A Relational Logic for Spatial Contact Based on Rough Set Approximation

• Autorzy: Düntsch I. , Orłowska E. , Wang H.

Identyfikatory

DOI

10.3233/FI-2016-1430

• Konferencja: Rough Set Theory Workshop (RST’2015); (6; 29-06-2015; University of Warsaw )
• Języki publikacji: EN

Abstrakty

EN

In previous work we have presented a class of algebras enhanced with two contact relations representing rough set style approximations of a spatial contact relation. In this paper, we develop a class of relational systems which is mutually interpretable with that class of algebras, and we consider a relational logic whose semantics is determined by those relational systems. For this relational logic we construct a proof system in the spirit of Rasiowa-Sikorski, and we outline the proofs of its soundness and completeness.

Słowa kluczowe

EN

rough sets; approximation theory; set theory; mathematical proofs; completeness theorem

• Wydawca: IOS Press
• Czasopismo: Fundamenta Informaticae
• Rocznik: 2016
• Tom: Vol. 148, nr 1/2
• Strony: 191--206
• Opis fizyczny: Bibliogr. 28 poz., tab.

Twórcy

autor

Düntsch I.

• Brock University, St. Catharines, Ontario, L2S 3A1, Canada

autor

Orłowska E.

• Institute of Telecommunications, Szachowa 1, 04–894, Warszawa, Poland

autor

Wang H.

• School of Computing and Mathematics, University of Ulster at Jordanstown, Newtownabbey, BT 37 0QB, N.Ireland

Bibliografia

• [1] Düntsch I, Orłowska E, Wang H. Algebras of approximating regions. Fundamenta Informaticae. 2001; 46:71–82. MR2009801. Available from: http://www.cosc.brocku.ca/~duentsch/archive/ar_alg.pdf.
• [2] Leśniewski S. Grundzüge eines neuen Systems der Grundlagen der Mathematik. Fundamenta Mathematicae. 1929;14:1–81. Available from: http://eudml.org/doc/212136.
• [3] Whitehead AN. Process and reality. New York: MacMillan; 1929.
• [4] Clarke BL. A calculus of individuals based on ‘connection’. Notre Dame Journal of Formal Logic. 1981;22: 204–218. Available from: http://projecteuclid.org/euclid.ndjfl/1093883455. doi: 10.1305/ ndjfl/1093883455.
• [5] Cohn AG, Hazarika SM. Qualitative spatial representation and reasoning: An overview. Fundamenta Informaticae. 2001;46:1–29. Available from: http://dl.acm.org/citation.cfm?id=1219982.1219984.
• [6] Pawlak Z. Rough sets. Internat J Comput Inform Sci. 1982;11:341–356.
• [7] Stell J. Boolean connection algebras: A new approach to the Region Connection Calculus. Artificial Intelligence. 2000;122:111–136. doi:10.1016/S0004-3702(00)00045-X.
• [8] Düntsch I,Wang H, McCloskey S. A relation algebraic approach to the Region Connection Calculus. Theoretical Computer Science. 2001;255:63–83. MR1819067. Available from: http://www.cosc.brocku.ca/~duentsch/archive/ra-rcc.pdf. doi:10.1016/S0304-3975(99)00156-5.
• [9] Dimov G, Vakarelov D. Contact algebras and region–based theory of space: A proximity approach – I,II. Fundamenta Informaticae. 2006;74:209-282.
• [10] Comer S. On connections between information systems, rough sets, and algebraic logic. In: Rauszer C, editor. Algebraic Methods in Logic and Computer Science. vol. 28 of Banach Center Publications. Warszawa: Polish Academy of Science; 1993. p. 117–124.
• [11] Pagliani P. Rough Sets Theory and Logic-Algebraic Structures. In: Orłowska E, editor. Incomplete Information – Rough Set Analysis. Heidelberg: Physica – Verlag; 1998. p. 109–190. doi:10.1007/978-3-7908-1888-8.
• [12] Pagliani P, Chakraborty M. A Geometry of Approximation. vol. 27 of Trends in Logic. Springer Verlag; 2008. doi:10.1007/978-1-4020-8622-9.
• [13] Orłowska E. Relational interpretation of modal logics. In: Andréka H, Monk JD, Németi I, editors. Algebraic Logic. vol. 54 of Colloquia Mathematica Societatis János Bolyai. Amsterdam: North Holland; 1991. p. 443–471.
• [14] Orłowska E. Relational Semantics for Non-classical Logics: Formulas are Relations. In: Wolenski J, editor. Philosophical Logic in Poland. Kluwer; 1994. p. 167–186.
• [15] Rasiowa H, Sikorski R. On the Gentzen Theorem. Fundamenta Mathematicae. 1960;48:47–69.
• [16] Jónsson B. The theory of binary relations. In: Andréka H, Monk JD, Németi I, editors. Algebraic Logic. vol. 54 of Colloquia Mathematica Societatis János Bolyai. Amsterdam: North Holland; 1991. p. 245–292.
• [17] Düntsch I, Orłowska E. A proof system for contact relation algebras. Journal of Philosophical Logic. 2000; 29:241–262. MR1773955. Available from: http://www.cosc.brocku.ca/~duentsch/archive/contra.pdf.
• [18] Düntsch I, Orłowska E. Mixing modal and sufficiency operators. Bulletin of the Section of Logic, Polish Academy of Sciences. 1999;28(2):99–106. MR1740612.
• [19] Orłowska E, Golińska-Pilarek J. Dual Tableaux: Foundations, Methodology, Case Studies. vol. 33 of Trends in Logic. Springer Verlag; 2011. doi:10.1007/978-94-007-0005-5_2.
• [20] Roy AJ, Stell JG. Spatial relations between indeterminate regions. Int J Approx Reasoning. 2001;27(3): 205–234. Available from: http://dx.doi.org/10.1016/S0888-613X(01)00033-0.
• [21] Polkowski L, Skowron A. Rough Mereology: A new paradigm for approximate reasoning. International Journal of Approximate Reasoning. 1996;15:333–365.
• [22] Rauszer C, editor. Algebraic Methods in Logic and Computer Science. vol. 28 of Banach Center Publications. Warszawa: Polish Academy of Science; 1993.
• [23] Andréka H, Monk JD, Németi I, editors. Algebraic Logic. vol. 54 of Colloquia Mathematica Societatis János Bolyai. Amsterdam: North Holland; 1991.
• [24] Bennett B. What is a Forest? On the vagueness of certain geographic concepts. Topoi. 2002;20:189–201.
• [25] Düntsch I, Wang H, McCloskey S. Relation algebras in qualitative spatial reasoning. Fundamenta Informaticae. 2000;p. 229–248. MR1735458. Available from: http://www.cosc.brocku.ca/~duentsch/archive/mereo.pdf.
• [26] Lehmann F, Cohn AG. The EGG/YOLK Reliability Hierarchy: Semantic Data Integration Using Sorts with Prototypes. In: Proc. Conf. on Information Knowledge Management. ACM Press; 1994. p. 272–279. Available from: http://doi.acm.org/10.1145/191246.191293. doi:10.1145/191246.191293.
• [27] Orłowska E, editor. Incomplete Information – Rough Set Analysis. Heidelberg: Physica – Verlag; 1998. doi:10.1007/978-3-7908-1888-8.
• [28] Rasiowa H, Sikorski R. The Mathematics of Metamathematics. vol. 41 of Polska Akademia Nauk. Monografie matematyczne. Warsaw: PWN; 1963.

Uwagi

Opracowanie ze środków MNiSW w ramach umowy 812/P-DUN/2016 na działalność upowszechniającą naukę (zadania 2017).