{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,11,6]],"date-time":"2025-11-06T19:53:43Z","timestamp":1762458823473},"reference-count":27,"publisher":"Springer Science and Business Media LLC","issue":"2","license":[{"start":{"date-parts":[[2010,7,17]],"date-time":"2010-07-17T00:00:00Z","timestamp":1279324800000},"content-version":"tdm","delay-in-days":0,"URL":"http:\/\/www.springer.com\/tdm"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["J Autom Reasoning"],"published-print":{"date-parts":[[2011,2]]},"DOI":"10.1007\/s10817-010-9191-0","type":"journal-article","created":{"date-parts":[[2010,7,16]],"date-time":"2010-07-16T12:36:16Z","timestamp":1279283776000},"page":"205-221","source":"Crossref","is-referenced-by-count":9,"title":["A Polynomial Model for Logics with a Prime Power Number of Truth Values"],"prefix":"10.1007","volume":"46","author":[{"given":"Antonio","family":"Hernando","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Eugenio","family":"Roanes-Lozano","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Luis M.","family":"Laita","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2010,7,17]]},"reference":[{"key":"9191_CR1","doi-asserted-by":"crossref","unstructured":"Adams, W.W., Loustaunau, P.: An Introduction to Gr\u00f6bner Bases. American Mathematical Society, Providence, RI (1994)","DOI":"10.1090\/gsm\/003"},{"key":"9191_CR2","unstructured":"Alonso, J.A., Briales, E.: L\u00f3gicas polivalentes y bases de Gr\u00f6bner. In: Martin, C. (ed.) Actas del V Congreso de Lenguajes Naturales y Lenguajes Formales, pp. 307\u2013315. University of Seville, Seville (1995)"},{"key":"9191_CR3","doi-asserted-by":"crossref","unstructured":"Becker, T., Weisspfenning, V.: Gr\u00f6bner Bases. A Computational Approach to Commutative Algebra. Graduate Studies in Mathematics-Springer, Berlin (1993)","DOI":"10.1007\/978-1-4612-0913-3_6"},{"key":"9191_CR4","unstructured":"Buchberger, B.: An Algorithm for Finding a Basis for the Residue Class Ring of a Zero-Dimensional Polynomial Ideal. Ph.D. thesis, Math. Institute\u2014University of Innsbruck (1965) (in German)"},{"key":"9191_CR5","doi-asserted-by":"crossref","unstructured":"Buchberger, B.: Applications of Gr\u00f6bner bases in non-linear computational geometry. In: Rice, J.R. (ed.) Mathematical Aspects of Scientific Software. IMA, vol. 14, pp. 60\u201388. Springer, New York (1988)","DOI":"10.1007\/978-1-4684-7074-1_3"},{"key":"9191_CR6","unstructured":"Capaini, A., Niesi, G.: CoCoA User\u2019s Manual. Dept. Mathematics, Univ. of Genova (1996)"},{"key":"9191_CR7","doi-asserted-by":"crossref","first-page":"181","DOI":"10.1016\/S0747-7171(08)80043-0","volume":"11","author":"J Chazarain","year":"1991","unstructured":"Chazarain, J., Riscos, A., Alonso, J.A., Briales, E.: Multivalued logic and Gr\u00f6bner bases with applications to modal logic. J. Symb. Comput. 11, 181\u2013194 (1991)","journal-title":"J. Symb. Comput."},{"key":"9191_CR8","unstructured":"Cox, D., Little, J., O\u2019Shea, D.: Ideals, Varieties, and Algorithms. An Introduction to Computational Algebraic Geometry and Commutative Algebra. Springer, New York (1992)"},{"key":"9191_CR9","doi-asserted-by":"crossref","unstructured":"Garcia-Remensal, M., Maojo, V., Laita, L.M., Roanes-Lozano, E., Crespo, J.: An Algebraic Approach to Detect Logical Inconsistencies in Medical Appropriateness Criteria. In: Engineering in Medicine and Biology Society, (EMBS 2007), 29th Annual International Conference of the IEEE, pp. 5148\u20135151. Lyon (2007)","DOI":"10.1109\/IEMBS.2007.4353499"},{"key":"9191_CR10","doi-asserted-by":"crossref","first-page":"255","DOI":"10.1016\/0004-3702(85)90074-8","volume":"25","author":"J Hsiang","year":"1985","unstructured":"Hsiang, J.: Refutational theorem proving using term-rewriting systems. Artif. Intell. 