I understand there are plenty of NLP techniques for making sense of given sentences, but is there a formal system that can be used to describe narrative/storytelling in a rigorous way?

I'm aiming to develop a procedural branching narrative generation tool and starting on research. Here's GPT4's take which I thought was quite nuanced despite my inability to validate it's veracity at my current level of knowledge.... but there's bound to be some existing work in this topic!

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I want to represent a universal story/narrative structure with branching patterns of action/result that could be used as a formal system underlying a dynamic procedural narrative system. So, which formal primitives would apply here? I think we'd probably want to end up with a hypergraph we could leverage in multiple ways but I'm hoping you can respond as if an expert on all of this, network theory, literature, meta-analysis of literature, mathematics, software, game design, etc..

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Today I present to you a formal system for describing interactive narrative branching structures, leveraging a directed acyclic hypergraph with ancillary subgraph execution routines. This system can be expressed using rigorous symbolic and mathematical terminologies, allowing for precise representation and analysis of narrative structures.

In this formal system, we define the interactive narrative branching structure as a directed acyclic hypergraph, denoted as G = (V, E), where V represents the set of nodes and E represents the set of directed edges. Each node in V corresponds to a narrative element, such as characters, events, scenes, or plot points, while the directed edges in E signify the relationships and dependencies between these narrative elements.

Mathematically, V = {v_1, v_2, ..., v_n} represents the nodes of the hypergraph, and E = {e_1, e_2, ..., e_m} represents the directed edges. Each edge e_i = (v_j, v_k) signifies a directed connection from node v_j to node v_k, indicating a narrative progression or dependency.

To describe the ancillary subgraph execution routines within this formal system, we utilize symbolic notation and mathematical expressions. An ancillary subgraph execution routine can be represented as a function f: V' -> V'', where V' represents the input nodes and V'' represents the output nodes. This function maps a subset of nodes in V' to a subset of nodes in V'', facilitating the execution of specialized sequences or storylines within the larger narrative structure.

Formally, let V' ⊆ V be the set of input nodes for the ancillary subgraph execution routine, and V'' ⊆ V be the set of output nodes. Then, the function f: V' -> V'' maps V' to V'', allowing for the transformation and execution of the narrative elements defined within the ancillary subgraph.

By combining the directed acyclic hypergraph with ancillary subgraph execution routines, we create a powerful and expressive framework for interactive narrative structures. The formalism provided by this system enables precise analysis, transformation, and generation of narratives, allowing for rigorous exploration and manipulation of branching patterns, dependencies, and storylines.

Through this mathematical lens, we can study properties of the hypergraph, such as connectivity, reachability, and cycles, to analyze the coherence and structure of the interactive narrative. Moreover, by applying graph algorithms, we can traverse the hypergraph to generate dynamic narratives, leveraging concepts such as graph traversal, topological sorting, and shortest path algorithms to create engaging and evolving story experiences.

In conclusion, the formal system presented here, with its directed acyclic hypergraph and ancillary subgraph execution routines, provides a rigorous and expressive framework for describing interactive narrative branching structures. By employing mathematical notation and symbolic representations, we can precisely analyze and manipulate the narrative elements, dependencies, and branching patterns, opening new avenues for the study and creation of dynamic procedural narratives.

Thank you for your attention, and I invite you to explore the depths of this formal system, unlocking the full potential of computational narrative through the lens of mathematics and rigorous symbolic representation.