Stage beliefs and the dynamics of performance • Alexandre Freiburghaus Mazuir

or, the place of knowledge in spontaneous fiction.

Introduction

The goal of this essay is to explore possible applications of the DEL framework to one specific case : that of improvised theater. We know that the relationship between knowledge and fiction has always been arduous, or at the very least complicated ; the paradox of fiction being a great example of their everlasting conflict. How can fictitious facts be known if knowing requires truth ? With only two ingredients already emerge incredibly intricate questions. However, I personally believe that improvisation, when added to the mix, results in even grander wonders. Indeed, it implies one major key difference : the text has not yet been written, and as such “truth”, even in its weakest definitions, appears frail, unstable, undetermined. There is a fundamental lack of, well, fundamentals, no baseline guiding the performance from start to end. Improvisers decide what the story will be as they go. And although they obviously must communicate it to the audience to make a compelling show, thus avoiding entre-soi, they must also, even more crucially, communicate it amongst themselves. This, more often than not, results in misunderstandings and multiple interpretations of a same scene, misunderstandings that the audience loves, as a peak behind the curtain of a performer’s mind, because the audience assumes what should have happened. They “know” the performer misremembered a character’s name. They “know” that what has been set up will come back later in the scene. And the improvisers “know” where they want to take it.

Could then the logical definition of knowledge, or at least certain belief, be applied to such cases ? What is the difference in treatment between truths from the point of view of the actors and that of the audience ? Why are there statements that are easy to retract or bend for great entertainment and some that, when reevaluated, make you wonder if the people on stage are actually listening to one another ? I will attempt to give an answer, albeit a very partial one, to those questions, using my knowledge and experience of improvised theater, both on and off stage.

A brief overview of improvised theater

Now, obviously, it would be hard to follow along without any idea of what improvised theater is. I will be explaining the style which I am most familiar with : the style most common to French-speaking Switzerland, particularly Geneva [Fédération d’Improvisation Genevoise], though it has similarities with that of Amsterdam.

Improvised theater is, as anyone could guess, theater that is improvised. In Geneva, it is played as a match, though this is of little importance to us here. Most of the time, the scenes¹ are quite short and have to respect both a constraint of form and a theme. The constraint can be any limitation or style imposed on the players (for instance that all lines must rhyme, or that the scene must be played following Western-movie codes). The theme on the other hand is generally a single word or sentence to kickstart dialogue and plot-lines. Respect of both is mandatory, under threat of a penalty for the unabiding team. This necessarily means there is some meta aspect to improvisations; that there are some elements that come from outside the dialogue and acting. We will come back to this a few pages down.

If you were to attend a show, you would notice that before a scene is played out, both the constraint and its theme are announced by a referee, then the players get a few seconds (called the “caucus”) to argue for a general story, or to decide who plays which character. Therefore, there is a small window of time to decide of what is, to bastardise the term, common knowledge to all the players. However, not all scenes allow for caucuses, as some constraints explicitly forbid it.

During improvisation, it is allowed for the actors not yet performing to enter the stage at any time, and for any actor to leave and return to the resting benches (again, if the constraint allows for it, as some like “huis-clos” explicitly anchor actors on stage). Thus, it is possible for actors to scheme and discuss amongst benchwarmers before they join in the scene. It is, however, not allowed for anyone outside the scene to address anyone inside : once a player is on stage, all exchange of information with them must go through acting, and acting alone.

Furthermore, all scenes are played under a time limit, imposed with the constraint. Time is regularly communicated through hand signals given by the referee, signals which are generally reproduced by all players outside, on the benches. The point of this limit is to pressure the players into actually developing a story rapidly and also resolving it at a satisfying time. Note however that the hand signals are very easy to miss, as they must be discreet enough not to bother the audience.

