Abstract
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.
Supported by the NRF-funded bilateral Poland/RSA research project GUN 2068034: Logical and Algebraic Methods in Formal Information Systems.
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Dzik, W., Orlowska, E., van Alten, C. (2006). Relational Representation Theorems for General Lattices with Negations. In: Schmidt, R.A. (eds) Relations and Kleene Algebra in Computer Science. RelMiCS 2006. Lecture Notes in Computer Science, vol 4136. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11828563_11
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DOI: https://doi.org/10.1007/11828563_11
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-37873-0
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