A Schema-aware Logic Reformulation for Graph Reachability

TL;DR

This paper introduces a schema-aware logic reformulation for graph reachability that leverages domain schemas to improve search efficiency, reducing backtracks, time, and space in graph traversal tasks.

Contribution

It proposes a novel first-order logic approach that uses schema information to prune and prioritize paths, enhancing traditional reachability algorithms.

Findings

Reduces the number of backtracks during search.

Saves time and space compared to traditional algorithms.

Improves efficiency by excluding unuseful paths using schema knowledge.

Abstract

Graph reachability is the task of understanding whether two distinct points in a graph are interconnected by arcs to which in general a semantic is attached. Reachability has plenty of applications, ranging from motion planning to routing. Improving reachability requires structural knowledge of relations so as to avoid the complexity of traditional depth-first and breadth-first strategies, implemented in logic languages. In some contexts, graphs are enriched with their schema definitions establishing domain and range for every arc. The introduction of a schema-aware formalization for guiding the search may result in a sensitive improvement by cutting out unuseful paths and prioritising those that, in principle, reach the target earlier. In this work, we propose a strategy to automatically exclude and sort certain graph paths by exploiting the higher-level conceptualization of instances. The aim is to obtain a new first-order logic reformulation of the graph reachability scenario, capable of improving the traditional algorithms in terms of time, space requirements, and number of backtracks. The experiments exhibit the expected advantages of the approach in reducing the number of backtracks during the search strategy, resulting in saving time and space as well.