This concludes our blitz summary of what the audience may see of an improvised theater show, the varnish, but there is one final aspect, one last meta-data the improvisers can use on stage, and that comes from training. Players usually know each other and train together multiple times a week. And players have habits, habits that you cannot help but notice once you’re familiar with them. For some, it is recurring themes in the narratives they lead, for others, it is recurring characters they incarnate. Once you know an improviser well enough, a lot can be inferred about what they are about to play from the simple fact that they are about to play it.

To sum it all up, here follow the different means of communication (which we will often call “actions”, to gamify) players have access to while performing : theme, dialogue, acting, caucus, bench-planning, time and habit. We order those in Table 1².

Available to the audience	to all improvisers	to some improvisers
theme	caucus	bench-planning
dialogue	time	habit
acting

Table 1 : means of communication

Constraints can be ignored for simplification, but they are crucial in the sense they allow or forbid some of these canals³. The ultimate goal of this essay is both to formalise each of these aspects into a relevant DEL framework, finding an appropriate system for us to do so, and to question the metaphysics behind the statements communicated themselves. So, first we must discuss the stance the remaining pages will assume on the place of knowledge in fiction.

Knowledge in fiction

“How can fictitious facts be known if knowing requires truth ?”. One could already discuss the nature of a “fictitious fact”, an apparent oxymoron, but let us treat facts as simple statements for now. The first thing to clarify is that, for the rest of the paper, our definition of knowledge (and belief) will not exactly match that which we are used to. Instead, it must be double. We separate cases where someone knows something about the play itself and cases where someone knows something about what is happening in the play. For example, we distinguish statements like “I know the play is in French” from “I know that Bob is Alice’s father”, given Bob and Alice two characters in the play. More specifically, for the second one, we will assume systematic cheeky ellipses, allowing for some rephrasing : “I know Bob is Alice’s father” will be interpreted as “I know that, in the scene, Bob is Alice’s father”. In short, knowledge of the scene being played out will always be relativised to the context of the scene itself. This allows us to merge both understandings of knowledge into one, of which the object is systematically the scene, and then either some of its properties, or some “aboutness” (the characters, their relationship, in general : what the scene is depicting). Suppose instead that “I know Bob is Alice’s father” was interpreted as is, then it would be one of those “fictitious facts”, in the sense that it refers to some fictitious non-entities. But how can a statement refer to something that is not ? Some researchers actually defend that “the use of a singular term is said to have ontological commitment iff it has been chosen while substituting a bounded variable that occurs in an existentially quantified expression. Accordingly, in an argumentative context, a proponent is not entitled to the thesis that, say, Vampires exist, by the opponent’s concession that Nosferatu is such a creature”[Rahman]. In a similar way, saying “Bob is Alice’s father” does not necessarily entail that both characters actually exist. It only talks about their relation, or properties.

But this bizarre disjointedness between what is true of the scene and of the outside world is far from the only quirk emerging from epistemically treated fiction. Consider the aforementioned paradox of fiction. Formulated by Radford and Weston in [Radford], it is constructed from three observations, inconsistent when taken altogether yet seemingly self-evident, which we reformulate as follows :

We have emotions for fictitious characters, despite knowing them not to be real.
We have emotions only for what we believe to be real.
We cannot know something to be fictitious yet believe it to be real.

Now, the goal of this section is far from trying to give an answer to this paradox, very much still debated, with philosophers usually claiming one of the statements is not as evident as it may seem. Instead, simply notice the use of believe and know in the clauses : this paradox fully relies on how we engage with the story, how we treat the characters and scenes that it portrays. Now, going back to the dichotomy we presented before, this type of belief here mentioned is not “contained” in the scene, it is not of the same kind as “I know Bob is Alice’s father”. Instead it appears to be that this knowledge disregards the relativisation of the characters to their scene. Knowing a character is not real is crucially different from knowing they are not real in the scene. Although there are many ways to treat characters and events of fiction (the Meinongian, possibilist, contextualist accounts, etc.[Thomasson]), it still seems that, at the core, we treat them as entities of their own, which can be extracted out of their scenes. This hints at the similarity in treatment between fictitious characters and actual entities, to which we will come back later on. Our recontextualisation’s main point is to handle factivity of knowledge, bounding truth to the scene, even if characters were to “leak out” ⁴.

