Slanted canonicity of analytic inductive inequalities
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 G\"odel-McKinsey-Tarski translations.
Keywords
Cite
@article{arxiv.2003.12355,
title = {Slanted canonicity of analytic inductive inequalities},
author = {Laurent De Rudder and Alessandra Palmigiano},
journal= {arXiv preprint arXiv:2003.12355},
year = {2021}
}
Comments
arXiv admin note: text overlap with arXiv:1603.08515, arXiv:1603.08341