GNTC satisfiability is 2ExpTime-complete and model checking is P^NP[O(log² n)]-complete via polynomial and exponential reductions to UNTC and 2-way alternating parity tree automata.
As Γ is split, we can let Γ = (∆ , Λ) where ∆ ̸= ∅, Λ ̸= ∅, and I (FV(∆)) ⊆ U¯A g,d for some d ∈ [92, 2] \ {0}
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Guarded Negation Transitive Closure Logic
GNTC satisfiability is 2ExpTime-complete and model checking is P^NP[O(log² n)]-complete via polynomial and exponential reductions to UNTC and 2-way alternating parity tree automata.