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Dialectical Rough Sets, Parthood and Figures of Opposition-I

verfasst von : A. Mani

Erschienen in: Transactions on Rough Sets XXI

Verlag: Springer Berlin Heidelberg

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Abstract

In one perspective, the main theme of this research revolves around the inverse problem in the context of general rough sets that concerns the existence of rough basis for given approximations in a context. Granular operator spaces and variants were recently introduced by the present author as an optimal framework for anti-chain based algebraic semantics of general rough sets and the inverse problem. In the framework, various sub-types of crisp and non-crisp objects are identifiable that may be missed in more restrictive formalism. This is also because in the latter cases concepts of complementation and negation are taken for granted - while in reality they have a complicated dialectical basis. This motivates a general approach to dialectical rough sets building on previous work of the present author and figures of opposition. In this paper dialectical rough logics are invented from a semantic perspective, a concept of dialectical predicates is formalized, connection with dialetheias and glutty negation are established, parthood analyzed and studied from the viewpoint of classical and dialectical figures of opposition by the present author. The proposed method become more geometrical and encompass parthood as a primary relation (as opposed to roughly equivalent objects) for algebraic semantics.

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Vorheriges Kapitel Double Successive Rough Set Approximations

Nächstes Kapitel A Logic for Spatial Reasoning in the Framework of Rough Mereology

Pawlak, Z.: Rough Sets: Theoretical Aspects of Reasoning About Data. Kluwer Academic Publishers, Dodrecht (1991)MATHCrossRef

Mani, A.: Algebraic methods for granular rough sets. In: Mani, A., Düntsch, I., Cattaneo, G. (eds.) Algebraic Methods in General Rough Sets. Trends in Mathematics, pp. 157–336. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-030-01162-8_3CrossRef

Mani, A.: Antichain based semantics for rough sets. In: Ciucci, D., Wang, G., Mitra, S., Wu, W.-Z. (eds.) RSKT 2015. LNCS (LNAI), vol. 9436, pp. 335–346. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-25754-9_30CrossRef

Mani, A.: Knowledge and consequence in AC semantics for general rough sets. In: Wang, G., Skowron, A., Yao, Y.Y., Ślȩzak, D., Polkowski, L. (eds.) Thriving Rough Sets. SCI, vol. 708, pp. 237–268. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54966-8_12CrossRef

Mani, A.: Pure rough mereology and counting. In: WIECON 2016, pp. 1–8. IEEXPlore (2016)

Mani, A.: On deductive systems of AC semantics for rough sets. ArXiv. Math (arXiv:1610.02634v1), pp. 1–12, October 2016

Mani, A.: Dialectics of counting and the mathematics of vagueness. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XV. LNCS, vol. 7255, pp. 122–180. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31903-7_4CrossRef

Polkowski, L.: Approximate Reasoning by Parts. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-22279-5CrossRef

Mani, A.: Super rough semantics. Fundamenta Informaticae 65(3), 249–261 (2005)MathSciNetMATH

10.

Mani, A.: Algebraic representation, duality and beyond. In: Mani, A., Düntsch, I., Cattaneo, G. (eds.) Algebraic Methods in General Rough Sets. Trends in Mathematics, pp. 459–552. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-030-01162-8_6CrossRef

11.

Banerjee, M., Chakraborty, M.K.: Rough sets through algebraic logic. Fundamenta Informaticae 28, 211–221 (1996)MathSciNetMATH

12.

Ioan, P.: Logic and Dialectics. Al. I. Cuza Universities Press (1998)

13.

Schang, F.: Opposites and oppositions around and beyond the square of opposition. In: Beziau, J.Y., Jacquette, D., et al. (eds.) Around and Beyond the Square of Opposition. Studies in Universal Logic, vol. I, pp. 147–174. Birkhauser, Basel (2012)MATHCrossRef

14.

Ciucci, D., Dubois, D., Prade, H.: Oppositions in rough set theory. In: Li, T., et al. (eds.) RSKT 2012. LNCS (LNAI), vol. 7414, pp. 504–513. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31900-6_62CrossRef

15.

Mani, A.: Integrated dialectical logics for relativised general rough set theory. In: International Conference on Rough Sets, Fuzzy Sets and Soft Computing, Agartala, India, 6 p. (Refereed) (2009). http://arxiv.org/abs/0909.4876

16.

Mani, A.: Ontology, rough Y-systems and dependence. Int. J. Comput. Sci. Appl. 11(2), 114–136 (2014). Special Issue of IJCSA on Computational IntelligenceMathSciNet

17.

Mani, A.: Algebraic semantics of proto-transitive rough sets. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XX. LNCS, vol. 10020, pp. 51–108. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53611-7_3CrossRef

18.

