Some Classes Containing a Fork Algebra Equivalent Variety Involving Projections

@article{Durn1998SomeCC,
  title={Some Classes Containing a Fork Algebra Equivalent Variety Involving Projections},
  author={Juan Eduardo Dur{\'a}n},
  journal={Log. J. IGPL},
  year={1998},
  volume={6},
  pages={203-226}
}
Some varieties that are extensions of relational algebras with two constants that play the role of projections are studied. The classes have as a subvariety the abstract fork algebra (AFA) equivalent variety involving projections. They are obtained by weakening some laws valid in AFA. Some applications of the varieties in the literature and in the specification of abstract data types are exhibited. For each of the classes obtained, an answer is given to the question: “Is the relational reduct… 
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References

SHOWING 1-10 OF 66 REFERENCES

Some varieties containing relation algebras

Three varieties of algebras are introduced which extend the variety RA of relation algebras. They are obtained from RA by weakening the associative law for relative product, and are consequently

Introductory course on relation algebras, finite-dimensional cylindric algebras, and their interc

These are notes for a short course on relation algebras, nite-dimensional cylindric algebras, and their interconnections, delivered at the Conference on Alge-Relation algebras (RA's) are closely

The derivation of identities involving projection functions

The \unsharpness problem" is solved by the construction of a nite Although this equation fails in general, it does hold under slightly stronger hypotheses. x1 In recent years various

Complexity of equational theory of relational algebras with projection elements

In connection with a problem of L. Henkin and J.D. Monk we show that the variety generated by TPA’s – relation algebras (RA’s) expanded with concrete set theoretical projection functions – and the

A Finite Axiomatization for Fork Algebras

TLDR
A representation theorem is presented that entails that proper fork algebras — whose underlying set is closed under an injective function — constitute a finitely based variety.

On the Smooth Calculation of Relational Recursive Expressions out of First-Order Non-Constructive Specifications Involving Quantifiers

TLDR
An extended abstract algebra of relations is devised for tackling the classic issue of lack of expressiveness of abstract relational algebras first stated by Tarski and later formally treated by Maddux, Nemeti, etc.

Free algebras in discriminator varieties

We investigate V-free algebras onn generators,Fn=Fr(V, n), where V is a discriminator variety and, more specifically, where V is a variety of relation algebras or of cylindricalgebras. Sample

Relational Algebraic Semantics of Deterministic and Nondeterministic Programs

A Short Proof of Representability of Fork Algebras

Abstract In this paper a strong relationship is demonstrated between fork algebras and quasi-projective relation algebras. With the help of Tarski's classical representation theorem for

Relation Algebraic Domain Constructions

  • Hans Zierer
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1991
...