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Representation theorem of interlaced bilattice with conflation. (English) Zbl 0935.06005

Summary: So far some representation theorems for extensions of pre-bilattices, for example those for interlaced bilattices and for distributive bilattices, except interlaced bilattices with negation or conflation, are obtained. In this paper, we obtain a representation theorem for interlaced bilattices with conflation. That is, every interlaced bilattice \(B\) with conflation can be represented as a product of a nontrivial lattice \(L\) with lattice negation \(\neg\), in the form \(B\cong L\odot(\neg L)\).

MSC:

06B15 Representation theory of lattices
68N17 Logic programming