 Łukasiewicz logic is the only t-norm based fuzzy logic where all connectives are interpreted by continuous functions, including the implication given by the function \(x \Rightarrow_{Ł} y=\min\{1,1-x+y\}\). McNaughton’s theorem (1951) states that real-valued functions over [0,1] that interpret formulas of Łukasiewicz logic are exactly the continuous piecewise linear functions with integer coefficients. In terms of computational complexity, the validity problem for this logic is asymptotically not worse than in classical logic: it remains coNP-complete.