25, 255\u2013300 (1985)","journal-title":"Artif. Intell."},{"key":"9191_CR11","unstructured":"Kapur, D., Narendran, P.: An equational approach to theorem proving in first-order predicate calculus. In: Proceedings of the 9th International Joint Conference on Artificial Intelligence (IJCAI-85), vol. 2, pp. 1146\u20131153 (1985)"},{"key":"9191_CR12","doi-asserted-by":"crossref","unstructured":"Laita, L.M., de Ledesma, L., Roanes-Lozano, E., Roanes-Mac\u00edas, E.: An interpretation of the propositional Boolean algebra as a k-algebra. Effective calculus. In: Campbell, J., Calmet,\u00a0J. (eds.) Proceedings of the Second International Workshop\/Conference on Artificial Intelligence and Symbolic Mathematical Computing (AISMC-2). Lecture Notes in Computer Science, vol. 958, pp. 255\u2013263. Springer (1995)","DOI":"10.1007\/3-540-60156-2_18"},{"key":"9191_CR13","unstructured":"Laita, L.M., Roanes-Lozano, E., Alonso, J.A., Briales, E.: Algebraic verification of KBSs. In: Proceedings of the 13th National Conference on Artificial Intelligence (AAAI-96) (Workshop on Verification and Validation of Knowledge Based Systems and Subsystems), pp. 122\u2013129. Portland, USA (1996)"},{"key":"9191_CR14","unstructured":"Laita, L.M., Roanes-Lozano, E.: A computer algebraic method for verification and deduction in KBSs: theory and implementation. In: Proceedings of the 12th European Conference on Artificial Intelligence (ECAI-96), pp. 5\u201310. Budapest University, Hungary (1996)"},{"issue":"1","key":"9191_CR15","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1007\/s005000050086","volume":"3","author":"LM Laita","year":"1999","unstructured":"Laita, L.M., Roanes-Lozano, E., de Ledesma, L., Alonso, J.A.: A computer algebra approach to verification and deduction in manyvalued knowledge systems. Soft Comput. 3(1), 7\u201319 (1999)","journal-title":"Soft Comput."},{"key":"9191_CR16","first-page":"473","volume":"51\/5","author":"LM Laita","year":"2000","unstructured":"Laita, L.M., Roanes-Lozano, E., Maojo, V., de Ledesma, L., Laita, L.: An expert system for managing medical appropriateness criteria based on computer algebra techniques. Comput. Math. Appl. 51\/5, 473\u2013481 (2000)","journal-title":"Comput. Math. Appl."},{"key":"9191_CR17","doi-asserted-by":"crossref","first-page":"2847","DOI":"10.1016\/j.eswa.2007.05.039","volume":"34","author":"M Lourdes Jimenez","year":"2008","unstructured":"Lourdes Jimenez, M., Santamar\u00eda, J.M., Barchino, R., Laita, L., Laita, L.M., Gonz\u00e1lez, L.A., Asenjo, A.: Knowledge representation for diagnosis of care problems through an expert system: model of the auto-care deficit situations. Expert Syst. Appl. 34, 2847\u20132857 (2008)","journal-title":"Expert Syst. Appl."},{"key":"9191_CR18","doi-asserted-by":"crossref","first-page":"183","DOI":"10.1016\/S0378-4754(01)00370-6","volume":"58","author":"C P\u00e9rez-Carretero","year":"2002","unstructured":"P\u00e9rez-Carretero, C., Laita, L.M., Roanes-Lozano, E., L\u00e1zaro, L., Gonz\u00e1lez-Cajal, J., Laita, L.: A logic and computer algebra-based expert system for diagnosis of anorexia. Math. Comput. Simul. 58, 183\u2013202 (2002)","journal-title":"Math. Comput. Simul."