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Frontiers of Philosophy in China

Front. Philos. China    2010, Vol. 5 Issue (2) : 294-311     https://doi.org/10.1007/s11466-010-0017-2
Research articles |
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.
Keywords model theory      first-order logic      modal logic      graded modalities      
Issue Date: 05 June 2010
 Cite this article:   
MA Minghui. Toward Model-Theoretic Modal Logics[J]. Front. Philos. China, 2010, 5(2): 294-311.
 URL:  
http://journal.hep.com.cn/fpc/EN/10.1007/s11466-010-0017-2
http://journal.hep.com.cn/fpc/EN/Y2010/V5/I2/294
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