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arXiv · 2203.09199

Unified inverse correspondence for DLE-Logics

Willem Conradie·Andrea De Domenico·Giuseppe Greco·Alessandra Palmigiano·Mattia Panettiere·Apostolos Tzimoulis
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Abstract

By exploiting the algebraic and order theoretic mechanisms behind Sahlqvist correspondence, the theory of unified correspondence provides powerful tools for correspondence and canonicity across different semantics and signatures, covering all the logics whose algebraic semantics are given by normal (distributive) lattice expansions (referred to as (D)LEs). In particular, the algorithm ALBA, parametric in each (D)LE, effectively computes the first order correspondents of (D)LE-inductive formulas. We present an algorithm that makes use of ALBA's rules and algebraic language to invert its steps in the DLE setting; therefore effectively computing an inductive formula starting from its first order correspondent.

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Willem Conradie, Andrea De Domenico, Giuseppe Greco, Alessandra Palmigiano, Mattia Panettiere, Apostolos Tzimoulis. 2022-03-17. Unified inverse correspondence for DLE-Logics. https://arxiv.org/abs/2203.09199

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