Incompleteness of a first-order gödel logic and some temporal logics of programs

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1092)


It is shown that the infinite-valued first-order Gödel logic G° based on the set of truth values {1/k: k ε w {0}} U {0} is not r.e. The logic G° is the same as that obtained from the Kripke semantics for first-order intuitionistic logic with constant domains and where the order structure of the model is linear. From this, the unaxiomatizability of Kröger's temporal logic of programs (even of the fragment without the nexttime operator O) and of the authors' temporal logic of linear discrete time with gaps follows.


temporal logic intermediate logic many-valued logic 


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Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Matthias Baaz
    • 1
  • Alexander Leitsch
    • 2
  • Richard Zach
    • 2
  1. 1.Institut für Algebra, und Diskrete Mathematik E118.2Technische Universität WienViennaAustria
  2. 2.Institut für Computersprachen E185.2Technische Universität WienViennaAustria

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