Abstract
Communicative approximations, as used in language, are equivalence relations that partition a continuum, as opposed to observational approximations on the continuum. While the latter can be addressed using tolerance interval approximations on interval algebra, new constructs are necessary for considering the former, including the notion of a “rough interval”, which is the indiscernibility region for an event described in language, and “rough points” for quantities and moments. We develop the set of qualitative relations for points and intervals in this “communicative approximation space”, and relate them to existing relations in exact and tolerance-interval formalisms. We also discuss the nature of the resulting algebra.
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References
Allen, J.F.: Maintaining knowledge about temporal intervals. CACM 26(11), 832–843 (1983)
Asher, N., Vieu, L.: Toward a geometry of common sense – a semantics and a complete axiomatization of mereotopology. In: IJCAI 1995, pp. 846–852 (1995)
Banerjee, M., Chakraborty, M.K.: Algebras from rough sets. In: Pal, S.K., Polkowski, L., Skowron, A. (eds.) Rough-neuro Computing: Techniques for Computing with Words, pp. 157–184. Springer, Berlin (2004)
Düntsch, I.: Rough sets and algebras of relations. In: Orłowska, E. (ed.) Incomplete Information: Rough Set Analysis, pp. 95–108. Physica-Verlag, Heidelberg (1998)
Luce, R.D., Narens, L.: Measurement of scales on the continuum. Science 236, 1527–1532 (1987)
Maddux, R.D.: Relation Algebras. Elsevier, Amsterdam (2006)
Mukerjee, A., Schnorrenberg, F.: Hybrid systems: reasoning across scales in space and time. In: AAAI Symposium on Principles of Hybrid Reasoning, Asilomar, CA, November 15-17 (1991)
Orłowska, E., Pawlak, Z.: Measurement and indiscernibility. Bull. Polish Acad. Sci. (Th. Comp. Sc.) 32(9-10), 617–624 (1984)
Pawlak, Z.: Rough sets. Int. J. Computer and Information Science 11(5), 341–356 (1982)
Pawlak, Z.: Rough classification. Int. J. Man-Machine Studies 20, 469–483 (1984)
Pawlak, Z.: Rough Sets. Theoretical Aspects of Reasoning about Data. Kluwer Academic, Dordecht (1991)
Polkowski, L., Skowron, A.: Rough mereological calculi of granules: a rough set approach to computation. Computational Intelligence 17(3), 472–492 (2001)
Renz, J., Nebel, B.: On the complexity of qualitative spatial reasoning: A maximal tractable fragment of the region connection calculus. Artificial Intelligence 108(1), 69–123 (1999)
Scott, D., Suppes, P.: Foundational aspects of theories of measurement. J. Symb. Logic 28, 113–128 (1958)
Taylor, B.N., Kuyatt, C.E.: Guidelines for evaluating and expressing the uncertainty of NIST measurement results. Technical Report 1297, NIST (1994)
Varzi, A.C.: Vagueness. In: Nadel, L., et al. (eds.) Encyclopedia of Cognitive Science, pp. 459–464. Macmillan and Nature Publishing Group, London (2003)
Warmus, M.: Calculus of approximations. Bull. Polish Acad. Sci. 4(5), 253–257 (1956)
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Banerjee, M., Pathak, A., Krishna, G., Mukerjee, A. (2010). Communicative Approximations as Rough Sets. In: Szczuka, M., Kryszkiewicz, M., Ramanna, S., Jensen, R., Hu, Q. (eds) Rough Sets and Current Trends in Computing. RSCTC 2010. Lecture Notes in Computer Science(), vol 6086. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13529-3_34
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DOI: https://doi.org/10.1007/978-3-642-13529-3_34
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