k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.
Now, we prove that the following holds: Γ, x|=ϕ a ⇐ ⇒atp Γ,k x =a,for allx∈ X k We prove this in two directions
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The Logical Expressiveness of Topological Neural Networks
k-CCWL isomorphism tests are equivalent to TC_{k+2} topological counting logic and topological (k+2)-pebble games, characterizing the logical expressiveness of TNNs.