Galois Connections for Operations and Relations

@inproceedings{Pschel2004GaloisCF,
  title={Galois Connections for Operations and Relations},
  author={Reinhard P{\"o}schel},
  year={2004}
}
This paper reports on various Galois connections between operations and relations. Several specifications and generalizations are discussed. 

Function classes and relational constraints stable under compositions with cloness

The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relations.

Connections arising in Clone Theory (Algebra and Computer Science)

Galois connections appear in various areas in mathematics and computer science. In this article a brief review is presented on Galois connections arising in clone theory.

Basics of Galois Connections

  • F. Börner
  • Mathematics
    Complexity of Constraints
  • 2008
Basic properties of Galois connections between sets of relations and sets of functions or generalized functions are given and some tools for the representation of several closure operators on relations as closure operators of some Galois connection are provided.

Invariance groups of functions and related Galois connections

Invariance groups of sets of Boolean functions can be characterized as Galois closures of a suitable Galois connection. We consider such groups in a much more general context using group actions of

Completeness Criteria and Invariants for Operation and Transformation Algebras

Operation algebras serve as representations of composition algebras (in the sense of Lausch/Nobauer). In this paper they are described and characterized by invariant relations as Galois-closed sets

On closed sets of relational constraints and classes of functions closed under variable substitutions

Abstract.Pippenger’s Galois theory of finite functions and relational constraints is extended to the infinite case. The functions involved are functions of several variables on a set A and taking

Reflections on and of minor-closed classes of multisorted operations

The minor relation of functions is generalized to multisorted functions. Pippenger’s Galois theory for minor-closed sets of functions is extended to multisorted functions and multisorted relation

A Short Introduction to Clones

Clausal relations and C-clones

We introduce a special set of relations called clausal relations. We study a Galois connection Pol−C Inv between the set of all finitary operations on a finite set D and the set of clausal relations,

CONTRIBUTIONS TO GENERAL ALGEBRA xx

In this paper we describe binary relations σ ⊆ A × A preserved by the endomorphisms of a quasiorder q ⊆ A × A, i.e. with the property End q ⊆ End σ. In particular we determine the quasiorder lattice

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