Optimised ExpTime Tableaux for 𝒮ℋℐ𝒩 over Finite Residuated Lattices

Algorithm 1

Calculate glb.

Data: Let 𝑡∈ℕ⁺, 𝑡≈𝑚/2, 𝑑,𝑑_𝑡∈𝑁^Σ, 𝑑=𝑑_𝑡.

Result:  glb(Σ,𝛼)=𝑑.

begin

  while  𝑁^Σ>1  do

   if  Σ⊨⟨𝛼⪰𝑑_𝑡⟩  then

     𝑑=𝑑_𝑡

     𝑁^Σ←𝑁^Σ∖ {𝑑^′: 𝑑⪰^′╱𝑑∪{𝑑}}

     𝑑_𝑡←𝑑_𝑡+1

   else

     𝑁^Σ←𝑁^Σ∖ {𝑑^′: 𝑑^′⪰𝑑}

     𝑑_𝑡←𝑑_𝑡−1