The Integration of Connectionism and First-Order Knowledge Representation and Reasoning as a Challenge for Artificial Intelligence

Intelligent systems based on first-order logic on the one hand, and on artificial neural networks (also called connectionist systems) on the other, differ substantially. It would be very desirable to combine the robust neural networking machinery with symbolic knowledge representation and reasoning paradigms like logic programming in such a way that the strengths of either paradigm will be retained. Current state-of-the-art research, however, fails by far to achieve this ultimate goal. As one of the main obstacles to be overcome we perceive the question how symbolic knowledge can be encoded by means of connectionist systems: Satisfactory answers to this will naturally lead the way to knowledge extraction algorithms and to integrated neural-symbolic systems.Comment: In Proceedings of INFORMATION'2004, Tokyo, Japan, to appear. 12 page

An Upper Bound on the Complexity of Recognizable Tree Languages

The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class $\Game (D\_n({\bf\Sigma}^0\_2))$ for some natural number $n\geq 1$, where $\Game$ is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space $2^\omega$ into the class ${\bf\Delta}^1\_2$, and the notions of Wadge degree and Veblen function, we argue that this upper bound on the topological complexity of regular tree languages is much better than the usual ${\bf\Delta}^1\_2$

Formal Development of Rough Inclusion Functions

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article, continuing the formalization of rough sets [12], we give the formal characterization of three rough inclusion functions (RIFs). We start with the standard one, κ£, connected with Łukasiewicz [14], and extend this research for two additional RIFs: κ 1, and κ 2, following a paper by Gomolińska [4], [3]. We also define q-RIFs and weak q-RIFs [2]. The paper establishes a formal counterpart of [7] and makes a preliminary step towards rough mereology [16], [17] in Mizar [13].Institute of Informatics, University of Białystok, PolandAnna Gomolinska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 2002.Anna Gomolinska. Rough approximation based on weak q-RIFs. In James F. Peters, Andrzej Skowron, Marcin Wolski, Mihir K. Chakraborty, and Wei-Zhi Wu, editors, Transactions on Rough Sets X, volume 5656 of Lecture Notes in Computer Science, pages 117–135, Berlin, Heidelberg, 2009. Springer. ISBN 978-3-642-03281-3. doi:10.1007/978-3-642-03281-3_4.Anna Gomolinska. On three closely related rough inclusion functions. In Marzena Kryszkiewicz, James F. Peters, Henryk Rybinski, and Andrzej Skowron, editors, Rough Sets and Intelligent Systems Paradigms, volume 4585 of Lecture Notes in Computer Science, pages 142–151, Berlin, Heidelberg, 2007. Springer. doi:10.1007/978-3-540-73451-2_16.Anna Gomolinska. On certain rough inclusion functions. In James F. Peters, Andrzej Skowron, and Henryk Rybinski, editors, Transactions on Rough Sets IX, volume 5390 of Lecture Notes in Computer Science, pages 35–55. Springer Berlin Heidelberg, 2008. doi:10.1007/978-3-540-89876-4_3.Adam Grabowski. On the computer-assisted reasoning about rough sets. In B. Dunin-Kęplicz, A. Jankowski, A. Skowron, and M. Szczuka, editors, International Workshop on Monitoring, Security, and Rescue Techniques in Multiagent Systems Location, volume 28 of Advances in Soft Computing, pages 215–226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371–385, 2014. doi:10.3233/FI-2014-1129.Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In Tamás Mihálydeák, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo Düntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225–238, Cham, 2019. Springer International Publishing. ISBN 978-3-030-22815-6. doi:10.1007/978-3-030-22815-6_18.Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and Michał Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183–191, 2018. doi:10.2478/forma-2018-0016.Adam Grabowski, Artur Korniłowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.Jan Łukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Łukasiewicz – Selected Works, pages 16–63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in Kraków, 1913.Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.Lech Polkowski. Rough mereology. In Approximate Reasoning by Parts, volume 20 of Intelligent Systems Reference Library, pages 229–257, Berlin, Heidelberg, 2011. Springer. ISBN 978-3-642-22279-5. doi:10.1007/978-3-642-22279-5_6.Lech Polkowski and Andrzej Skowron. Rough mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning, 15(4):333–365, 1996. doi:10.1016/S0888-613X(96)00072-2.Andrzej Skowron and Jarosław Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245–253, 1996. doi:10.3233/FI-1996-272311.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.27433734

A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances

Spaced seeds have been recently shown to not only detect more alignments, but also to give a more accurate measure of phylogenetic distances (Boden et al., 2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower misclassification rate when used with Support Vector Machines (SVMs) (On-odera and Shibuya, 2013), We confirm by independent experiments these two results, and propose in this article to use a coverage criterion (Benson and Mak, 2008, Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both cases in order to design better seed patterns. We show first how this coverage criterion can be directly measured by a full automaton-based approach. We then illustrate how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance. At the end, for alignment-free distances, we propose an extension by adopting the coverage criterion, show how it performs, and indicate how it can be efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017

A Coverage Criterion for Spaced Seeds and its Applications to Support Vector Machine String Kernels and k-Mer Distances

