1,022 research outputs found

    A syntax for semantics in P-Lingua

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    P-Lingua is a software framework for Membrane Computing, it includes a programming language, also called P-Lingua, for writting P system de nitions using a syntax close to standard scienti c notation. The rst line of a P-Lingua le is an unique identi er de ning the variant or model of P system to be used, i.e, the semantics of the P system. Software tools based on P-Lingua use this identi er to select a simulation algorithm implementing the corresponding derivation mode. Derivation modes de ne how to obtain a con guration Ct+1 from a con guration Ct. This information is usually hard-coded in the simulation algorithm. The P system model also de nes what types or rules can be used, the P-Lingua compiler uses the identi er to select an speci c parser for the le. In this case, a set of parsers is codi ed within the compiler tool. One for each unique identi er. P-Lingua has grown during the last 12 years, including more and more P system models. From a software engineering point of view, this approximation implies a continous development of the framework, leading to a monolithic software which is hard to debug and maintain. In this paper, we propose a new software approximation for the framework, including a new syntax for de ning rule patterns and derivation modes. The P-Lingua users can now de ne custom P system models instead of hard-coding them in the software. This approximation leads to a more exible solution which is easier to maintain and debug. Moreover, users could de ne and play with new/experimental P system models

    Formal Development of Rough Inclusion Functions

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    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 Ɓukasiewicz [14], and extend this research for two additional RIFs: Îș 1, and Îș 2, following a paper by GomoliƄska [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 BiaƂystok, 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 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 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 MichaƂ Sielwiesiuk. Formalizing two generalized approximation operators. Formalized Mathematics, 26(2):183–191, 2018. doi:10.2478/forma-2018-0016.Adam Grabowski, Artur KorniƂowicz, and Adam Naumowicz. Four decades of Mizar. Journal of Automated Reasoning, 55(3):191–198, 2015. doi:10.1007/s10817-015-9345-1.Jan Ɓukasiewicz. Die logischen Grundlagen der Wahrscheinlichkeitsrechnung. In L. Borkowski, editor, Jan Ɓukasiewicz – Selected Works, pages 16–63. North Holland, Polish Scientific Publ., Amsterdam London Warsaw, 1970. First published in KrakĂłw, 1913.ZdzisƂaw 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 JarosƂaw 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 Proof Theoretic View of Constraint Programming

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    We provide here a proof theoretic account of constraint programming that attempts to capture the essential ingredients of this programming style. We exemplify it by presenting proof rules for linear constraints over interval domains, and illustrate their use by analyzing the constraint propagation process for the {\tt SEND + MORE = MONEY} puzzle. We also show how this approach allows one to build new constraint solvers.Comment: 25 page

    Preface

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    Formalizing Two Generalized Approximation Operators

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    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 GomoliƄska [2]. We continue the formalization of rough sets in Mizar [1] started in [6].Adam Grabowski - Institute of Informatics, University of BiaƂystok, PolandMichaƂ Sielwiesiuk - Institute of Informatics, University of BiaƂystok, PolandGrzegorz Bancerek, CzesƂaw ByliƄski, Adam Grabowski, Artur KorniƂowicz, 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 GomoliƄska. 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 JĂ€rvinen. 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.ZdzisƂaw 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

    A Framework for Complexity Classes in Membrane Computing

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    The purpose of the present work is to give a general idea about the existing results and open problems concerning the study of complexity classes within the membrane computing framework. To this aim, membrane systems (seen as computing devices) are briefly introduced, providing the basic definition and summarizing the key ideas, trying to cover the various approaches that are under investigation in this area – of course, special attention is paid to the study of complexity classes. The paper concludes with some final remarks that hint the reasons why this field (as well as other unconventional models of computation) is attracting the attention of a growing community.Ministerio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC-58

    A map of dependencies among three-valued logics

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    International audienceThree-valued logics arise in several fields of computer science, both inspired by concrete problems (such as in the management of the null value in databases) and theoretical considerations. Several three-valued logics have been defined. They differ by their choice of basic connectives, hence also from a syntactic and proof-theoretic point of view. Different interpretations of the third truth value have also been suggested. They often carry an epistemic flavor. In this work, relationships between logical connectives on three-valued functions are explored. Existing theorems of functional completeness have laid bare some of these links, based on specific connectives. However we try to draw a map of such relationships between conjunctions, negations and implications that extend Boolean ones. It turns out that all reasonable connectives can be defined from a few of them and so all known three-valued logics appear as a fragment of only one logic. These results can be instrumental when choosing, for each application context, the appropriate fragment where the basic connectives make full sense, based on the appropriate meaning of the third truth-value
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