However, it is essential to notice that everything we have said so far only holds for fiction with set in stone statements, for we have only been talking about knowledge. You, as the author, know what will happen next if, for instance, you have already written it. But when it comes to the audience (and improvisers), there is but one way of engaging with the material : belief, not knowledge. The audience does not know that a certain character is nice, for said character might be a traitor later on, they only believe so. And similarly for improvisers. Although, one could argue that in a one person improvised show, said improviser could know what is going to happen, or whether said character is nice, as they are in full control and might have already decided on it. However, most improvisation is played in groups, and no one knows whether the others are planning the same thing as them, nor whether they have understood the story so far at all. As such, knowledge must be ruled out, for there is undeniable uncertainty in improvised fiction. This crucially prevents us from modeling improvisation with standard public announcements logic. As, not only the facts themselves can be later on contested (as we will see further down), but the players themselves cannot know whether the announcement has truly reached everyone, and for we know that common knowledge requires this infinite chain of “knowledge of someone else’s knowledge”, that also cannot be used in our model. There is nevertheless one point at which knowledge is possible : the very end. After an improvised show, the scene played out is set in stone. Both the audience and the improvisers can retrospectively know what happened. This will come back.

Thoughts and communication

As established previously, we are actually working with belief rather than knowledge, as knowledge only comes at the end of the play, when everything has been settled and no changes can be made. As such, there is one appropriate framework for us to use : belief revision. We will be using the standard system of belief revision, with however two small additions :

To account for multiple agents, and a fortiori to clearly show divergences in belief, we will structure the belief orderings into a grid, where each line is the belief order of a specific agent. Additionally, we also link together identical worlds across multiple agents’ belief. This implies that inconsistencies in ordering are visually represented as crossing lines, and that “the wider the cross, the more different the agents’ beliefs are”.
We also suppose, for clarity, that the possible worlds present in the belief orders are merely representative of an equivalence class, and only considering a new proposition can separate said classes into two, depending on what those imply for the truth of said proposition.

But what do we mean by considering ? Well, anytime a proposition is the object of one of our aforementioned means of communication, no matter whether it has been correctly transferred or not. That and, crucially, inner thoughts. Indeed, given the creative nature of improvised theater, one key difference emerges with usual cases of belief revision : the agent does not necessarily need a trusted source of information to change their beliefs, but instead we can consider that, by actively contributing to the play itself, the beliefs of the agent may later on turn into truth. Indeed, “as a result of the Success postulate, the incoming formula F that brings about the belief change is assumed to be completely trustworthy : the agent accepts without question the incoming information F and incorporates it into her set of beliefs as per the belief change process.”⁵[The Stanford Encyclopedia of Philosophy]. As such, improvisers could be seen as their own trusted source, strongly separating them from the audience in how they engage with the material and the proposition. The audience received, the players create. This change, simple in appearance, is actually more akin to a paradigm shift⁶ : where truth generally precedes belief, here we go the other way around. Despite belief revision being usually perceived as “corrective”, despite generally assuming that it is when “our beliefs are wrong, [that] we engage in dynamic procedures of belief revision”[van Benthem], improvisation requires to treat belief revision as a creative tool in itself. Now, it is still essential to consider what each agent knows of the concerned mean of communication, or the thought, i.e. whether it is discreet, obvious, an aside, a private joke, etc. indeed, “in order to understand and formalize belief revision, it is essential to take into account the actual ‘learning event’ that ‘triggered’ the belief change. For example, our beliefs about the current situation after hearing a public announcement are different from our beliefs after receiving a fully private announcement. [...] In contrast, our beliefs about the triggering action are irrelevant as far our static revision is concerned : our conditional beliefs about the current situation given some hypothetical information do not depend on the way this information might be acquired” [Baltag]. Also, note that, in the spirit of standard DEL, we assume discrete intervals of time, with every action spanning a whole unit⁷.

