Similarity and bisimilarity notions appropriate for characterizing indistinguishability in fragments of the calculus of relations

TL;DR

This paper investigates how different fragments of the calculus of binary relations can be used to determine when two structures are indistinguishable, providing characterizations based on adapted simulation and bisimulation concepts.

Contribution

It introduces new characterizations of indistinguishability in relation calculus fragments using adapted simulation and bisimulation notions.

Findings

Characterizations for indistinguishability in various relation calculus fragments

Adapted notions of simulation and bisimulation for each fragment

Framework applicable to database theory and relational structures

Abstract

Motivated by applications in databases, this paper considers various fragments of the calculus of binary relations. The fragments are obtained by leaving out, or keeping in, some of the standard operators, along with some derived operators such as set difference, projection, coprojection, and residuation. For each considered fragment, a characterization is obtained for when two given binary relational structures are indistinguishable by expressions in that fragment. The characterizations are based on appropriately adapted notions of simulation and bisimulation.