Spaced seeds have been recently shown to not only detect more alignments, but also to give a more accurate measure of phylogenetic distances (Boden et al., 2013, Horwege et al., 2014, Leimeister et al., 2014), and to provide a lower misclassification rate when used with Support Vector Machines (SVMs) (On-odera and Shibuya, 2013), We confirm by independent experiments these two results, and propose in this article to use a coverage criterion (Benson and Mak, 2008, Martin, 2013, Martin and No{\'e}, 2014), to measure the seed efficiency in both cases in order to design better seed patterns. We show first how this coverage criterion can be directly measured by a full automaton-based approach. We then illustrate how this criterion performs when compared with two other criteria frequently used, namely the single-hit and multiple-hit criteria, through correlation coefficients with the correct classification/the true distance. At the end, for alignment-free distances, we propose an extension by adopting the coverage criterion, show how it performs, and indicate how it can be efficiently computed.Comment: http://online.liebertpub.com/doi/abs/10.1089/cmb.2014.017

Formalizing Two Generalized Approximation Operators

Rough sets, developed by Pawlak [15], are important tool to describe situation of incomplete or partially unknown information. In this article we give the formal characterization of two closely related rough approximations, along the lines proposed in a paper by Gomolińska [2]. We continue the formalization of rough sets in Mizar [1] started in [6].Adam Grabowski - Institute of Informatics, University of Białystok, PolandMichał Sielwiesiuk - Institute of Informatics, University of Białystok, PolandGrzegorz Bancerek, Czesław Byliński, Adam Grabowski, Artur Korniłowicz, Roman Matuszewski, Adam Naumowicz, Karol Pąk, and Josef Urban. Mizar: State-of-the-art and beyond. In Manfred Kerber, Jacques Carette, Cezary Kaliszyk, Florian Rabe, and Volker Sorge, editors, Intelligent Computer Mathematics, volume 9150 of Lecture Notes in Computer Science, pages 261–279. Springer International Publishing, 2015. ISBN 978-3-319-20614-1. doi:10.1007/978-3-319-20615-8_17.Anna Gomolińska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103–119, 2002.Adam Grabowski. Automated discovery of properties of rough sets. Fundamenta Informaticae, 128:65–79, 2013. doi:10.3233/FI-2013-933.Adam Grabowski. Lattice theory for rough sets – a case study with Mizar. Fundamenta Informaticae, 147(2–3):223–240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Formalization of generalized almost distributive lattices. Formalized Mathematics, 22(3):257–267, 2014. doi:10.2478/forma-2014-0026.Adam Grabowski. Basic properties of rough sets and rough membership function. Formalized Mathematics, 12(1):21–28, 2004.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55–64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets – an automated approach. Formalized Mathematics, 24(2):143–155, 2016. doi:10.1515/forma-2016-0011.Adam Grabowski and Magdalena Jastrzębska. A note on a formal approach to rough operators. In Marcin S. Szczuka and Marzena Kryszkiewicz et al., editors, Rough Sets and Current Trends in Computing – 7th International Conference, RSCTC 2010, Warsaw, Poland, June 28-30, 2010. Proceedings, volume 6086 of Lecture Notes in Computer Science, pages 307–316. Springer, 2010. doi:10.1007/978-3-642-13529-3_33.Adam Grabowski and Magdalena Jastrzębska. Rough set theory from a math-assistant perspective. In Rough Sets and Intelligent Systems Paradigms, International Conference, RSEISP 2007, Warsaw, Poland, June 28–30, 2007, Proceedings, pages 152–161, 2007. doi:10.1007/978-3-540-73451-2_17.Adam Grabowski and Christoph Schwarzweller. On duplication in mathematical repositories. In Serge Autexier, Jacques Calmet, David Delahaye, Patrick D. F. Ion, Laurence Rideau, Renaud Rioboo, and Alan P. Sexton, editors, Intelligent Computer Mathematics, 10th International Conference, AISC 2010, 17th Symposium, Calculemus 2010, and 9th International Conference, MKM 2010, Paris, France, July 5–10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300–314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and Christoph Schwarzweller. Rough Concept Analysis - theory development in the Mizar system. In Asperti, Andrea and Bancerek, Grzegorz and Trybulec, Andrzej, editor, Mathematical Knowledge Management, Third International Conference, MKM 2004, Bialowieza, Poland, September 19–21, 2004, Proceedings, volume 3119 of Lecture Notes in Computer Science, pages 130–144, 2004. doi:10.1007/978-3-540-27818-4_10. 3rd International Conference on Mathematical Knowledge Management, Bialowieza, Poland, Sep. 19-21, 2004.Jouni Järvinen. Lattice theory for rough sets. Transactions of Rough Sets, VI, Lecture Notes in Computer Science, 4374:400–498, 2007.Eliza Niewiadomska and Adam Grabowski. Introduction to formal preference spaces. Formalized Mathematics, 21(3):223–233, 2013. doi:10.2478/forma-2013-0024.Zdzisław Pawlak. Rough sets. International Journal of Parallel Programming, 11:341–356, 1982. doi:10.1007/BF01001956.Y.Y. Yao. Two views of the theory of rough sets in finite universes. International Journal of Approximate Reasoning, 15(4):291–317, 1996. doi:10.1016/S0888-613X(96)00071-0.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997–5011, 2007.26218319