, Volume 5, Issue 2, pp 294-311
Date: 21 May 2010

Toward model-theoretic modal logics

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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Translated from Luojixue Yanjiu 逻辑学研究 (Researches of Logics), 2009, (1): 62–77