DeepAI AI Chat
Log In Sign Up

Comparing Downward Fragments of the Relational Calculus with Transitive Closure on Trees

by   Jelle Hellings, et al.

Motivated by the continuing interest in the tree data model, we study the expressive power of downward navigational query languages on trees and chains. Basic navigational queries are built from the identity relation and edge relations using composition and union. We study the effects on relative expressiveness when we add transitive closure, projections, coprojections, intersection, and difference; this for boolean queries and path queries on labeled and unlabeled structures. In all cases, we present the complete Hasse diagram. In particular, we establish, for each query language fragment that we study on trees, whether it is closed under difference and intersection.


page 1

page 2

page 3

page 4


Existential Calculi of Relations with Transitive Closure: Complexity and Edge Saturations

We study the decidability and complexity of equational theories of the e...

Free Kleene algebras with domain

First we identify the free algebras of the class of algebras of binary r...

Exact Learning of Multitrees and Almost-Trees Using Path Queries

Given a directed graph, G=(V,E), a path query, path(u,v), returns whethe...

On the expressive power of query languages for matrices

We investigate the expressive power of MATLANG, a formal language for ma...

Relational Diagrams: a pattern-preserving diagrammatic representation of non-disjunctive Relational Queries

Analyzing relational languages by their logical expressiveness is well u...

The Complexity of Boolean Conjunctive Queries with Intersection Joins

Intersection joins over interval data are relevant in spatial and tempor...

The Programming of Algebra

We present module theory and linear maps as a powerful generalised and c...