Finite Model Theory of the Triguarded Fragment and Related Logics - Kieronski, Emanuel; Rudolph, Sebastian (Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science, 2021)
The Triguarded Fragment (TGF) is among the most expressive decidable fragments of first-order logic, subsuming both its two-variable and guarded fragments without equality. We show that the TGF has the finite model property (providing a tight doubly exponential bound on the model size) and hence finite satisfiability coincides with satisfiability known to be N2ExpTime-complete. Using similar constructions, we also establish 2ExpTime-completeness for finite satisfiability of the constant-free (tri)guarded fragment with transitive guards.