Residuated Lattices

 

Title: Residuated Lattices
Authors: Victor B. F. Gomes (vb358 /at/ cam /dot/ ac /dot/ uk) and Georg Struth (g /dot/ struth /at/ sheffield /dot/ ac /dot/ uk)
Submission date: 2015-04-15
Abstract: The theory of residuated lattices, first proposed by Ward and Dilworth, is formalised in Isabelle/HOL. This includes concepts of residuated functions; their adjoints and conjugates. It also contains necessary and sufficient conditions for the existence of these operations in an arbitrary lattice. The mathematical components for residuated lattices are linked to the AFP entry for relation algebra. In particular, we prove Jonsson and Tsinakis conditions for a residuated boolean algebra to form a relation algebra.
BibTeX:
@article{Residuated_Lattices-AFP,
  author  = {Victor B. F. Gomes and Georg Struth},
  title   = {Residuated Lattices},
  journal = {Archive of Formal Proofs},
  month   = apr,
  year    = 2015,
  note    = {\url{http://isa-afp.org/entries/Residuated_Lattices.html},
            Formal proof development},
  ISSN    = {2150-914x},
}
License: BSD License
Depends on: Kleene_Algebra, Relation_Algebra