Bilattices and modal operators

Authors:
Matthew L. Ginsberg
Affiliations:
Stanford University, Stanford, California
Venue:
TARK '90 Proceedings of the 3rd conference on Theoretical aspects of reasoning about knowledge
Year:
1990

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Abstract

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.