Completeness of Ticl

Determine whether the Temporal Interaction and Choice Logic (Ticl) is complete; specifically, ascertain whether every semantically valid Ticl specification over ictree-based programs is derivable using the Ticl entailment rules and the provided library of structural lemmas.

Background

Ticl is introduced as a structural temporal logic designed to reason about liveness and safety properties directly over executable programs modeled as ictrees, with semantics given via Kripke-style transitions and entailment relations. The paper provides a substantial library of structural, syntax-directed lemmas for composition, nondeterminism, and iteration and demonstrates their use on several examples.

However, despite this extensive metatheory, the authors note that the overall completeness of Ticl remains unresolved. In the feature table summarizing coverage of operators and combinators, they explicitly state that completeness is an open question, indicating that it is unknown whether all semantically valid specifications are derivable within their proof framework.