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Toward Model-Theoretic Modal Logics |
| MA Minghui, |
| Department of Philosophy,
Tsinghua University, Beijing 100084, China; |
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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.
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| Keywords
model theory
first-order logic
modal logic
graded modalities
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Issue Date: 05 June 2010
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