[Paper Review] Towards a Formal Model of Narratives

Louis Castricato, Stella Biderman+2 more|arXiv (Cornell University)|Mar 23, 2021

Artificial Intelligence in Games27 references4 citations

TL;DR

This paper introduces a model-theoretic framework for formalizing narrative structure, modeling information flow from Narrator to Reader, belief evolution, and uncertainty using logical semantics and entropy. It proposes novel, experimentally verifiable metrics—Entropy of World Coherence and Entropy of Transitional Coherence—for measuring story coherence and information accuracy in computational narratology.

ABSTRACT

In this paper, we propose the beginnings of a formal framework for modeling narrative extit{qua} narrative. Our framework affords the ability to discuss key qualities of stories and their communication, including the flow of information from a Narrator to a Reader, the evolution of a Reader's story model over time, and Reader uncertainty. We demonstrate its applicability to computational narratology by giving explicit algorithms for measuring the accuracy with which information was conveyed to the Reader and two novel measurements of story coherence.

Motivation & Objective

• To establish a formal, model-theoretic foundation for narrative that reconciles diverse research approaches in computational narratology.
• To formalize core narratological concepts such as fabula, story world, and narrative communication using logical semantics.
• To model the dynamic evolution of a Reader’s mental story model (situation model) over time through belief updates.
• To quantify Reader uncertainty and information conveyance accuracy using entropy-based measures.
• To develop experimentally testable metrics for narrative coherence and plot relevance grounded in formal logic and model theory.

Proposed method

• Formalizes narrative as a model-theoretic structure, where a story's fabula is represented as a set of possible worlds and propositions in a boolean lattice.
• Models information flow via filtration of possible worlds, restricting the Reader’s belief set to consistent, temporally prior states.
• Defines Entropy of World Coherence (ETC) as the average probability of propositions in a reader’s belief set relative to a filtered ground truth.
• Defines Entropy of Transitional Coherence (ETC) as a measure of faithfulness in belief transitions across plot points, using implications (A ⇒ B) between pre- and post-kernel beliefs.
• Uses model theory and modal logic to formalize necessity and possibility across narrative frames, ensuring temporal consistency in belief evolution.
• Applies pullback operations to align reader models with ground truth at earlier time points, enabling measurement of coherence and accuracy.

Experimental results

Research questions

• RQ1 How can narrative structure be formally modeled using model theory to capture information flow from Narrator to Reader?
• RQ2 In what way do readers’ mental story models evolve over time through belief updates, and how can this be formalized?
• RQ3 How can Reader uncertainty be quantified and measured using entropy within a logical framework?
• RQ4 What role do plot points (kernels) play in shaping belief transitions, and how can their coherence be assessed?
• RQ5 How can narrative coherence be measured as a function of consistency across story world models and belief transitions?

Key findings

• The framework enables precise formalization of Barthes’ concepts of kernels and satellites through a rigorous notion of plot relevance based on belief transitions.
• Entropy of World Coherence (ETC) provides a measurable metric for how well a reader’s story world model aligns with ground truth, with higher entropy indicating greater coherence.
• Entropy of Transitional Coherence (ETC) quantifies the faithfulness of belief transitions across plot points, with higher values indicating more coherent reasoning patterns.
• The model supports experimentally verifiable conjectures about how readers respond to under-specified story worlds, particularly in terms of belief revision and uncertainty.
• The framework allows for the conversion of theoretical narrative concepts into practical, computable metrics for evaluating story consistency and coherence.
• The use of filtration and pullback operations enables accurate measurement of information conveyance even when readers lack full information, by restricting belief sets to temporally consistent states.