Incompleteness of First-Order Temporal Logic with Until
Article in journal (Refereed)
Theoretical Computer Science(ISSN 0304-3975)
Engineering and Technology
The results presented in this paper concern the axiomatizability problem of first-order temporal logic with linear and discrete time. We show that the logic is incomplete, i.e., it cannot be provided with a finitistic and complete proof system. We show two incompleteness theorems. Although the first one is weaker (it assumes some first-order signature), we decided to present it, for its proof is much simpler and contains an interesting fact that finite sets are characterizable by means of temporal formulas. The second theorem shows that the logic is incomplete independently of any particular signature.