On the completeness and decidability of a restricted first order linear temporal logic

Abstract

The paper describes a class of FC-sequents of a restricted first order linear temporal logic with “next” and “always”. It is shown that the first order linear temporal logic is finitary complete for FC-sequents. If FC-sequents are logically decidable, i.e., all sequents, constructed from all possible subformulas of logical formulas of FC-sequents are decidable in first-order logic, then FC-sequents are decidable in the restricted first order linear temporal logic. To obtain these results a saturation calculus [6, 7] for FC-sequents is constructed.