Algebraic modal correspondence: Sahlqvist and beyond

Willem Conradie, Alessandra Palmigiano*, Sumit Sourabh

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

The present paper proposes a new introductory treatment of the very well known Sahlqvist correspondence theory for classical modal logic. The first motivation for the present treatment is a consideration regarding exposition: classical Sahlqvist correspondence is presented in a uniform and modular way, and, unlike the existing textbook accounts, extends itself to a class of formulas laying outside the Sahlqvist class proper. The second motivation is methodological: the present treatment aims at highlighting the algebraic and order-theoretic nature of the correspondence mechanism. The exposition remains elementary and does not presuppose any previous knowledge or familiarity with the algebraic approach to logic. However, it provides the underlying motivation and basic intuitions for the recent developments in the Sahlqvist theory of nonclassical logics, which compose the so-called unified correspondence theory.

Original languageEnglish
Pages (from-to)60-84
Number of pages25
JournalJournal of Logical and Algebraic Methods in Programming
Volume91
DOIs
Publication statusPublished - 1 Oct 2017
Externally publishedYes

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