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Journal of Logic and Computation 1990 1(1):41-69; doi:10.1093/logcom/1.1.41
© 1990 by Oxford University Press
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Original Articles

Bilattices and Modal Operators

MATTHEW L. GINSBERG

Department of Computer Science, Stanford University Stanford, California 94305

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. We show that this definition generalizes both Kripke's possible worlds approach and Moore's autoepistemic logic, and also use recent developments in the formalization of logic programs to construct a procedure for determining the truth value of a sentence when the underlying knowledge base involves modal operators of this form.


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