Redcap

Our architecture is based on two components: an Interactive Storytelling rendering and an Interactive Storytelling controller.

The controller aims to manage the unfolding of the history by taking into account the player actions and according to the structure of the narrative pre-defined. The controller is based on a computational model of Interactive Storytelling: Linear Logic. We adapt Greimas analysis to the constraints of Interactive Storytelling.

Greimas was the first to develop narrative formalism as an abstract formula to represent an action (narrative program). He proposed to define an action as a transition from one state to another state where the subject gains or loses an object (conjunctive or disjunctive narrative program).

Linear Logic has been introduced by J.-Y. Girard as a restriction of classical logic. Unlike classical logic, Linear Logic is not used to determine whether an assertion is true or not but rather the validity of how formulas are used (and then consumed) when proving an assertion. Linear Logic is well suited to derive a computational model to partially ordered problems with resource sharing.

The main connector of Linear Logic are:

• ⊸: Implication (imply), express the possibility of deduction. Example: 2€ ⊸ trawberries . Means that I can give 2 € to buy strawberries.
• ⊗: Multiplicative conjunction (times), a set of resources (not ordered). Example: strawberry ⊗ strawberry . Means that there are two different strawberries (strawberry ⊗²)

• ℘: Multiplicative disjunction (par). Example: strawberry ⊗² ℘ strawberry ⊗⁵. Means that there is two set of strawberries (one belongs to Alice and the other one to Bob for instance)

• ⊕: Additive disjunction (plus), external choice. Example: strawberry ⊕ raspberry . Expresses a choice (external to the process). The player can choose strawberry or raspberry 

• &: Additive conjunction (with). Example: strawberry & raspberry . Expresses a choice (internal to the process). The game can choose strawberry or raspberry 

• ⊢: Turnstile, separate the left part (antecedent) and the right part (consequent) of a sequent. Example: D , D ⊸ E ⊢ E Linear implication express the possibility to produce a copy of E by consuming a copy of D AND a copy of D ⊸ E 

A sequent of Linear Logic expresses all the possible narratives of a story. Each narrative corresponds to a proof of the sequent (Proving a sequent consists in rewriting the sequent by making a substitution of the formulas in order to have an initial sequent). As the proof is not unique, we can deduce various narratives.

The following sequent: A, C , D , A ⊗ C ⊸ B ⊗ C , D ⊸ E , E ⊗ C ⊸ F ⊗ C ⊢ B ⊗ C ⊗ F; gives the following proof graph (simplified to the substitution of the linear implication).

It is then possible to compute a sequent by using Petri nets. It has been proved that there is an equivalence between a sequent of Linear Logic and a Petri net (with some restrictions). A token player algorithm is then used to compute the model of Interactive Storytelling.

Our system aims to derive an interactive storytelling where the player can influence the unfolding of the story (the discourse). As a consequence for a given storyworld we define various possible discourses (that are base on the same pattern of story structure).

The storyworld (character, setting, etc.):  the Little Red Riding Hood history. The Little Red Riding Hood, the mother, the grandmother, the wolf, the hunters, a wood between the two houses, a cake and a little pot of butter.

The player is cast as the Little Red Riding Hood and act within the time and space of the fictional world of the Little Red Riding Hood history.

Three possible narratives :

- N1: Folk tales: based on Grimms’ narrative. The Little Red Riding Hood walks through the woods to deliver food to her sick grandmother. The wolf wants to eat her, and goes to the grandmother house. A hunter help her to kill the wolf.

- N2: Fairy tales: a witch put a spell on the little Red Riding Hood. She has one day to marry a prince otherwise she will become a dwarf. The wolf, who is a princess that was put a spell, fells in love with the Little Red Ridding Hood and try to seduce her. Finally the Little Red Riding Hood gives a kiss to the wolf that becomes a wonderful prince. They get married, etc.

- N3: Action tales: the Little Red Ridding Hood wants to kill the wolf. The wolf escapes and meets hunter that protect him against the Little Red Riding Hood. The Wolf encounter Grandmother, take her as hostage, and there is a final fight. The Little Red Riding kills the wolf.

Each narrative follows a basic structure:

1- Introduction

2- The task

3- Encounter with the Wolf

4- The two ways

5- The Wolf and the Grandmother

6- Arrival of Little Red Ridding Hood

7- First dialogue

8- Second dialogue

9- Conclusion

 An authoring tool gives the storyworld and the narrative program.

It is then transformed into a sequent of Linear Logic. An automatic translator transforms the sequent into a Petri net. Finally the Petri nets performs the execution of the model and can interact with the Interactive Storytelling Rendering.