Decidability and incompleteness results for first-order temporal logics of linear time

Abstract

ABSTRACT The question of axiomatizability of first-order temporal logics is studied w.r.t. different semantics and several restrictions on the language. The validity problem for logics admitting flexible interpretations of the predicate symbols or allowing at least binary predicate symbols is shown to be Π1 1-complete. In contrast, it is decidable for temporal logics with rigid monadic predicate symbols but without function symbols and identity.