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
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 , 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.