  This paper studies which truth-values are most likely to be taken on finite
models by arbitrary sentences of a many-valued predicate logic. We obtain
generalizations of Fagin's classical zero-one law for any logic with values in
a finite lattice-ordered algebra, and for some infinitely valued logics,
including \L ukasiewicz logic. The finitely valued case is reduced to the
classical one through a uniform translation and Oberschelp's generalization of
Fagin's result. Moreover, it is shown that the complexity of determining the
almost sure value of a given sentence is PSPACE-complete, and for some logics
we may describe completely the set of truth-values that can be taken by
sentences almost surely.
