Abstract
An algebraic and set-theoretical approach to approximation reasoning as proposed in [10] and [5] leads to a formulation of a class of first order logics. They are certain intermediate logics equipped with approximation operators dt for t ε T — where (T, ≤) is a poset establishing a type of logic under consideration — and with modal connectives Ct of possibility and It of necessity, t ε T and possibly with CT and IT. Their semantics is based on the idea that a set of objects to be recognized in a process of an approximation reasoning is approximated by means of a family of sets covering this set and by their intersection. Approximating sets with equivalence classes of equivalence relations, as connected with Pawlak's rough sets methods (see [8], [7], [12], [13]) is an additional tool. The main task of this paper is to formulate and prove the completeness theorem for the logics under consideration. For that purpose a theory of plain semi-Post algebras as introduced and developed in [3] has been applied. These algebras replace more complicated semi-Post algebras occurring in [10].
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Ng. Cat Ho and H. Rasiowa, Semi-Post algebras, Studia Logica 46, 2 (1987), 147–158
Ng. Cat Ho and H. Rasiowa, Subalgebras and homomorphisms of semi-Post algebras, ibidem, 159–173
Ng. Cat Ho and H. Rasiowa, Plain semi-Post algebras and their representations, manuscript to be published elsewhere
M.J. Cresswell and G.E. Hughes, An introduction to modal logic, London: Methuen and Co Ltd., 1980
G. Epstein and H. Rasiowa, Approximation Reasoning and Scott's Information Systems, Proc. 2-nd Int. Symp. on Methodologies for Intelligent Systems, ISMIS '87; Charlotte, NC, USA, North Holland, 33–42
Y. Halpern, Reasoning about knowledge, Ed. Y. Halpern, Morgan, Kaufman, 1986
W. Marek and H. Rasiowa, Approximating Sets with Equivalence Relations, Theoretical Computer Science, 48 (1986), 145–152
Z. Pawlak, Rough Sets, Int. Journal of Computer and Information Science 11(5), 1982, 341–356
H. Rasiowa, Logic approximating sequences of sets, invited lecture, Proc. Advanced Int. School and Symp. on Mathematical Logic and its Applications, Drushba, Bulgara 1986, Plenum Press 1987, 167–186
H. Rasiowa, An algebraic approach to some approximate reasonings, Invited lecture, Proc. ISMVL 87, Boston, USA, IEEE Computer Society Press, 342–347
H. Rasiowa and R. Sikorski, The Mathematics of Metamathematics, 3rd Ed. 1970
H. Rasiowa and A. Skowron, Rough concepts logic, in: Computation Theory, ed. A. Skowron, LNCS 208 (1985), 288–297
H. Rasiowa and A. Skowron, Approximation logic, in: Mathematical Methods of Specification and Synthesis of Software Systems 85, ed.. Bibel and K.P. Jantke, Mathematical Research 31, Akademie Verlag, Berlin, 123–139
D. Scott, Domains for denotational semantics, A corrected and expanded version of a paper prepared for ICALP 1982 Aarhus, Denmark 1982
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© 1988 Springer-Verlag
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Rasiowa, H. (1988). Logic of approximation reasoning. In: Börger, E., Büning, H.K., Richter, M.M. (eds) CSL '87. CSL 1987. Lecture Notes in Computer Science, vol 329. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-50241-6_38
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DOI: https://doi.org/10.1007/3-540-50241-6_38
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