According to wikipedia the prelinearity condition of a monoidal t-norm logic is expressed as $(x\implies y) \vee (y\implies x) = 1$.
As far as I know, the 'pre' prefixed version of a rule or classification is indicative of a condition that's just slightly different from (weaker than?) the un-prefixed rule (e.g. pre-Hilbert space).
Is there such a relationship between 'prelinearity' as used here and some 'linearity' axiom and, if there is, what is it?
A lattice, L, is linear if for each $x,y\in L$ either $x\leq y$ or $y\leq x$. It may be noted that any linear lattice is prelinear but the converse is not true in general. Hence the prefix "pre" is justified.