Residuated Park theories

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

When L is a complete lattice, the collection MonL of all monotone functions Lp → Ln, n,p,0, forms a Lawvere theory. We enrich this Lawvere theory with the binary supremum operation, an operation of (left) residuation Crossed D sign and the parameterized least fixed point operation. We exhibit a system of equational axioms which is sound and proves all valid equations of the theories MonL involving only the theory operations, and, i.e. all valid equations not involving residuation. We also present an alternative axiomatization, where is replaced by a star operation, and provide an application to regular tree languages.

Original languageEnglish
Pages (from-to)453-471
Number of pages19
JournalJournal of Logic and Computation
Volume25
Issue number2
DOIs
Publication statusPublished - Apr 1 2015

Keywords

  • Least fixed points
  • equational theory
  • iteration theory
  • residuals

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Arts and Humanities (miscellaneous)
  • Hardware and Architecture
  • Logic

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