Right-Adjoints for Datalog Programs, and Homomorphism Dualities over Restricted Classes

TL;DR

This paper explores conditions under which certain Datalog programs have generalized right-adjoints, providing new methods for constructing homomorphism dualities and characterizing data examples in restricted database classes.

Contribution

It establishes large classes of Datalog and atalog programs with generalized right-adjoints, advancing understanding of homomorphism dualities and data characterization.

Findings

Identifies classes of Datalog programs with right-adjoints

Provides methods for constructing homomorphism dualities

Derives results on uniquely characterizing data examples

Abstract

A Datalog program can be viewed as a syntactic specification of a functor from database instances over some schema to database instances over another schema. The same holds more generally for $\exists$Datalog. We establish large classes of Datalog and $\exists$Datalog programs for which the corresponding functor admits a generalized right-adjoint. We employ these results to obtain new insights into the existence of, and methods for constructing, homomorphism dualities within restricted classes of instances. We also derive new results regarding the existence of uniquely characterizing data examples for database queries.