Weak and strong assertions

Before properly describing each action, or “trigger”, in belief revision terms, let us test the waters first and come back to one of our key challenges to account for : that when some new piece of information contradicts what the audience believes, they can have two main types of reaction : acceptance or rejection. Suppose that in a scene, some actor presents themselves as “Alice” and that, later on, for the same character, someone calls them “Bob”. The audience is most likely going to notice the change and resist against it, assuming the second improviser has made a mistake, as it contradicts what was previously established. Now, on the other hand, suppose that a whole scene is depicted with gravitas, a solemn tone, characters fearing they might die, all to later realise, as the punchline, that they were simply going to the dentist. Now, once again, this contradicts what the audience believed, as they probably expected stakes matching with the tone. Notice however that such a thing would not be considered a mistake, but as we said a punchline. Breaking expectations and pre-established facts is one of the key methods to constructing jokes. Improvisers constantly walk a tight rope, with on one side the risk of breaking immersion and, on the other, that of simply not being funny, or just being too predictable. Our model should then account for these differences.

One easy way to treat rejection is to assign to our first example a belief update, and to our second multiple radical belief upgrades. Indeed, one can notice that the key difference between our two examples is that, in one case, the new information contradicts a statement that was clearly communicated (the name), and that in the other it simply contradicts was was implied yet never confirmed (the tone). This system, at first glance, seems perfectly efficient, allowing us to explain the visceral rejection of the audience as a simple mismatch between the worlds left after the upgrade (all the worlds where the character’s name is Alice) and the new statement (that it is Bob). Our second case of pure implication, on the other hand, does not result in rejection from the audience as it was never mentioned that the play was about anything other than going to the dentist. Hence no contradiction.

Another approach would be to claim that rejection does not only arise from contradiction with the pre-established facts, but also with an implied, pragmatical statement. For instance, that “No one has more than one name”, and similar propositions or “rules” that, in general, we use and assume day to day. In that case, both types of assertion could be understood as radical belief upgrades, with rejection emerging from the impossibility for the audience of finding a best world satisfying all propositions at once (both names and the meta-statement about names) without being contradictory.

Now, both methods seem to work on their own. However, there is an argument to be made in favour of the second one. Consider our previous example with one improviser renaming the character Alice to “Bob”. Usually, players will solve this mistake by claiming that the character played by the improviser who made mistake was in fact the one misremembering. In short, we shift the mistake from the improviser to the character, with someone saying something the likes of “You can’t even remember the names of my friends, how am I supposed to trust you ?”, simultaneously addressing the mistake and utilising it to add depth to the scene, introducing new stakes. This could still work with our first method were we to treat both the mistake and the players addressing it as the cause of a singular update, but the other most common way of treating such a mistake does not grant the same favour. That other technique is to actually have the mistake be right. Suppose that, later on, Alice comes out and says “I have been lying this whole time, going under many aliases”. Then, because our initial statement that “the character’s name is Alice” was taken, as we assumed, as a belief update, there exists no world left satisfying the proposition that “the character’s name is not Alice”. As such, this new revelation should also end in a contradiction, and therefore be rejected by the audience as some kind of mistake. Yet it is not. It is, as we said, taken as a revelation, in much the same ways as the dentist example was, a plot-twist. This double nature of how people interpret contradiction seems to be the final nail in the coffin for that particular method. One could argue that instead of taking naming statements as “the character’s name is Alice”, we should take them as “that character was called Alice”, weakening the proposition, and allowing worlds where the wrong name was used in the beginning to still hold true. This however prevents us from explaining the perceived mistake, as “that character was called Alice” and “that character was called Bob”, are non-contradictory⁸.

