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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
  • Batch simulation processing
  • Automated report generation

Installation

To install the required dependencies:

pip install -r requirements.txt

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
  • batch_runner.py – Run multiple simulations with various parameters
  • report_generator.py – Generate Markdown reports from simulation results
  • requirements.txt – Python dependencies
  • 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
    • simulate_relations() - Generate intervals with different parameters for each interval

  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
    • chi_square_against_theory() - Compare against theoretical distributions
    • describe() - Get comprehensive statistics

  4. Use batch_runner.py to run large-scale simulations:

    • Automatically runs simulations with various probability combinations
    • Saves results to a JSON file for further analysis

  5. Use report_generator.py to create reports:

    • Generates a Markdown table summarizing simulation results
    • Includes entropy, ratio statistics, and chi-square tests against different distributions

Workflow

  1. Run batch simulations: python batch_runner.py
  2. Generate a summary report: python report_generator.py
  3. View the results in the generated REPORT.md file