Abstract
We have introduced the major semantic modelling frameworks for natural language, and made reference to the main theoretical schools which use mathematical logic to capture our intuitions of how natural language is or should be used.
Our main conclusion is that the Mathematical Logic being used throughout seems to be a modal logic with different modalities and with simple first order quantification, based on a constructive set theory usually named First-Order Intensional Logic.
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As [Pitt, 1990] observes, meaning postulates corrupt modularity because although they operate on translations (semantic objects) they refer to information specified in the syntactic component.
Previous treatments of this paradox can be found for instance in [Tarski, 1931] and [Barwise and Etchemendy, 1987]. Gödel's famous proof is as well a form of this paradox and [Popper, 1945] (vol.2, pp.355) uses another form of it to argue that Wittgenstein's theories in the ‘Tratactus’ are not valid.
Type Theoretic Semantics (see section 3.2) is very critical of the use of this element in value-based interpretations, i.e. model theoretic semantics. Type Theoretic Semantics argues that if model theoretic semantics needs such undefined element than something is wrong with it ([de Queiroz, 1990], pp 180–185).
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© 1991 Springer-Verlag Berlin Heidelberg
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Falcão e Cunha, J. (1991). Some remarks on first-order intensional logic. In: Filgueiras, M., Damas, L., Moreira, N., Tomás, A.P. (eds) Natural Language Processing. EAIA 1990. Lecture Notes in Computer Science, vol 476. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-53678-7_10
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DOI: https://doi.org/10.1007/3-540-53678-7_10
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