FLUTED FORMULAS AND THE LIMITS OF DECIDABILITY

In the predicate calculus, variables provide a flexible indexing servi ce which selects the actual arguments to a predicate fetter 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 ser vice is withheld, so that arguments must be the immediately preceding ones, taken in the order in which they occur, the formula is said to b e fluted. Quine showed that if a fluted formula contains only homogene ous conjunction (conjoins only subformulas of equal arity), then the s atisfiability of the formula is decidable. It remained an open questio n whether the satisfiability of a fluted formula without this restrict ion is decidable. This paper answers that question.