IA-RAG: Interval-Algebra-Driven Temporal Reasoning for Dynamic Knowledge Retrieval

Abstract: Retrieval-Augmented Generation (RAG) has shown strong effectiveness in grounding LLMs with external knowledge. However, existing RAG and Graph RAG frameworks largely treat knowledge as static or associate time with coarse-grained timestamps or metadata, failing to capture rich temporal structures such as duration, overlap, and containment. We propose IA-RAG, a hierarchical temporal RAG framework that models knowledge as time intervals and performs retrieval under formal temporal constraints. IA-RAG represents facts as Interval Event Units (IEUs) and organizes them into a hierarchical Thematic Forest, where temporal dependencies are governed by Allen's Interval Algebra. To handle incomplete or uncertain temporal boundaries, IA-RAG further introduces a Sub-graph Time Tightening mechanism that refines fuzzy intervals through logical constraints within connected event subgraphs. In addition, IA-RAG supports implicit temporal semantic retrieval through interval-algebra-guided traversal. Experiments on multiple temporal question answering benchmarks, including TimeQA, TempReason, and ComplexTR, demonstrate that IA-RAG achieves strong temporal retrieval and reasoning performance, particularly on complex compositional temporal reasoning tasks. Our code is released at https://github.com/xiaoAugenstern/LogicalRAG_TemporalQA.

• The paper introduces IA-RAG, a hierarchical Graph RAG framework that represents facts as temporal intervals, refines uncertain boundaries using local constraints, and guides retrieval with Allen’s 13 interval relations.
• IA-RAG achieves the best results on TimeQA and ComplexTR, reaching 61.72% and 65.95% accuracy respectively, with a particularly strong 14.07-point improvement over the leading baseline on compositional ComplexTR tasks.
• The paper shows that directional interval-guided traversal contributes most to performance, while moderate hierarchy depth and tuned retrieval granularity improve efficiency and reduce temporally irrelevant evidence.

Motivation and problem statement

IA-RAG addresses a structural deficiency in retrieval-augmented generation (RAG): the treatment of time as a shallow attribute rather than a first-class relational structure. Existing RAG and Graph RAG systems—GraphRAG, LightRAG, HippoRAG, and temporal variants such as T-GRAG, TG-RAG, TA-RAG, and DyG-RAG—represent temporal information as discrete timestamps, metadata filters, or chronological orderings. The authors argue this induces three concrete failure modes: temporal boundary ambiguity, where semantically similar queries about different periods ("policies before 2008" vs. "policies after 2008") yield nearly identical embeddings; inability to refine implicit temporal attributes, leaving facts without explicit timestamps unanchored and unsearchable; and topological reasoning deficiency, where interval relations such as overlap, containment, and duration between events are never modeled, forcing the LLM to perform brittle linguistic inference over disjoint retrieved chunks.

The framework's central design decision is to ground event representation in Allen's Interval Algebra [allen1984towards], whose 13 mutually exclusive qualitative relations (before, meets, overlaps, starts, during, finishes, equals, plus inverses) provide a formal semantics for interval topology that prior RAG systems lack.

Framework architecture

IA-RAG operates in three stages: interval event unit extraction, interval-aware graph construction, and query-driven temporal retrieval.

Interval Event Units (IEUs). Each atomic fact is represented as a tuple containing the event sentence, optional context, a closed temporal interval $[t^{start}, t^{end}]$, a binary fuzzy flag indicating boundary uncertainty, and the source document. Extraction proceeds over overlapping chunks with an LLM-based protocol that normalizes vague expressions (e.g., "early 1990s") to coarse intervals flagged as uncertain. A local semantic neighborhood strategy performs deduplication: for each IEU, its top-$Q$ cosine-similar neighbors are jointly audited by an LLM to merge redundant descriptions of the same occurrence.

Interval-aware graph and Thematic Forest. Edges are established only between semantically compatible IEUs (cosine similarity above $\tau_{sem}=0.8$) and are labeled with one of the 13 Allen relations computed from their intervals. A key component is Sub-graph Time Tightening: connected components of the graph serve as grounded local contexts within which an LLM-based operator refines fuzzy intervals using the logical constraints imposed by neighboring events' Allen relations; refinements must narrow uncertainty and are anchored strictly in provided text. Components are then aggregated into Macro Event Units (MEUs), and this abstraction is applied recursively up to four layers, yielding a hierarchical "Thematic Forest" in which roots represent abstract themes and leaves correspond to atomic IEUs. The authors report complexity of $O(N \log N)$ for ANN-based retrieval plus $O(NK)$ for graph construction under geometric shrinkage across levels, with LLM summarization cost proportional to the number of components per level.

Interval-algebra-guided traversal. At query time, an LLM parser infers the query's temporal window $T_w$. Retrieval is coarse-to-fine over both MEU and IEU spaces via embedding similarity, after which traversal direction is determined dynamically by the relative position of each seed unit's interval to $T_w$: forward-only if the seed ends before the window, backward-only if it starts after, bidirectional otherwise. Traversal follows only the Allen relation set consistent with that direction, filtering out temporally irrelevant neighbors before merging supplementary units into the final evidence set.

