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


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

January 19, 2003
March 3, 2003
June 20, 2003
graded modality, modifier, modifier logic, modifier calculus
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:
J. 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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