A Formalization of Observational and Theoretical Languages

  • Petr Hájek
  • Tomáš Havránek
Part of the Universitext book series (UTX)


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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Copyright information

© Springer-Verlag Berlin Heidelberg 1978

Authors and Affiliations

  • Petr Hájek
    • 1
  • Tomáš Havránek
    • 2
  1. 1.Mathematical InstituteCzechoslovak Academy of SciencesPrahaCzechoslovakia
  2. 2.Department of BiomathematicsCzechoslovak Academy of SciencesPrahaCzechoslovakia

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