},{"key":"9191_CR19","unstructured":"Perkinson, D.: CoCoA 4.0 Online Help (electronic file acompanying CoCoA v.4.0) (2000)"},{"key":"9191_CR20","first-page":"65","volume":"14","author":"E Roanes-Lozano","year":"1995","unstructured":"Roanes-Lozano, E., Laita, L.M., Roanes-Mac\u00edas, E.: Maple V in A.I.: the boolean algebra associated to a KBS. Comput. Algebra Ned. Nieuwsbrief 14, 65\u201370 (1995)","journal-title":"Comput. Algebra Ned. Nieuwsbrief"},{"key":"9191_CR21","unstructured":"Roanes-Lozano, E., Laita, L.M.: Verification of knowledge based systems with commutative algebra and computer algebra techniques. In: Proceedings of the 1st International Conference on Applications of Computer Algebra (IMACS). New Mexico University, USA (electronic book) (1995)"},{"key":"9191_CR22","unstructured":"Roanes-Lozano, E., Laita, L.M.: Verification of knowledge based systems: an algebraic interpretation. In: Proceedings of the International Conference on Artificial Intelligence (IJCAI-95) (Workshop on Verification and Validation of Knowledge Based Systems), pp. 91\u201395. MCGill University, Montreal, Canada (1995)"},{"key":"9191_CR23","doi-asserted-by":"crossref","unstructured":"Roanes-Lozano, E., Laita, L.M., Roanes-Mac\u00edas, E.: An inference engine for propositional two-valued logic based on the radical membership problem. In: Campbell, J., Calmet,\u00a0J., Pfalzgraf,\u00a0J. (eds.) Proceedings of the Third International Workshop\/Conference on Artificial Intelligence and Symbolic Mathematical Computing (AISMC-3). Lecture Notes in Computer Science, vol. 1138, , pp. 71\u201386. Springer, Berlin (1996)","DOI":"10.1007\/3-540-61732-9_51"},{"key":"9191_CR24","doi-asserted-by":"crossref","first-page":"83","DOI":"10.1016\/S0378-4754(97)00088-8","volume":"45\/1","author":"E Roanes Lozano","year":"1998","unstructured":"Roanes Lozano, E., Laita, L.M., Roanes-Mac\u00edas, E.: A polynomial model for multivalued logics with a touch of algebraic geometry and computer algebra. Math. Comput. Simul. 45\/1, 83\u201399 (1998)","journal-title":"Math. Comput. Simul."},{"key":"9191_CR25","doi-asserted-by":"crossref","unstructured":"Roanes-Lozano, E., Hernando, A., Laita, L.M., Roanes-Mac\u00edas, E.: A Groebner bases-based approach to backward reasoning in rule based expert systems. Ann. Math. Artif. Intell. doi: 10.1007\/s10472-009-9147-4","DOI":"10.1007\/s10472-009-9147-4"},{"key":"9191_CR26","doi-asserted-by":"crossref","first-page":"47","DOI":"10.1016\/j.eswa.2005.09.011","volume":"31","author":"C Rodr\u00edguez-Solano","year":"2006","unstructured":"Rodr\u00edguez-Solano, C., Laita, L.M., Roanes Lozano, E., L\u00f3pez Corral, L., Laita, L.: A computational system for diagnosis of depressive situations. Expert Syst. Appl. 31, 47\u201355 (2006)","journal-title":"Expert Syst. Appl."},{"key":"9191_CR27","doi-asserted-by":"crossref","unstructured":"Winkler, F.: Polynomial Algorithms in Computer Algebra. Springer, Vienna (1996)","DOI":"10.1007\/978-3-7091-6571-3"}],"container-title":["Journal of Automated Reasoning"],"original-title":[],"language":"en","link":[{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10817-010-9191-0.pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/article\/10.1007\/s10817-010-9191-0\/fulltext.html","content-type":"text\/html","content-version":"vor","intended-application":"text-mining"},{"URL":"http:\/\/link.springer.com\/content\/pdf\/10.1007\/s10817-010-9191-0","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2021,10,31]],"date-time":"2021-10-31T15:31:35Z","timestamp":1635694295000},"score":1,"resource":{"primary":{"URL":"http:\/\/link.springer.com\/10.1007\/s10817-010-9191-0"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2010,7,17]]},"references-count":27,"journal-issue":{"issue":"2","published-print":{"date-parts":[[2011,2]]}},"alternative-id":["9191"],"URL":"https:\/\/doi.org\/10.1007\/s10817-010-9191-0","relation":{},"ISSN":["0168-7433","1573-0670"],"issn-type":[{"value":"0168-7433","type":"print"},{"value":"1573-0670","type":"electronic"}],"subject":[],"published":{"date-parts":[[2010,7,17]]}}}