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JACIII Vol.7 No.2 pp. 72-78
doi: 10.20965/jaciii.2003.p0072
(2003)

Paper:

Modifier Logics Based on Graded Modalities

Jorma K. Mattila

Lappeenranta University of Technology, Laboratory of Applied Mathematics, P.O. Box 20, FIN-53851, Lappeenranta, Finland

Received:
January 19, 2003
Accepted:
March 3, 2003
Published:
June 20, 2003
Keywords:
graded modality, modifier, modifier logic, modifier calculus
Abstract

Modifier logics are considered as generalizations of “classical” modal logics. Thus modifier logics are so-called multimodal logics. Multimodality means here that the basic logics are modal logics with graded modalities. The interpretation of modal operators is more general, too. Leibniz’s motivating semantical ideas (see [8], p. 20-21) give justification to these generalizations. Semantics of canonical frames forms the formal semantic base for modifier logics. Several modifier systems are given. A special modifier calculus is combined from some “pure” modifier logics. Creating a topological semantics to this special modifier logic may give a basis to some kind of fuzzy topology. Modifier logics of S4-type modifiers will give a graded topological interior operator systems, and thus we have a link to fuzzy topology.

Cite this article as:
Jorma K. Mattila, “Modifier Logics Based on Graded Modalities,” J. Adv. Comput. Intell. Intell. Inform., Vol.7, No.2, pp. 72-78, 2003.
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