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Injecting Finiteness to Prove Completeness for Finite Linear Temporal Logic (2107.06045v1)
Published 13 Jul 2021 in cs.LO
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.