%0 Journal Article
%T Canonicity and Relativized Canonicity via Pseudo-Correspondence: an Application of ALBA
%A Willem Conradie
%A Alessandra Palmigiano
%A Sumit Sourabh
%A Zhiguang Zhao
%J Computer Science
%D 2015
%I arXiv
%X We generalize Venema's result on the canonicity of the additivity of positive terms, from classical modal logic to a vast class of logics the algebraic semantics of which is given by varieties of normal distributive lattice expansions (normal DLEs), aka `distributive lattices with operators'. We provide two contrasting proofs for this result: the first is along the lines of Venema's pseudo-correspondence argument but using the insights and tools of unified correspondence theory, and in particular the algorithm ALBA; the second closer to the style of J\'onsson. Using insights gleaned from the second proof, we define a suitable enhancement of the algorithm ALBA, which we use prove the canonicity of certain syntactically defined classes of DLE-inequalities (called the meta-inductive inequalities), relative to the structures in which the formulas asserting the additivity of some given terms are valid.
%U http://arxiv.org/abs/1511.04271v1