Abstract
Based on Alasdair Urquhart’s representation of not necessarily distributive bounded lattices we exhibit several discrete dualities in the spirit of the “duality via truth” concept by Orłowska and Rewitzky. We also exhibit a discrete duality for Urquhart’s relevant algebras and their frames.
Second Reader
I. Rewitzky
University of Stellenbosch
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Notes
- 1.
Not to be confused with the concept of the same name used in Physics.
- 2.
The example was found by Mace4 (McCune 2010).
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Acknowledgements
We dedicate this article to Alasdair Urquhart, our friend and esteemed colleague, on the occasion of his 75th birthday. His work has been a valuable source of inspiration for us for many years. We also thank the second reader for her valuable comments. I. Düntsch gratefully acknowledges support by the National Natural Science Foundation of China, Grant No. 61976053.
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Düntsch, I., Orłowska, E. (2022). Application of Urquhart’s Representation of Lattices to Some Non–classical Logics. In: Düntsch, I., Mares, E. (eds) Alasdair Urquhart on Nonclassical and Algebraic Logic and Complexity of Proofs. Outstanding Contributions to Logic, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-030-71430-7_13
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