Journal of Symbolic Logic

Conservative Reduction Classes of Krom Formulas

Stal O. Aanderaa, Egon Borger, and Harry R. Lewis

Full-text is available via JSTOR, for JSTOR subscribers. Go to this article in JSTOR.


A Krom formula of pure quantification theory is a formula in conjunctive normal form such that each conjunct is a disjunction of at most two atomic formulas or negations of atomic formulas. Every class of Krom formulas that is determined by the form of their quantifier prefixes and which is known to have an unsolvable decision problem for satisfiability is here shown to be a conservative reduction class. Therefore both the general satisfiability problem, and the problem of satisfiability in finite models, can be effectively reduced from arbitrary formulas to Krom formulas of these several prefix types.

Article information

J. Symbolic Logic, Volume 47, Issue 1 (1982), 110-130.

First available in Project Euclid: 6 July 2007

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier



Aanderaa, Stal O.; Borger, Egon; Lewis, Harry R. Conservative Reduction Classes of Krom Formulas. J. Symbolic Logic 47 (1982), no. 1, 110--130.

Export citation