An incomplete relevant modal logic

Journal of Philosophical Logic 29 (1):103-119 (2000)
The relevant modal logic G is a simple extension of the logic RT, the relevant counterpart of the familiar classically based system T. Using the Routley-Meyer semantics for relevant modal logics, this paper proves three main results regarding G: (i) G is semantically complete, but only with a non-standard interpretation of necessity. From this, however, other nice properties follow. (ii) With a standard interpretation of necessity, G is semantically incomplete; there is no class of frames that characterizes G. (iii) The class of frames for G characterizes the classically based logic T
Keywords relevant modal logic  relevance logic  modal logic  semantic incompleteness  semantic completeness  Routley–Meyer semantics
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DOI 10.1023/A:1004774422224
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