Toward model-theoretic modal logics

Frontiers of Philosophy in China 5 (2):294-311 (2010)
Abstract
Adding certain cardinality quantifiers into first-order language will give substantially more expressive languages. Thus, many mathematical concepts beyond first-order logic can be handled. Since basic modal logic can be seen as the bisimular invariant fragment of first-order logic on the level of models, it has no ability to handle modally these mathematical concepts beyond first-order logic. By adding modalities regarding the cardinalities of successor states, we can, in principle, investigate modal logics of all cardinalities. Thus ways of exploring model-theoretic logics can be transferred to modal logics.
Keywords model theory  first-order logic  modal logic  graded modalities
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References found in this work BETA
Kit Fine (1972). In so Many Possible Worlds. Notre Dame Journal of Formal Logic 13 (4):516-520.

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