English

Injecting Finiteness to Prove Completeness for Finite Linear Temporal Logic

Logic in Computer Science 2021-07-14 v1

Abstract

Temporal logics over finite traces are not the same as temporal logics over potentially infinite traces. Ro\c{s}u first proved completeness for linear temporal logic on finite traces (LTLf) with a novel coinductive axiom. We offer a different proof, with fewer, more conventional axioms. Our proof is a direct adaptation of Kr\"{o}ger and Merz's Henkin-Hasenjaeger-style proof. The essence of our adaption is that we "inject" finiteness: that is, we alter the proof structure to ensure that models are finite. We aim to present a thorough, accessible proof.

Keywords

Cite

@article{arxiv.2107.06045,
  title  = {Injecting Finiteness to Prove Completeness for Finite Linear Temporal Logic},
  author = {Eric Campbell and Michael Greenberg},
  journal= {arXiv preprint arXiv:2107.06045},
  year   = {2021}
}
R2 v1 2026-06-24T04:08:57.999Z