| Title: | A Duality Theory for Bilattices |
| Author: | Bamshad Mobasher, D. Pigozzi, G. Slutzki and G. Voutsadakis |
| Abstract: | Recent studies of the algebraic properties of bilattices have provided
insight into their internal structures, and have led to practical results,
especially in reducing the computational complexity of bilatticebased multivalued logic programs. In this paper the representation theorem
for interlaced bilattices with negation found in [16] is extended to arbitrary interlaced bilattices without negation. A natural equivalence is
then established between the category of interlaced bilattices and the cartesian square of the category of bounded lattices. As a consequence
a dual natural equivalence is obtained between the category of distributive bilattices and the coproduct of the category of bounded Priestley
spaces with itself. Some applications of these equivalences are given.
The subdirectly irreducible interlaced bilattices are characterized in terms of subdirectly irreducible lattices. A known characterization of
the joinirreducible elements of the ``knowledge'' lattice of an interlaced
bilattice is used to establish a natural equivalence between the category of finite, distributive bilattices and the category of posets of the form P \Phi ? Q: |
| Full Paper: | [postscript ] |