ACUOS: A System for Modular ACU Generalization with Subtyping and Inheritance

The final publication is available at Springer via http://dx.doi.org/10.1007/978-3-319-11558-0_40Computing generalizers is relevant in a wide spectrum of automated reasoning areas where analogical reasoning and inductive inference are needed. The ACUOS system computes a complete and minimal set of semantic generalizers (also called “anti-unifiers”) of two structures in a typed language modulo a set of equational axioms. By supporting types and any (modular) combination of associativity (A), commutativity (C), and unity (U) algebraic axioms for function symbols, ACUOS allows reasoning about typed data structures, e.g. lists, trees, and (multi-)sets, and typical hierarchical/structural relations such as is a and part of. This paper discusses the modular ACU generalization tool ACUOS and illustrates its use in a classical artificial intelligence problem.This work has been partially supported by the EU (FEDER) and the Spanish MINECO under grants TIN 2010-21062-C02-02 and TIN 2013-45732-C4-1-P, by Generalitat Valenciana PROMETEO2011/052, and by NSF Grant CNS 13-10109. J. Espert has also been supported by the Spanish FPU grant FPU12/06223.Alpuente Frasnedo, M.; Escobar Román, S.; Espert Real, J.; Meseguer, J. (2014). ACUOS: A System for Modular ACU Generalization with Subtyping and Inheritance. En Logics in Artificial Intelligence. Springer. 573-581. https://doi.org/10.1007/978-3-319-11558-0_40S573581Alpuente, M., Escobar, S., Espert, J., Meseguer, J.: A Modular Order-sorted Equational Generalization Algorithm. Information and Computation 235, 98–136 (2014)Alpuente, M., Escobar, S., Meseguer, J., Ojeda, P.: A Modular Equational Generalization Algorithm. In: Hanus, M. (ed.) LOPSTR 2008. LNCS, vol. 5438, pp. 24–39. Springer, Heidelberg (2009)Alpuente, M., Escobar, S., Meseguer, J., Ojeda, P.: Order–Sorted Generalization. ENTCS 246, 27–38 (2009)Alpuente, M., Espert, J., Escobar, S., Meseguer, J.: ACUOS: A System for Modular ACU Generalization with Subtyping and Inheritance. Tech. rep., DSIC-UPV (2013), http://www.dsic.upv.es/users/elp/papers.htmlArmengol, E.: Usages of Generalization in Case-Based Reasoning. In: Weber, R.O., Richter, M.M. (eds.) ICCBR 2007. LNCS (LNAI), vol. 4626, pp. 31–45. Springer, Heidelberg (2007)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C. (eds.): All About Maude - A High-Performance Logical Framework. LNCS, vol. 4350. Springer, Heidelberg (2007)Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.L.: Reflection, metalevel computation, and strategies. In: All About Maude [6], pp. 419–458Gentner, D.: Structure-Mapping: A Theoretical Framework for Analogy*. Cognitive Science 7(2), 155–170 (1983)Krumnack, U., Schwering, A., Gust, H., Kühnberger, K.-U.: Restricted higher order anti unification for analogy making. In: Orgun, M.A., Thornton, J. (eds.) AI 2007. LNCS (LNAI), vol. 4830, pp. 273–282. Springer, Heidelberg (2007)Kutsia, T., Levy, J., Villaret, M.: Anti-Unification for Unranked Terms and Hedges. Journal of Automated Reasoning 520, 155–190 (2014)Meseguer, J.: Conditioned rewriting logic as a united model of concurrency. Theor. Comput. Sci. 96(1), 73–155 (1992)Muggleton, S.: Inductive Logic Programming: Issues, Results and the Challenge of Learning Language in Logic. Artif. Intell. 114(1-2), 283–296 (1999)Ontañón, S., Plaza, E.: Similarity measures over refinement graphs. Machine Learning 87(1), 57–92 (2012)Plotkin, G.: A note on inductive generalization. In: Machine Intelligence, vol. 5, pp. 153–163. Edinburgh University Press (1970)Pottier, L.: Generalisation de termes en theorie equationelle: Cas associatif-commutatif. Tech. Rep. INRIA 1056, Norwegian Computing Center (1989)Schmid, U., Hofmann, M., Bader, F., Häberle, T., Schneider, T.: Incident Mining using Structural Prototypes. In: García-Pedrajas, N., Herrera, F., Fyfe, C., Benítez, J.M., Ali, M. (eds.) IEA/AIE 2010, Part II. LNCS, vol. 6097, pp. 327–336. Springer, Heidelberg (2010