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arXiv · 1511.04271

Canonicity and Relativized Canonicity via Pseudo-Correspondence: an Application of ALBA

Willem Conradie·Alessandra Palmigiano·Sumit Sourabh·Zhiguang Zhao
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Abstract

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 Jónsson. 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.

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Willem Conradie, Alessandra Palmigiano, Sumit Sourabh, Zhiguang Zhao. 2016-12-18. Canonicity and Relativized Canonicity via Pseudo-Correspondence: an Application of ALBA. https://arxiv.org/abs/1511.04271

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