Experimental results

Experiments use Qwen2.5-14B-Instruct for all generation and construction tasks and BGE-M3 embeddings, evaluated on TimeQA, TempReason, and ComplexTR following DyG-RAG's processed corpora with token-level accuracy and recall metrics.

Method	TimeQA Acc./Rec.	TempReason Acc./Rec.	ComplexTR Acc./Rec.
Vanilla RAG	56.33 / 64.98	70.96 / 82.53	55.01 / 68.68
HippoRAG	39.99 / 45.39	69.80 / 80.54	44.68 / 55.28
DyG-RAG	58.78 / 67.02	84.75 / 91.47	55.62 / 69.88
IA-RAG	61.72 / 69.25	80.21 / 89.64	65.95 / 77.42

IA-RAG achieves the best results on TimeQA (+2.94 accuracy over DyG-RAG) and ComplexTR (+10.33 accuracy, +7.54 recall). On TempReason, DyG-RAG remains superior; the authors attribute this to that benchmark's predominance of single-timestamp matching (all 5,397 questions are classified as explicit time-anchored), where DyG-RAG's temporal-semantic embedding alignment is particularly effective. This concession is notable: the advantage of interval-algebraic modeling materializes specifically on benchmarks requiring directional or compositional temporal reasoning rather than point lookup.

The breakdown on ComplexTR substantiates this claim. IA-RAG attains 57.85 accuracy on explicit, 73.97 on relative, and 68.88 on compositional temporal reasoning, exceeding the strongest baseline by +14.07 points on compositional tasks—the category involving numerical offsets and multi-hop event-duration computation. This is the paper's strongest quantitative result and directly supports the claim that interval-level dependency modeling enables reasoning inaccessible to timestamp-based systems.

Ablations isolate each component's contribution. Removing interval-algebra-guided traversal causes the largest degradation (e.g., ComplexTR accuracy falls from 65.95 to 61.70), confirming that pure semantic similarity is insufficient. Removing sub-graph tightening or the hierarchical forest also degrades performance consistently, with the hierarchy mattering most on ComplexTR. Traversal-strategy comparisons show that traversing all Allen relations indiscriminately or replacing dynamic direction selection with LLM-predicted top-5 relations both underperform the proposed directional scheme, indicating that unrestricted expansion introduces temporally irrelevant noise while LLM-predicted relations lack stable chronological consistency.

On efficiency, IA-RAG maintains compact prompt sizes relative to baselines despite dual-level traversal, reducing input tokens on ComplexTR while improving accuracy—an indication that constrained traversal retrieves more relevant evidence than exhaustive graph expansion.

Sensitivity and robustness findings

Sensitivity analyses reveal non-monotonic behavior in both hyperparameters. Forest depth of 4 layers is optimal; depth 0 (flat graph) degrades performance uniformly, but depths of 6 and 10 also degrade results, attributed to over-fragmented thematic partitions weakening semantic coherence. MEU retrieval granularity shows dataset-dependent optima ($K_1=10$ for TimeQA/ComplexTR, $K_1=20$ for TempReason), with too few units limiting coverage and too many introducing noisy subgraphs. These findings imply the framework's gains depend on moderate, tuned hierarchy depth rather than deeper abstraction being universally beneficial.

An appendix analysis of Allen relation distributions across the three benchmarks shows that although before/after dominates, substantial numbers of overlaps, during/contains, and meets relations exist in real QA corpora, providing empirical justification for interval-aware retrieval beyond simple chronological ordering.

Limitations and open questions

The authors identify two limitations explicitly. First, the framework depends on the quality of temporal extraction and interval normalization; ambiguous or noisy temporal expressions can propagate errors into the graph structure, and the LLM-based tightening operator is bounded by the requirement that refinements be textually grounded—IEUs lacking sufficient contextual evidence remain permanently fuzzy. Second, the framework models only interval topology and does not capture causal relations or evolving event dynamics. A further unstated dependency is the semantic-compatibility threshold ($\tau_{sem}=0.8$): edges form only between semantically similar events, so temporally related but lexically distant events may be disconnected, and the interaction of this threshold with recall on corpora with heterogeneous vocabulary is not analyzed. The near-miss on TempReason also leaves open whether interval-algebraic machinery adds value when queries reduce to point-in-time matching, or whether its benefit is confined to compositional and relational query types.

Conclusion

IA-RAG integrates Allen's Interval Algebra into a hierarchical Graph RAG pipeline, combining interval-based fact representation, constraint-driven refinement of uncertain boundaries, and directionally constrained traversal. Its empirical profile is consistent with its design intent: largest gains appear on compositional temporal reasoning (+14.07 on ComplexTR), while remaining competitive but not dominant on timestamp-centric benchmarks. The results indicate that formal temporal topology is a productive signal for retrieval when queries involve interval dependencies, though the approach's sensitivity to extraction quality and hierarchy hyperparameters constrains its plug-and-play applicability.