Chakraborty, M.K.: On some issues in the foundation of rough sets: the problem of definition. Fundamenta Informaticae 148, 123–132 (2016)MathSciNetMATHCrossRef

19.

Grätzer, G.: General Lattice Theory. Birkhauser, New York (1998)MATH

20.

Koh, K.: On the lattice of maximum-sized antichains of a finite poset. Algebra Universalis 17, 73–86 (1983)MathSciNetMATHCrossRef

21.

Mani, A.: Algebraic Semantics of Proto-Transitive Rough Sets, 1st edn. arXiv:1410.0572, July 2014

22.

Mani, A.: Approximation dialectics of proto-transitive rough sets. In: Chakraborty, M.K., Skowron, A., Kar, S. (eds.) Facets of Uncertainties and Applications. Springer Proceedings in Math and Statistics, vol. 125, pp. 99–109. Springer, New Delhi (2015). https://doi.org/10.1007/978-81-322-2301-6_8CrossRef

23.

Ciucci, D.: Approximation algebra and framework. Fundamenta Informaticae 94, 147–161 (2009)MathSciNetMATH

24.

Cattaneo, G., Ciucci, D.: Lattices with interior and closure operators and abstract approximation spaces. In: Peters, J.F., Skowron, A., Wolski, M., Chakraborty, M.K., Wu, W.-Z. (eds.) Transactions on Rough Sets X. LNCS, vol. 5656, pp. 67–116. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-03281-3_3CrossRef

25.

Yao, Y.Y.: Relational interpretation of neighbourhood operators and rough set approximation operators. Inf. Sci. 111, 239–259 (1998)MATHCrossRef

26.

Iwinski, T.B.: Rough orders and rough concepts. Bull. Pol. Acad. Sci. (Math.) 3–4, 187–192 (1988)MathSciNetMATH

27.

Cattaneo, G.: Algebraic methods for rough approximation spaces by lattice interior-closure operations. In: Mani, A., Düntsch, I., Cattaneo, G. (eds.) Algebraic Methods in General Rough Sets. Trends in Mathematics, pp. 13–152. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-030-01162-8_2CrossRef

28.

Pagliani, P., Chakraborty, M.: A Geometry of Approximation: Rough Set Theory: Logic, Algebra and Topology of Conceptual Patterns. Springer, Berlin (2008). https://doi.org/10.1007/978-1-4020-8622-9MATHCrossRef

29.

Polkowski, L., Skowron, A.: Rough mereology: a new paradigm for approximate reasoning. Int. J. Approx. Reason. 15(4), 333–365 (1996)MathSciNetMATHCrossRef

30.

Mani, A.: Esoteric rough set theory: algebraic semantics of a generalized VPRS and VPFRS. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 175–223. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85064-9_9CrossRef

31.

Mani, A.: Choice inclusive general rough semantics. Inf. Sci. 181(6), 1097–1115 (2011)MathSciNetMATHCrossRef

32.

Mani, A.: Axiomatic granular approach to knowledge correspondences. In: Li, T., et al. (eds.) RSKT 2012. LNCS (LNAI), vol. 7414, pp. 482–487. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-31900-6_59CrossRef

33.

Mani, A.: Granular Foundations of the Mathematics of Vagueness, Algebraic Semantics and Knowledge Interpretation. University of Calcutta (2016)

34.

Moore, E.F., Shannon, C.E.: Reliable circuits using less reliable relays-I. II. Bell Syst. Tech. J. 191–208, 281–297 (1956)MATH

35.

Shannon, C.E.: A mathematical theory of communication. Bell Syst. Tech. J. 27(379–423), 623–656 (1948)MathSciNetMATHCrossRef

36.

Lin, T.Y.: Granular computing-1: the concept of granulation and its formal model. Int. J. Granular Comput. Rough Sets Int. Syst. 1(1), 21–42 (2009)

37.

Mani, A.: Approximations from anywhere and general rough sets. In: Polkowski, L., et al. (eds.) IJCRS 2017. LNCS (LNAI), vol. 10314, pp. 3–22. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-60840-2_1CrossRef

38.

Ciucci, D.: Back to the beginnings: Pawlak’s definitions of the terms information. In: Wang, G., Skowron, A., Yao, Y., Ślȩzak, D., Polkowski, L. (eds.) Thriving Rough Sets. Studies in Computational Intelligence, vol. 708. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-54966-8_11CrossRef

39.

Cattaneo, G., Ciucci, D.: Algebraic methods for orthopairs and induced rough approximation spaces. In: Mani, A., Düntsch, I., Cattaneo, G. (eds.) Algebraic Methods in General Rough Sets. Trends in Mathematics, pp. 553–640. Birkhäuser, Basel (2018). https://doi.org/10.1007/978-3-030-01162-8_7CrossRef

40.

