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Slanted Canonicity of Analytic Inductive Inequalities

Slanted Canonicity of Analytic Inductive Inequalities We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LE-inequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png ACM Transactions on Computational Logic (TOCL) Association for Computing Machinery

Slanted Canonicity of Analytic Inductive Inequalities

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Publisher
Association for Computing Machinery
Copyright
Copyright © 2021 Copyright held by the owner/author(s). Publication rights licensed to ACM.
ISSN
1529-3785
eISSN
1557-945X
DOI
10.1145/3460973
Publisher site
See Article on Publisher Site

Abstract

We prove an algebraic canonicity theorem for normal LE-logics of arbitrary signature, in a generalized setting in which the non-lattice connectives are interpreted as operations mapping tuples of elements of the given lattice to closed or open elements of its canonical extension. Interestingly, the syntactic shape of LE-inequalities which guarantees their canonicity in this generalized setting turns out to coincide with the syntactic shape of analytic inductive inequalities, which guarantees LE-inequalities to be equivalently captured by analytic structural rules of a proper display calculus. We show that this canonicity result connects and strengthens a number of recent canonicity results in two different areas: subordination algebras, and transfer results via Gödel-McKinsey-Tarski translations.

Journal

ACM Transactions on Computational Logic (TOCL)Association for Computing Machinery

Published: Aug 1, 2021

Keywords: Sahlqvist canonicity

References