On two-variable guarded fragment logic with expressive local Presburger constraints

TL;DR

This paper extends the two-variable guarded fragment logic with local Presburger quantifiers, enabling expressive counting properties, and establishes its satisfiability problem as EXP-complete using a new graph-based algorithm.

Contribution

It introduces local Presburger quantifiers into the two-variable guarded fragment logic and proves EXP-completeness with a novel deterministic algorithm.

Findings

Satisfiability for the extended logic is EXP-complete.

The upper bound is shown via a new deterministic graph-based algorithm.

The lower bound matches that of the standard two-variable guarded fragment logic.

Abstract

We consider the extension of the two-variable guarded fragment logic with local Presburger quantifiers. These are quantifiers that can express properties such as "the number of incoming blue edges plus twice the number of outgoing red edges is at most three times the number of incoming green edges" and captures various description logics with counting, but without constant symbols. We show that the satisfiability problem for this logic is EXP-complete. While the lower bound already holds for the standard two-variable guarded fragment logic, the upper bound is established by a novel, yet simple deterministic graph-based algorithm.