Both mending cases can however be explained by our second method. Suppose the mistake is taken as wrong, and the blame shifted to the character, then the contradiction arises for there was a presupposition that “What characters say is right”, which gets canceled or at least weakened by addressing the mistake. On the other hand, suppose that Alice turned out to be lying, then that same statement (or the weaker “Characters do not lie”⁹) is the one at the core of the contradiction, canceled by the revelation. This, however, crucially relies on the audience’s own pragmatic inference, and therefore relies on the characters being treated in much the same way we treat actual people, it relies on the scenes being treated in the same way that we treat real life situations. Once again, we come back to the paradox of fiction, where we treat fictional beings and scenarios as if they were true, despite knowing they are not¹⁰.

A final point to raise, which we have not yet addressed, is the nature of said pragmatic inferences. We assumed earlier that those were bound to the scene. Saying “Alice does not lie” is akin to saying that “In the scene, the character of Alice does not lie”. We could also consider these inferences to be about the scene itself, of the meta kind mentioned above. In theory, that could be possible, but, and this strictly comes from personal experience with fiction and arts in general, it does not seem to be how people think of the content. We assume values and properties of the characters. There still are assumptions of the improvisers (for example that “the improvisers treat traumatic subjects appropriately”), assumptions outside the scene, but those do not seem to produce the same kind of rejection. Forgetting a name will get a laugh, breaking a social rule will make people wince.

Upgrade and updates

Let us finally properly scrutinise each action, and determine whether they should be treated as belief updates or radical belief revisions, as well as their reach. We suppose a toy example, with two improvisers and an audience, respectively named I1, I2 and A. Each action will be considered in a vacuum, that is without any pre-established beliefs from any agent¹¹. Therefore, we represent our starting situation as :

Dialogue

As mentioned in the previous section, it seems that dialogue, to allow for retroactive changes, must be considered as a radical belief upgrade. There might however be some exceptions to that treatment, mainly one that comes to mind : fairytales. In fairytale-style improvisation scenes, one of the improvisers plays the role of the narrator, describing and setting up the scene. As it is traditionally taken to be an omniscient narrator, it would appear logical to treat what is said as gospel, and therefore view it under the light of an update. To account for both interpretations, let us make a more precise distinction between two types of dialogue : in and out-of character. The reason is simple : we previously advocated for dialogues as radical belief upgrades for it was possible to mend mistakes by shifting the blame from the improviser to the character. However, if the sentence itself was not said in-character, then this strategy is not possible anymore. Treating out-of-character statements as updates therefore does not risk leading to any contradiction. From there on, two philosophical stances can be assumed : either we choose to treat every piece of information coming from dialogue as a radical belief upgrade to avoid splitting cases, or we choose to allow for some belief updates, as a way of simplifying the models by removing worlds that would never be re-instantiated. Purely arbitrarily, let us choose the latter. We must also note that, although it is always possible for one of the agents to miss the information¹², dialogue is always targeted towards both the audience and all other players. This leaves us with the two following cases, assuming dialogue is clearly communicating $\varphi$ .

In-character :

Out-of-character :

Interestingly, note that knowing which improviser said $\varphi$ is irrelevant for our system. Indeed, it is only useful when treating cases where one of the agents did not understand what was communicated. Indeed, suppose that I1 said it, then there would be no model where I1 is mistaken¹³.

Acting

Acting is even easier to treat than dialogue. By acting we mean facial expressions, gestures, voices, occupation of the space, etc. All these can absolutely communicate information (think of, for instance, an actor crying, which would usually communicate that their character is sad), but, given that the parallel between acting and propositions is even more obscure than with dialogue itself, there is no guarantee for anyone that they have understood the actual intent of the actor. As such, only radical belief upgrades can be considered. Acting is also, very much like dialogue, directed towards both the audience and all improvisers, making it another symmetrical revision. It can therefore be modeled in much the same way as in-character dialogue, that being :

Theme

Let us consider the formula statement $\varphi$ as “the scene is about [the theme]”¹⁴, whatever the announced theme may be. As mentioned earlier, respecting the theme is one of the mandatory constraints to all improvisers, and the audience knows it. Therefore, there is no possibility for the scene to play out in a way that contradicts the theme. It can thus be safely considered a belief update. As it is clearly announced and known of everyone, we treat it similarly to out-of-character dialogue, that being :

