The poset of all logics II: Leibniz classes and hierarchy
Logic
2021-07-01 v1
Abstract
A Leibniz class is a class of logics closed under the formation of term-equivalent logics, compatible expansions, and non-indexed products of sets of logics. We study the complete lattice of all Leibniz classes, called the Leibniz hierarchy. In particular, it is proved that the classes of truth-equational and assertional logics are meet-prime in the Leibniz hierarchy, while the classes of protoalgebraic and equivalential logics are meet-reducible. However, the last two classes are shown to be determined by Leibniz conditions consisting of meet-prime logics only.
Keywords
Cite
@article{arxiv.2002.07792,
title = {The poset of all logics II: Leibniz classes and hierarchy},
author = {R. Jansana and T. Moraschini},
journal= {arXiv preprint arXiv:2002.07792},
year = {2021}
}