ia-rag-interval-algebra-temporal

name	ia-rag-interval-algebra-temporal
description	Hierarchical temporal RAG using Allen's Interval Algebra for formal temporal constraint reasoning with Interval Event Units (IEUs) organized in Thematic Forest
version	1.0.0
category	ai_collection
tags	["deep-learning","RAG","temporal-reasoning","knowledge-graph","interval-algebra"]
arxiv	2606.06044v1
paper_title	IA-RAG: Interval-Algebra-Driven Temporal Reasoning for Dynamic Knowledge Retrieval
authors	["Xiaoman Wang","Yaoze Zhang","Wenzhuo Fan","Hongwei Zhang","Ding Wang et al."]
published	2026-06-04T00:00:00.000Z
activation_keywords	["temporal RAG","interval algebra","Allen's relations","temporal reasoning","dynamic knowledge","time-aware retrieval"]
github	https://github.com/xiaoAugenstern/LogicalRAG_TemporalQA

IA-RAG: Interval-Algebra Temporal Reasoning

Core Innovation

Models knowledge as time intervals with formal temporal constraints governed by Allen's Interval Algebra.

Problem Addressed

Existing RAG limitations:

• Treat knowledge as static
• Associate time with coarse-grained timestamps
• Fail to capture temporal structures: duration, overlap, containment

Methodology

Knowledge Representation

1. Interval Event Units (IEUs): Facts as time intervals
2. Thematic Forest: Hierarchical organization of IEUs
3. Allen's Interval Algebra: 13 temporal relations

Allen's Interval Relations

Before (b)     After (bi)
Meets (m)      Met-by (mi)
Overlaps (o)   Overlapped-by (oi)
Starts (s)     Started-by (si)
During (d)     Contains (di)
Finishes (f)   Finished-by (fi)
Equals (=)

Key Mechanisms

Sub-graph Time Tightening:

• Refines fuzzy intervals through logical constraints
• Handles incomplete/uncertain temporal boundaries
• Propagates constraints across connected events

Interval-Algebra-Guided Traversal:

• Implicit temporal semantic retrieval
• Query-compatible interval relations
• Temporal constraint-aware navigation

Implementation Pattern

from datetime import datetime

class IntervalEventUnit:
    def __init__(self, start, end, content):
        self.interval = (start, end)
        self.content = content
        self.duration = end - start
        
    def allen_relation(self, other_ieu):
        """Compute Allen's Interval Algebra relation"""
        s1, e1 = self.interval
        s2, e2 = other_ieu.interval
        
         e1 < s2:    
         e1 == s2:    
         s1 < s2 < e1 < e2:    
         s1 == s2  e1 < e2:    
         s2 < s1  e1 < e2:    
         s2 < s1 < e2 < e1:    
         s1 < s2  e1 == e2:    
         s1 == s2  e1 == e2:    

 :
     ():
        .themes = {}  
        
     ():
        
        candidates = []
         theme  .themes:
             ieu  theme:
                 ieu.allen_relation(query_interval) == relation:
                    candidates.append(ieu)
         candidates
    
     ():
        
        neighbors = .get_connected_events(uncertain_ieu)
        tightened = propagate_constraints(uncertain_ieu, neighbors)
         tightened