  FL$_\mathrm{ew}$-algebras form the algebraic semantics of the full Lambek
calculus with exchange and weakening. We investigate two relations, called
satisfiability and positive satisfiability, between FL$_\mathrm{ew}$-terms and
FL$_\mathrm{ew}$-algebras. For each FL$_\mathrm{ew}$-algebra, the sets of its
satisfiable and positively satisfiable terms can be viewed as fragments of its
existential theory; we identify and investigate the complements as fragments of
its universal theory. We offer characterizations of those algebras that
(positively) satisfy just those terms that are satisfiable in the two-element
Boolean algebra providing its semantics to classical propositional logic. In
case of positive satisfiability, these algebras are just the nontrivial weakly
contractive FL$_\mathrm{ew}$-algebras. In case of satisfiability, we give a
characterization by means of another property of the algebra, the existence of
a two-element congruence. Further, we argue that (positive) satisfiability
problems in FL$_\mathrm{ew}$-algebras are computationally hard. Some previous
results in the area of term satisfiability in MV-algebras or BL-algebras are
thus brought to a common footing with known facts on satisfiability in Heyting
algebras.
