 Different axiomatic specifications may produce the same logic. Notice, e.g., that the table’s axiomatic specification \(\{\text{K},\text{T},\text{5}\}\) of S5 does not match that given in the definition preceding Theorem 1, \(\{\text{K},\text{T},\text{B},\text{4}\}\). Note also, there is more than one axiomatization of S5: the axioms \(\{\text{K},\text{T},\text{5}\}\), \(\{\text{K},\text{T},\text{B},\text{4}\}\), \(\{\text{K},\text{D},\text{B},\text{4}\}\) and \(\{\text{K},\text{D},\text{B},\text{5}\}\) all give the S5 logic (cf., e.g., Chellas 1980). An often seen variant is \(\{\text{K},\text{T},\text{4},\text{5}\}\). However, it is redundant to add it as all its instances can be proven from K, T and 5. But as both 4 and 5 capture important epistemic principles (see  Section 2.6),  4 is often sometimes included for the sake of philosophical transparency. For more equivalences between modal logics, see, e.g., the entry on  modal logic  or Chellas (1980) or Blackburn, de Rijke, and Venema (2001).