  We study self-referential sentences of the type related to the Liar paradox.
In particular, we consider the problem of assigning consistent fuzzy truth
values to collections of self-referential sentences. We show that the problem
can be reduced to the solution of a system of nonlinear equations. Furthermore,
we prove that, under mild conditions, such a system always has a solution (i.e.
a consistent truth value assignment) and that, for a particular implementation
of logical ``and'', ``or'' and ``negation'', the ``mid-point'' solution is
always consistent. Next we turn to computational issues and present several
truth-value assignment algorithms; we argue that these algorithms can be
understood as generalized sequential reasoning. In an Appendix we present a
large number of examples of self-referential collections (including the Liar
and the Strengthened Liar), we formulate the corresponding truth value
equations and solve them analytically and/ or numerically.
