@article{Bezhanishvili:20,
	abstract = {This article provides an algebraic study of the propositional system InqB of inquisitive logic. We also investigate the wider class of DNA-logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, DNA-varieties. We prove that the lattice of DNA-logics is dually isomorphic to the lattice of DNA-varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Tarski's and Birkhoff's classic variety theorems. We also introduce finite DNA-varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of InqB is dually isomorphic to the ordinal ω + 1 and give an axiomatisation of these logics via Jankov DNA-formulas. This shows that these extensions coincide with the so-called
inquisitive hierarchy of Ciardelli (2009).},
	author = {Bezhanishvili, Nick and Grilletti, Gianluca and Quadrellaro, Davide Emilio},
	date-added = {2021-08-17 00:00:00 +0000},
	date-modified = {2021-08-17 00:00:00 +0000},
	keywords = {ongoing},
	note = {Submitted for publication, April 2020},
	title = {An Algebraic Approach to Inquisitive and DNA-Logics},
	url = {https://staff.fnwi.uva.nl/n.bezhanishvili/Papers/InqDNA.pdf},
	year = {2020},
	Bdsk-Url-1 = {https://staff.fnwi.uva.nl/n.bezhanishvili/Papers/InqDNA.pdf}}

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