Research articles

Toward Model-Theoretic Modal Logics

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  • Department of Philosophy, Tsinghua University, Beijing 100084, China;

Published date: 05 Jun 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.

Cite this article

MA Minghui, . Toward Model-Theoretic Modal Logics[J]. Frontiers of Philosophy in China, 2010 , 5(2) : 294 -311 . DOI: 10.1007/s11466-010-0017-2

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