1,080 research outputs found
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, ÎșÂŁ, connected with Ćukasiewicz [14], and extend this research for two additional RIFs: Îș 1, and Îș 2, following a paper by GomoliĆska [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 BiaĆystok, PolandAnna Gomolinska. A comparative study of some generalized rough approximations. Fundamenta Informaticae, 51:103â119, 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 117â135, 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 142â151, 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 35â55. 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-KÄplicz, 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 215â226, Berlin, Heidelberg, 2005. Springer-Verlag. doi:10.1007/3-540-32370-8_15.Adam Grabowski. Efficient rough set theory merging. Fundamenta Informaticae, 135(4): 371â385, 2014. doi:10.3233/FI-2014-1129.Adam Grabowski. Building a framework of rough inclusion functions by means of computerized proof assistant. In TamĂĄs MihĂĄlydeĂĄk, Fan Min, Guoyin Wang, Mohua Banerjee, Ivo DĂŒntsch, Zbigniew Suraj, and Davide Ciucci, editors, Rough Sets, volume 11499 of Lecture Notes in Computer Science, pages 225â238, 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 â a case study with Mizar. Fundamenta Informaticae, 147(2â3):223â240, 2016. doi:10.3233/FI-2016-1406.Adam Grabowski. Relational formal characterization of rough sets. Formalized Mathematics, 21(1):55â64, 2013. doi:10.2478/forma-2013-0006.Adam Grabowski. Binary relations-based rough sets â an automated approach. Formalized Mathematics, 24(2):143â155, 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 5â10, 2010. Proceedings, volume 6167 of Lecture Notes in Computer Science, pages 300â314. Springer, 2010. doi:10.1007/978-3-642-14128-7_26.Adam Grabowski and MichaĆ Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183â191, 2018. doi:10.2478/forma-2018-0016.Adam Grabowski, Artur KorniĆowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191â198, 2015. doi:10.1007/s10817-015-9345-1.Jan Ćukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Ćukasiewicz â Selected Works, pages 16â63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in KrakĂłw, 1913.ZdzisĆaw Pawlak. Rough sets. International Journal of Parallel Programming, 11:341â356, 1982. doi:10.1007/BF01001956.Lech Polkowski. Rough mereology. In Approximate Reasoning by Parts, volume 20 of Intelligent Systems Reference Library, pages 229â257, 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):333â365, 1996. doi:10.1016/S0888-613X(96)00072-2.Andrzej Skowron and JarosĆaw Stepaniuk. Tolerance approximation spaces. Fundamenta Informaticae, 27(2/3):245â253, 1996. doi:10.3233/FI-1996-272311.William Zhu. Generalized rough sets based on relations. Information Sciences, 177: 4997â5011, 2007.27433734
Computational aspects of tomographic and neuroscientific problems
4siopenopenBrunetti, S.; Dulio, P.; Frosini, A.; Rozenberg, G.Brunetti, S.; Dulio, P.; Frosini, A.; Rozenberg, G
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
for some natural number , where 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
into the class , 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
An algebraic semantics for QVT-relations check-only transformations
Fundamenta Informaticae, 114 1, Juan de Lara, Esther Guerra, An algebraic semantics for QVT-relations check-only transformations, 73-101, Copyright 2012, with permission from IOS PressQVT is the standard for model transformation defined by the OMG in the context of the Model-Driven Architecture. It is made of several transformation languages. Among them, QVT-Relations is the one with the highest level of abstraction, as it permits developing bidirectional transformations in a declarative, relational style. Unfortunately, the standard only provides a semiformal description of its semantics, which hinders analysis and has given rise to ambiguities in existing tool implementations. In order to improve this situation, we propose a formal, algebraic semantics for QVT-Relations check-only transformations, defining a notion of satisfaction of QVT-Relations specifications by models.This work has been supported by the Spanish Ministry of Science and Innovation with projects METEORIC (TIN2008-02081) and Go Lite (TIN2011-24139), and by the R&D program of the Community of Madrid with project âe-Madridâ (S2009/TIC-1650)
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