Abstract
Provided here is an account, both syntactic and semantic, of first-order and monadic second-order quantification theory for domains that may be non-atomic. Although the rules of inference largely parallel those of classical logic, there are important differences in connection with the identification of argument places and the significance of the identity relation.
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Roeper, P. (1983). Semantics for mass terms with quantifiers, Noûs 17, 251-265.
Roeper, P. (1985). Generalisation of first-order logic to nonatomic domains, J. Symbolic Logic 50(3), 815-838.
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Roeper, P. First- and Second-Order Logic of Mass Terms. Journal of Philosophical Logic 33, 261–297 (2004). https://doi.org/10.1023/B:LOGI.0000031380.24201.26
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DOI: https://doi.org/10.1023/B:LOGI.0000031380.24201.26