A conceptual modelling formalism for temporal database applications

∃! Τ name(T) = name(X) + "_" + name(rel(x,y)) + "_" + name(Y) ∧ ∃! F1 ∈ Τ name(F1) = name(X) + "$" ∧ ∃! F2 ∈ Τ (is_entity(Y) → name(F2) = name(Y) + "$" ∨ is_value(Y) → name(F2) = name(Y)) ∧ ∃! F3 ∈ Τ name(F3) = name(validity_period(rel(X,Y))) + "$" ∧ is_entity(X) ∃! Τ name(T) = name(X) + "_" + name(rel(x,y)) + "_" + name(Y) ∧ ∃! F1 ∈ Τ name(F1) = name(X) + "$" ∧ ∃! F2 ∈ Τ (is_entity(Y) → name(F2) = name(Y) + "$" ∨ is_value(Y) → name(F2) = name(Y)) ∧ ∃! F3 ∈ Τ name(F3) = name(validity_period(rel(X,Y))) + "$" ∧ Pk(T) = (F1,F2,F3) R8: ∀CE ∃! Τ1 name(T1) = name(CE) + "_Components" ∧ ∃! F1 ∈ Τ1 name(F1) = name(CE) + "$" ∧ Pk(T1) = F1 ∧ (∀rel(CE,X1) where name(rel(CE,X1)) = IS_PART_OF ∧ card(rel(CE,X1)) = (0,1) or (1,1) ∧ validity_period(rel(CE,X1)) = always ∃! F2 ∈ Τ1 (is_simple_value(X1) → name(F2) = name(X1) ∨ name(F2) = name(X1) + "$")) ∧ (∀rel(CE,X2) where name(rel(CE,X2)) = IS_PART_OF ∧ (card(rel(CE,X1)) ≠ (0,1) or (1,1) ∨ validity_period(rel(CE,X1)) ≠ always) ∃! F3 ∈ Τ1 name(F3) = name(X2) + "#" ∧ ∃! Τ2 name(T2) = name(CE) + name(X2) +"_set" ∧ ∃! F4 ∈ Τ2 name(F4) = name(X2) + "#" ∧ ∃! F5 ∈ Τ2 name(F5) = name(X2) + "$" ∧ ∃! F6 ∈ Τ2 name(F6) = name(validity_period(CE,X2)) + "$"