Bilattices and Modal Operators
A bilattice is a set equipped with two partial orders and a negation operation that inverts one of them while leaving the other unchanged; it has been suggested that the truth values used by inference systems should be chosen from such a structure instead of the two-point set {t, f}. Given such a choice, we redefine a modal operator to be a function on the bilattice selected, and show that this definition generalizes both Kripke's possible worlds approach and Moore's autoepistemic logic. Extensions to causal and temporal reasoning are also discussed.