Constructive canonicity of inductive inequalities

Willem Conradie, Alessandra Palmigiano

Research output: Contribution to JournalArticleAcademicpeer-review


We prove the canonicity of inductive inequalities in a constructive meta-theory, for classes of logics algebraically captured by varieties of normal and regular lattice ex-pansions. This result encompasses Ghilardi-Meloni’s and Suzuki’s constructive canonicity results for Sahlqvist formulas and inequalities, and is based on an application of the tools of unified correspondence theory. Specifically, we provide an alternative interpretation of the language of the algorithm ALBA for lattice expansions: nominal and conominal variables are respectively interpreted as closed and open elements of canonical extensions of normal/regular lattice expansions, rather than as completely join-irreducible and meet-irreducible elements of perfect normal/regular lattice expansions. We show the correctness of ALBA with respect to this interpretation. From this fact, the constructive canonicity of the inequalities on which ALBA succeeds follows by an adaptation of the standard argument. The claimed result then follows as a consequence of the success of ALBA on inductive inequalities.

Original languageEnglish
Article number8
Pages (from-to)8:1-8:39
Number of pages39
JournalLogical Methods in Computer Science
Issue number3
Publication statusPublished - 5 Aug 2020


  • Algorithmic correspondence theory
  • Constructive canonicity
  • Lattice theory
  • Modal logic
  • Sahlqvist theory


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