Yao, Y.Y., Yao, B.: Covering based rough set approximations. Inf. Sci. 200, 91–107 (2012)MathSciNetMATHCrossRef

41.

Düntsch, I., Gediga, G.: Rough Set Data Analysis: A Road to Non-invasive Knowledge Discovery. Methodos Publishers, Bangor (2000)

42.

Pagliani, P.: Covering rough sets and formal topology – a uniform approach through intensional and extensional constructors. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets XX. LNCS, vol. 10020, pp. 109–145. Springer, Heidelberg (2016). https://doi.org/10.1007/978-3-662-53611-7_4MATHCrossRef

43.

Sambin, G.: Intuitionistic formal spaces - a first communication. In: Skordev, D. (ed.) Mathematical Logic and Its Applications, pp. 187–204. Plenum Press, New York (1987)CrossRef

44.

Sambin, G., Gebellato, S.: A preview of the basic picture: a new perspective on formal topology. In: Altenkirch, T., Reus, B., Naraschewski, W. (eds.) TYPES 1998. LNCS, vol. 1657, pp. 194–208. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48167-2_14CrossRef

45.

da Costa, N., Wolf, R.G.: Studies in paraconsistent logic-1: the dialectical principle of the unity of opposites. Philosophia - Philos. Q. Israel 15, 497–510 (1974)

46.

Pagliani, P.: Rough set theory and logic-algebraic structures. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 109–190. Physica Verlag, Heidelberg (1998). https://doi.org/10.1007/978-3-7908-1888-8_6CrossRef

47.

Pagliani, P.: Local classical behaviours in three-valued logics and connected systems. Part 1. J. Multiple Valued Log. 5, 327–347 (2000)MathSciNetMATH

48.

Cattaneo, G., Ciucci, D.: Algebras for rough sets and fuzzy logics. In: Peters, J.F., Andrzej, S., Grzymała-Busse, J.W., Kostek, B., Świniarski, R.W., Szczuka, M.S. (eds.) Transactions on Rough Sets. LNCS, vol. 3100, pp. 208–252. Springer, Heidelberg (2004)MATH

49.

Mani, A.: Algebraic semantics of similarity-based bitten rough set theory. Fundamenta Informaticae 97(1–2), 177–197 (2009)MathSciNetMATH

50.

Ślȩzak, D., Wasilewski, P.: Granular sets – foundations and case study of tolerance spaces. In: An, A., Stefanowski, J., Ramanna, S., Butz, C.J., Pedrycz, W., Wang, G. (eds.) RSFDGrC 2007. LNCS (LNAI), vol. 4482, pp. 435–442. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-72530-5_52CrossRefMATH

51.

Cattaneo, G., Ciucci, D., Dubois, D.: Algebraic models of deviant modal operators based on De Morgan and Kleene lattices. Inf. Sci. 181, 4075–4100 (2011)MathSciNetMATHCrossRef

52.

Ficara, E.: Hegel’s Glutty negation. Hist. Philos. Log. 36, 1–10 (2014)MathSciNetMATH

53.

Brandom, R.: Between Saying and Doing. Oxford University Press, Oxford (2008)CrossRef

54.

McGill, V.P., Parry, W.T.: The unity of opposites - a dialectical principle. Sci. Soc. 12, 418–444 (1948)

55.

Mani, A.: Towards formal dialectical logics. Technical report (1999)

56.

Priest, G.: Doubt Truth to be a Liar. Oxford University Press, Oxford (2008)MATH

57.

Gabbay, D.: Oxford Logic Guides, vol. 1, 1st edn, p. 33. Clarendon Press, Oxford (1996)

58.

Batens, D.: Narrowing Down Suspicion in Inconsistent Premise Set (2006, preprint)

59.

Batens, D.: Against global paraconsistency. Stud. Soviet Thought 39, 209–229 (1990)CrossRef

60.

Apostol, L.: Logique et Dialectique. Gent (1979)

61.

Hoffmann, W.C.: A formal model for dialectical psychology. Int. Log. Rev. 40–67 (1986)

62.

Gorren, J.: Theorie Analytique de la Dialectique. South West Philos. Stud. 6, 41–47 (1981)

63.

Marx, K., Engels, F.: Marx and Engels: Collected Works, vol. 24. Progress Publishers, Delhi (1989)

64.

Batens, D.: Dynamic dialectical logics. In: Paraconsistent Logic - Essays. Philosophia Verlag, Munich (1989)

65.

