 Because the symbol formula_36 via its use in lattice theory is very closely associated with the idempotence property, it can be useful to switch to a different symbol for conjunction that is not necessarily idempotent.In the fuzzy logic tradition one sometimes uses formula_37 for this "strong" conjunction, but this article follows the substructural logic tradition of using formula_38 for the strong conjunction; thus formula_8 is the confidence we ascribe to the statement formula_40 (still read ‘formula_5 and formula_6’, perhaps with ‘strong’ or ‘multiplicative’ as qualification of the ‘and’).Having formalised conjunction formula_38, one wishes to continue with the other connectives.