Group in Logic and the Methodology of Science
Three roads to complete lattices: orders, compatibility, polarity
- Author(s): Holliday, Wesley Halcrow
- et al.
This note aims to clarify the relations between three ways of constructing complete lattices that appear in three different areas: (1) using ordered structures, as in set-theoretic forcing, or doubly ordered structures, as in a recent semantics for intuitionistic logic; (2) using compatibility relations, as in semantics for quantum logic based on ortholattices; (3) using Birkhoff’s polarities, as in formal concept analysis.