Unified Correspondence

  • Willem Conradie
  • Silvio Ghilardi
  • Alessandra Palmigiano
Chapter

Abstract

The present chapter is aimed at giving a conceptual exposition of the mathematical principles underlying Sahlqvist correspondence theory. These principles are argued to be inherently algebraic and order-theoretic. They translate naturally on relational structures thanks to Stone-type duality theory. The availability of this analysis in the setting of the algebras dual to relational models leads naturally to the definition of an expanded (object) language in which the well-known ‘minimal valuation’ meta-arguments can be encoded, and of a calculus for correspondence of a proof-theoretic style in the expanded language, mechanically computing the first-order correspondent of given propositional formulas. The main advantage brought about by this formal machinery is that correspondence theory can be ported in a uniform way to families of nonclassical logics, ranging from substructural logics to mu-calculi, and also to different semantics for the same logic, paving the way to a uniform correspondence theory.

Keywords

Sahlqvist correspondence theory Duality Algorithmic correspondence Intuitionistic modal logic mu-calculus 

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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Willem Conradie
    • 1
  • Silvio Ghilardi
    • 2
  • Alessandra Palmigiano
    • 3
  1. 1.Department of MathematicsUniversity of JohannesburgJohannesburgSouth Africa
  2. 2.Department of MathematicsUniversità degli Studi di MilanoMilanItaly
  3. 3.Faculty of Technology Policy and ManagementDelft University of TechnologyDelftThe Netherlands

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