Linguistic classification: T-norms, fuzzy distances and fuzzy distinguishabilities

Back in 1967 the linguist 2. Mullane used an additive distance between ill-defined linguistic features which is a forerunner of the fuzzy Hamming distance between strings of truth values in standard fuzzy logic. Here we show that if the logical frame is changed one obtains additive distances which are either sorely inadequate, as in the Lukasiewicz or probabilistic case, or coincide with the distance originally envisaged by Mullane, as happens with a whole class of T-norms (abstract logical conjunctions) which includes the nilpotent minimum. All this strengthens the role of Mullane distances in linguistic clustering and of Mullane distinguishabilities (a notion subtly different from distances, but quite inalienable) in linguistic evolution. As a preliminary example we re-take and re-examine Mullane original data. (C) 2017 The Authors. Published by Elsevier B.V.