A Formalization of Observational and Theoretical Languages
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Recall our notion of a semantic system as consisting of sentences, models, abstract values and an evaluation function assigning to each sentence and each model M the value |ϕ| M of ϕ in M. In the present chapter we are going to analyse possible structures of φ sentences and of models and the dependence of |ϕ| M the structure of ϕ and of M. Our aim is to generalize and modify the classical predicate calculus in various ways, in particular by admitting generalized quantifiers. (The following are preliminary examples of sentences containing generalized quantifiers: (i) For sufficiently many x, P(x). (ii) The property Q(x) is associated with R(x).)
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