Tzouvaras, A.: Periodicity of negation. Notre Dame J. Form. Log. 42(2), 88–99 (2001)MathSciNetMATHCrossRef

66.

Priest, G.: What not? A defence of a dialetheic theory of negation. In: Gabbay, D. (ed.) What is Negation?, pp. 101–120. Kluwer, Dordrecht (1999)MATHCrossRef

67.

Priest, G.: To be and not to be: dialectical tense logic. Studia Logica 41(2/3), 249–268 (1984)MathSciNetMATH

68.

Zeleny, J.: Paraconsistency and dialectical consistency. Log. Point View 1, 35–51 (1994)MATH

69.

Priest, G.: Logicians setting together contradictories - a perspective on relevance, paraconsistency and dialetheism. In: Jacquette, D. (ed.) Blackwell Handbook to Philosophical Logic. Blackwell, Hoboken (2007)

70.

Grim, P.: What is contradiction? In: Priest, G. (ed.) The Law of Non-contradiction. Oxford Universities Press, Oxford (2007)MATH

71.

Woods, J.: Dialectical Considerations on the Logic of Contradiction: Part I, II (2004, preprint)

72.

Priest, G.: Dialectic and dialetheic. Sci. Soc. 53(4), 388–415 (1990)

73.

Priest, G.: Contradictory concepts. In: Weber, E., Wouters, D., Meheus, J. (eds.) Logic, Reasoning and Rationality. Interdisciplinary Perspectives from The Humanities and Social Sciences, vol. 5, pp. 197–216. Springer, Dordrecht (2014). https://doi.org/10.1007/978-94-017-9011-6_10CrossRef

74.

Swaminathan, M., Rawal, V.: A Study of Agrarian Relations. Tulika Books, New Delhi (2015)

75.

Zimmerman, B. (ed.): Lesbian Histories and Cultures: An Encyclopedia. Garland Reference Library of the Social Sciences, vol. 1008. Garland Publishers, New York (2000)

76.

Saha, A., Sen, J., Chakraborty, M.K.: Algebraic structures in the vicinity of pre-rough algebra and their logics II. Inf. Sci. 333, 44–60 (2015)MathSciNetMATHCrossRef

77.

Mani, A.: Contamination-free measures and algebraic operations. In: 2013 IEEE International Conference on Fuzzy Systems (FUZZ), pp. 1–8. IEEE (2013)

78.

Bunder, M.W., Banerjee, M., Chakraborty, M.K.: Some rough consequence logics and their interrelations. In: Peters, J.F., Skowron, A. (eds.) Transactions on Rough Sets VIII. LNCS, vol. 5084, pp. 1–20. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-85064-9_1CrossRef

79.

Pawlak, Z.: Rough logic. Bull. Pol. Acad. Sci. (Tech.) 35, 253–258 (1987)MathSciNetMATH

80.

Hyde, D., Colyvan, M.: Paraconsistent Vagueness-why not? Aust. J. Log. 6, 207–225 (2008)MathSciNetMATH

81.

Avron, A., Konikowska, B.: Rough sets and 3-valued logics. Studia Logica 90, 69–92 (2008)MathSciNetMATHCrossRef

82.

Mani, A.: Towards logics of some rough perspectives of knowledge. In: Suraj, Z., Skowron, A. (eds.) Intelligent Systems Reference Library Dedicated to the Memory of Professor Pawlak ISRL, vol. 43, pp. 419–444. Springer, Heidelberg (2013). https://doi.org/10.1007/978-3-642-30341-8_22CrossRef

83.

Rasiowa, H.: An Algebraic Approach to Nonclassical Logics. Studies in Logic, vol. 78. North Holland, Warsaw (1974)MATH

84.

Ciucci, D.: Orthopairs and granular computing. Granular Comput. 1(3), 159–170 (2016)MathSciNetCrossRef

85.

Belnap, N.D.: A useful four-valued logic. In: Dunn, J.M., Epstein, G. (eds.) Modern Uses of Multiple-valued Logic. Episteme, vol. 2, pp. 5–37. Springer, Dordrecht (1977). https://doi.org/10.1007/978-94-010-1161-7_2CrossRef

86.

Moretti, A.: Why the logical hexagon? Logica Univers 6, 69–107 (2012)MathSciNetMATHCrossRef

Titel: Dialectical Rough Sets, Parthood and Figures of Opposition-I
verfasst von: A. Mani
Verlag: Springer Berlin Heidelberg
Buch: Transactions on Rough Sets XXI
Print ISBN: 978-3-662-58767-6

Electronic ISBN: 978-3-662-58768-3

Copyright-Jahr: 2019
DOI: https://doi.org/10.1007/978-3-662-58768-3_4

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