Journal of Symbolic Logic

Fluted Formulas and the Limits of Decidability

William C. Purdy

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

Abstract

In the predicate calculus, variables provide a flexible indexing service which selects the actual arguments to a predicate letter from among possible arguments that precede the predicate letter (in the parse of the formula). In the process of selection, the possible arguments can be permuted, repeated (used more than once), and skipped. If this service is withheld, so that arguments must be the immediately preceding ones, taken in the order in which they occur, the formula is said to be fluted. Quine showed that if a fluted formula contains only homogeneous conjunction (conjoins only subformulas of equal arity), then the satisfiability of the formula is decidable. It remained an open question whether the satisfiability of a fluted formula without this restriction is decidable. This paper answers that question.

Article information

Source
J. Symbolic Logic, Volume 61, Issue 2 (1996), 608-620.

Dates
First available in Project Euclid: 6 July 2007

Permanent link to this document
https://projecteuclid.org/euclid.jsl/1183745017

Mathematical Reviews number (MathSciNet)
MR1394617

Zentralblatt MATH identifier
0858.03012

JSTOR
links.jstor.org

Citation

Purdy, William C. Fluted Formulas and the Limits of Decidability. J. Symbolic Logic 61 (1996), no. 2, 608--620. https://projecteuclid.org/euclid.jsl/1183745017


Export citation