j : **absDis**(i : flex k i
) ∩ j : ψ ¬(stubi ∧ τi,j (ψ))
i : **absDis**(j : ψ) ∩ i : *flex* k+1 i
(AD-AD)
j : **absDis**(i : *flex* k i
) ∩ j : ψ (stubi ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i ∧ τi,j (ψ))
i : **essDis**(j : ψ) ∩ i : *flex* k+1 i
(AD-ED)
j : **absDis**(i : flex k i
) ∩ j : ψ (*flex* k+1 i ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **comp**(j : ψ) ∩ i : *flex* k+1 i
(AD-Co)
j : **absDis**(i : flex k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **relDis**(j : ψ) ∩ i : *flex* k+1 i
(AD-RD)
j : **absDis**(i : *flex* k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ))
i : **agree**(j : ψ) ∩ i : τi,j (ψ)(AD-Ag)
j : **essDis**(i : *flex* k i
) ∩ j : ψ ¬(stubi ∧ τi,j (ψ))
i : **absDis**(j : ψ) ∩ i : *flex* k+1 i
(ED-AD)
j : **essDis**(i : *flex* k i
) ∩ j : ψ (stubi ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i ∧ τi,j (ψ))
i : **essDis**(j : ψ) ∩ i : *flex* k+1 i
(ED-ED)
j : **essDis**(i : flex k i
) ∩ j : ψ (*flex* k+1 j ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **comp**(j : ψ) ∩ i : *flex* k+1 i
(ED-Co)
j : **essDis**(i : flex k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **relDis**(j : ψ) ∩ i : *flex* k+1 i
(ED-RD)
j : **essDis**(i : *flex* k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ))
i : **agree**(j : ψ) ∩ i : τi,j (ψ)(ED-Ag)
j : **comp**(i : flex k i
) ∩ j : ψ (stubi ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i ∧ τi,j (ψ))
i : **essDis**(j : ψ) ∩ i : *flex* k+1 i
(Co-ED)
j : **comp**(i : flex k i
) ∩ j : ψ (*flex* k+1 j ∨ τi,j (ψ)) ∧ ¬(*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **comp**(j : ψ) ∩ i : *flex* k+1 i
(Co-Co)
j : **comp**(i : *flex* k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ)) ∧ ¬(τi,j (ψ) → *flex* k+1 i)
i : **relDis**(j : ψ) ∩ i : *flex* k+1 i
(Co-RD)
j : **comp**(i : *flex* k i
) ∩ j : ψ (*flex* k+1 i → τi,j (ψ))
i : **agree**(j : ψ) ∩ i : τi,j (ψ)(Co-Ag)
j : **relDis**(i : ϕ) ∩ j : ψ i : **agree**(j : ψ) ∩ i : τi,j (ψ)
(RD-Ag)
Table 3 Rules for the following proposing agents.