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Prefix classes of krom formulae with identity

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Abstract

Two small classes of first order formulae without function symbols but with identity, in prenex conjunctive normal form with all disjunctions binary, are shown to have a recursively unsolvable decision problem, whereas for another such class an algorithm is developed which solves the decision problem of that class. This solves the prefix problem for such classes of formulae except for the Gödel-Kalmàr-Schütte case.

Zusammenfassung

Für zwei Klassen erststufiger Formeln in pränexer konjunktiver Normalform mit Identität aber ohne Funktionssymbole wird das Entscheidungsproblem als rekursiv unlösbar nachgewiesen. Für eine weitere solche Ausdrucksklasse wird ein Algorithmus zur Lösung des Entscheidungsproblems angegeben. Bis auf den Gödel-Kalmàr-Schütte-Fall löst dies das Präfixproblem für derartige Ausdrucksklassen.

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References

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Author information

Authors and Affiliations

  1. Matematisk Institutt, Universitetet i Oslo, Blindern, Oslo 3, Norway

    Stal O. Aanderaa

  2. Universität Dortmund Lehrstuhl Informatik II, Postfach 500 500, D-4600, Dortmund 50, Germany

    Egon Börger

  3. University of the Negev, Beer Sheva, Israel

    Yuri Gurevich

Authors
  1. Stal O. Aanderaa
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  2. Egon Börger
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  3. Yuri Gurevich
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Additional information

Part of this work was done during a 3-week stay of the third author at the Institut für mathematische Logik und Grundlagenforschung of the University of Münster i.W. in February 1978. The help of the Heinrich-Hertz-Stiftung which financed this stay is gratefully acknowledged.

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Aanderaa, S.O., Börger, E. & Gurevich, Y. Prefix classes of krom formulae with identity. Arch math Logik 22, 43–49 (1980). https://doi.org/10.1007/BF02318025

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  • DOI: https://doi.org/10.1007/BF02318025

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