We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$\mathtt {DNA}$-LOGICS
This article provides an algebraic study of the propositional system 
$\mathtt {InqB}$ of inquisitive logic. We also investigate the wider class of 
$\mathtt {DNA}$-logics, which are negative variants of intermediate logics, and the corresponding algebraic structures, 
$\mathtt {DNA}$-varieties. We prove that the lattice of 
$\mathtt {DNA}$-logics is dually isomorphic to the lattice of 
$\mathtt {DNA}$-varieties. We characterise maximal and minimal intermediate logics with the same negative variant, and we prove a suitable version of Birkhoff’s classic variety theorems. We also introduce locally finite 
$\mathtt {DNA}$-varieties and show that these varieties are axiomatised by the analogues of Jankov formulas. Finally, we prove that the lattice of extensions of 
$\mathtt {InqB}$ is dually isomorphic to the ordinal 
$\omega +1$ and give an axiomatisation of these logics via Jankov 
$\mathtt {DNA}$-formulas. This shows that these extensions coincide with the so-called inquisitive hierarchy of [9].1
