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Fluted formulas and the limits of decidability

Published online by Cambridge University Press:  12 March 2014

William C. Purdy
William C. Purdy*
Affiliation:
School of Computer and Information Science, Syracuse University, Syracuse, NY 13244-4100, USA, E-mail: wcpurdy@top.cis.syr.edu
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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.

Type
Research Article
Information
The Journal of Symbolic Logic , Volume 61 , Issue 2 , June 1996 , pp. 608 - 620
Copyright
Copyright © Association for Symbolic Logic 1996

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