Emergent Mind
Finite Model Theory of the Triguarded Fragment and Related Logics
(2101.08377)
Published Jan 21, 2021
in
cs.LO
,
cs.AI
,
cs.CC
,
and
math.LO
Abstract
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.
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