The authors define an extension of the MTL logic of \textit{F. Esteva} and \textit{L. Godo} [ibid. 124, 271--288 (2001; Zbl 0994.03017)] by introducing the new fuzzy logic NMG in order to cope with the ordinal sum t-norms and their residua. The corresponding standard algebra is \(([0,1],*_W, {\to_W,} \max, \min,0,1)\), where \(*_W : [0,1]^2\to[0,1]\) is defined as \((a*_W b) = 0\) if \(a + b \leq 1/2, (a*_W b) = \min(a,b)\) otherwise for all \(a,b\in[0,1]\), and \(\to_W : [0,1]^2\to[0,1]\) is defined as \((a\to_W b) = 1\) if \(a \leq b,\) \((a\to_W b) = \max(1/2 - a,b)\) otherwise for all \(a,b\in[0,1].\) A completeness theorem is proved for both related propositional and predicate calculi.