On the Existential Fragments of Local First-Order Logics with Data

TL;DR

This paper investigates the complexity of existential fragments of local first-order logic over data-structured structures, providing precise complexity classifications based on data values and neighborhood radius.

Contribution

It offers a detailed complexity analysis of the satisfiability problem for existential local logic fragments with data, extending previous work on these logical systems.

Findings

Complexity depends on data values per element and neighborhood radius.

Satisfiability is characterized precisely for various fragment parameters.

Provides a complexity classification for local first-order logic with data.

Abstract

We study first-order logic over unordered structures whose elements carry a finite number of data values from an infinite domain which can be compared wrt. equality. As the satisfiability problem for this logic is undecidable in general, in a previous work, we have introduced a family of local fragments that restrict quantification to neighbourhoods of a given reference point. We provide here the precise complexity characterisation of the satisfiability problem for the existential fragments of this local logic depending on the number of data values carried by each element and the radius of the considered neighbourhoods.