Algorithmic correspondence and canonicity for distributive modal logic

Willem Conradie, Alessandra Palmigiano
<span title="">2012</span> <i title="Elsevier BV"> <a target="_blank" rel="noopener" href="https://fatcat.wiki/container/bnojym2hjzcgnpa4wixi2axhnq" style="color: black;">Annals of Pure and Applied Logic</a> </i> &nbsp;
We define the algorithm ALBA for the language of the same distributive modal logic (DML) for which a Sahlqvist theorem was proved by Gehrke, Nagahashi, and Venema. Successful executions of ALBA compute the local first-order correspondents of input DML inequalities, and also guarantee their canonicity. The class of inequalities on which ALBA is successful is strictly larger than the newly introduced class of inductive inequalities, which in its turn properly extends the Sahlqvist inequalities of
more &raquo; ... Gehrke et. al. As their name suggests, evidence is given to the effect that inductive inequalities are the distributive counterpart of the inductive formulas of Goranko and Vakarelov in the classical setting.
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