Probabilities of Allen Interval Relations

Final Year Project — B.A. (Mod.) in Computer Science, Linguistics and a Language

Trinity College Dublin

Overview

This project extends Allen's Interval Algebra (1983) by introducing probabilistic modeling and simulations to handle uncertainty in temporal relations and their composition.

Features

• Implementation of the 13 Allen interval relations
• Composition (transitivity) table logic
• Probabilistic birth/death state transition simulations
• Interval generation with customizable parameters
• Statistical analysis and hypothesis testing
• Multiple simulation modes with varying parameters

Project Structure

• constants.py – Allen relation and state definitions
• relations.py – Allen relations and composition logic
• intervals.py – Interval generation and relation detection
• simulations.py – Birth/death process simulation engine
• stats.py – Statistical analysis and hypothesis testing
• README.md – Project description
• LICENSE – MIT License

Usage

The project provides multiple ways to simulate and analyze interval relations:

1. Use intervals.py functions to generate random intervals and determine their relations:

   • gen() - Generate single intervals with birth/death probabilities
   • run() - Generate two intervals and determine their relation
   • many() - Run multiple simulations with identical parameters

2. Use simulations.py for more complex state transition simulations:

   • arSimulate() - Run birth/death process simulations
   • demo() - Run a series of simulations with different parameters

3. Use stats.py to analyze relation distributions:

   • entropy() - Calculate information entropy
   • chi_square_uniform() - Test against uniform distribution
   • describe() - Get comprehensive statistics