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Erschienen in:
2006 | OriginalPaper | Buchkapitel
Relational Representation Theorems for General Lattices with Negations
verfasst von : Wojciech Dzik, Ewa Orlowska, Clint van Alten
Erschienen in: Relations and Kleene Algebra in Computer Science
Verlag: Springer Berlin Heidelberg
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Relational representation theorems are presented for general (i.e., non-distributive) lattices with the following types of negations: De Morgan, ortho, Heyting and pseudo-complement. The representation is built on Urquhart’s representation for lattices where the associated relational structures are doubly ordered sets and the canonical frame of a lattice consists of its maximal disjoint filter-ideal pairs. For lattices with negation, the relational structures require an additional binary relation satisfying certain conditions which derive from the properties of the negation. In each case, these conditions are sufficient to ensure that the lattice with negation is embeddable into the complex algebra of its canonical frame.