"10.1016\/S1389-0417(01)00057-2_BIB17","doi-asserted-by":"crossref","first-page":"152","DOI":"10.1145\/42372.42377","article-title":"Connectionist expert systems","volume":"31","author":"Gallant","year":"1998","journal-title":"Communications of the ACM"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB18","doi-asserted-by":"crossref","unstructured":"Geisser, S., (1993). Predictive inference: an introduction. New York: Chapman and Hall.","DOI":"10.1007\/978-1-4899-4467-2"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB19","doi-asserted-by":"crossref","unstructured":"Li, M., & Vit\u00e0nyi, P. (1993). An introduction to Kolmogorov complexity and its applications. Berlin: Springer.","DOI":"10.1007\/978-1-4757-3860-5"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB20","doi-asserted-by":"crossref","first-page":"865","DOI":"10.1109\/72.329683","article-title":"Network information criterion\u2014determining the number of hidden units for an artificial neural network model","volume":"5","author":"Murata","year":"1995","journal-title":"IEEE Transactions on Neural Networks"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB21","unstructured":"Papadimitriou, C. H., (1994). Computational complexity. Reading, MA: Addison-Wesley."},{"issue":"4","key":"10.1016\/S1389-0417(01)00057-2_BIB22","doi-asserted-by":"crossref","first-page":"965","DOI":"10.1145\/48014.63140","article-title":"Computational limitations on learning from examples","volume":"35","author":"Pitt","year":"1988","journal-title":"Journal of the ACM"},{"issue":"45","key":"10.1016\/S1389-0417(01)00057-2_BIB23","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1016\/0004-3702(90)90005-K","article-title":"Recursive distributed representations","volume":"1\u20132","author":"Pollack","year":"1990","journal-title":"Artificial Intelligence"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB24","series-title":"C4.5: programs for machine learning","author":"Qunilan","year":"1993"},{"issue":"2","key":"10.1016\/S1389-0417(01)00057-2_BIB25","doi-asserted-by":"crossref","first-page":"416","DOI":"10.1214\/aos\/1176346150","article-title":"A universal prior for integers and estimation by minimum description length","volume":"11","author":"Rissanen","year":"1983","journal-title":"Annals of Statistics"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB26","series-title":"Theory of recoursive functions and effective computability","author":"Roger","year":"1967"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB27","series-title":"An introduction to probability theory and mathematical statistics","author":"Rohatgi","year":"1976"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB28","series-title":"Learning internal representations by error propagation","first-page":"318","author":"Rumelhart","year":"1986"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB29","first-page":"130","article-title":"Some related problems from network flows, game theory, and integer programming","author":"Sahni","year":"1972"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB30","unstructured":"The PHYSTA project (2001) Principled hybrid systems: theory and applications (physta). Retrieved June 6 2001 from http:\/\/www.image.ece.ntua.gr\/physta."},{"key":"10.1016\/S1389-0417(01)00057-2_BIB31","doi-asserted-by":"crossref","first-page":"1057","DOI":"10.1109\/72.728352","article-title":"The truth will come to light: Directions and challenges in extracting the knowledge embedded within trained artificial neural networks","volume":"9","author":"Tickle","year":"1998","journal-title":"IEEE Transactions on Neural Networks"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB32","first-page":"177","article-title":"Refinement of approximately correct domain theories by knowledge-based neural networks","author":"Towell","year":"1990"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB33","series-title":"Estimation of dependencies based on empirical data","author":"Vapnik","year":"1982"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB34","series-title":"The nature of statistical learning theory","author":"Vapnik","year":"1995"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB35","series-title":"The complexity of boolean functions","author":"Wegener","year":"1987"},{"key":"10.1016\/S1389-0417(01)00057-2_BIB36","series-title":"Mathematical statistics","author":"Wilks","year":"1962"}],"container-title":["Cognitive Systems Research"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1389041701000572?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1389041701000572?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2024,1,6]],"date-time":"2024-01-06T09:01:28Z","timestamp":1704531688000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1389041701000572"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2002,6]]},"references-count":36,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2002,6]]}},"alternative-id":["S1389041701000572"],"URL":"https:\/\/doi.org\/10.1016\/s1389-0417(01)00057-2","relation":{},"ISSN":["1389-0417"],"issn-type":[{"value":"1389-0417","type":"print"}],"subject":[],"published":{"date-parts":[[2002,6]]}}}