Caucus

Caucus is our first example of asymmetrical revision, that is that there will be a difference between the belief order of improvisers and that of the audience. Indeed, caucus is specifically intended for the audience to miss, as it would otherwise spoil what may happen in the scene. But when it comes down to which revision we should choose, we are presented with a dilemma : on one hand, caucus is the closest thing in improvisation to a set in stone truth, it is the intent of bringing the story in a certain direction, of which everyone is aware. But on the other, it is still possible for an improviser to go off the rails, especially if they notice during the scene that there is a much more interesting story available if they stray for the supposed path. The first would encourage us to see it as a belief update, the second as an upgrade. Despite the fact that caucus is in general overwhelmingly respected, the slight chance of deviation seems to tilt the scales in favour of radical belief upgrades. Were we to use a probabilistic model, we could model the difference between belief in the caucus and belief in dialogue as of different magnitude, but our current system cannot account for this. Therefore, we model caucus of $\varphi$ as :

Bench-planning

In that regard, bench planning is very similar to caucus, with one simple difference : not all improvisers are involved. Suppose for this example that we add an extra improviser I3 to the mix, the only one not involved in the planning. Then, because I3 could go against what I1 and I2 discuss, it is not possible to treat planning of $\varphi$ as a belief update. Note that this does not apply to the caucus case despite it also having an agent not involved in the discussion (the audience) because the audience cannot interact with the play. I3, however, can. Therefore, we must treat bench-planning similarly to caucus, with a subset of all improvisers being concerned. In our expanded example, this would result in :

Thoughts

We treat inner thought as an even more restricted case of bench-planning, one which involves only one improviser. Note that for the same reasons as previously it must be considered a radical belief upgrade, and not an update. One small exception here : we can also consider thought of the audience. This could allow us to treat cases of suggestion, where nothing is explicitly communicated but the audience themselves come to a conclusion. This however escapes the scope of this particular essay. Let us suppose that I1 is the one having a thought, then we model it as such :

Habit

For habit is an assumption from some improvisers, we treat it identically to bench planning. There is a philosophical difference however, namely that bench planning is a collective effort, whereas noticing habits is an individual thought happening in multiple people. However, this is irrelevant to our modeling, similarly to how the precise speaker was irrelevant to the dialogue case (for only the result here matters¹⁵), and, supposing I1 knows I2 well and predicts their habits of doing $\varphi$ , we represent the situation as :

Time

As mentioned earlier, time indications are extremely discreet as not to perturb the audience. This means that they can very easily be missed by the improvisers too, especially if they happen to not be facing the referee. We consider the statement $\varphi$ as “the scene is about to end” which, once again, as it is a requirement players must abide to, cannot be contested and thus can be interpreted as a belief update to those who saw it. Similarly to how bench planning was an upgrade to a subset of the improvisers, time is instead an update to a subset of the improvisers. Supposing only I1 sees the signs, we model it as :

Ending

There is one final action that we have not yet mentioned, or at least not claimed we would properly look at, and that is the announcement of the end of the play. When the play ends, as we have said previously, there is no possibility of change, no rectification allowed. We treat endings as private updates to every agent, where $\varphi$ is the formula singling out the best worlds of each belief order. There is no need for $\varphi$ to be the same for all agents, as everyone might have a different perception (especially if improvisers had planned things that where never communicated, then their best world would not necessarily be the best world of the audience, and there is no reason to believe that what the improvisers believed yet never said would influence what the audience takes away from the play).

Framework limitations and possible expansions

Now, it is important to notice that the system here presented has some very obvious caveats. Other than the ones mentioned in footnotes and the main text itself, here follow a few :

First of all, the structure and wording of both communicated propositions and pragmatic inferences are still very much hazy. We mentioned the possibility to account for naming as “This character’s name is Alice” or “This character was called Alice”, but actually there seems to be a semi-infinite amount of relevant information. For instance, maybe we should word it as “This character was called Alice and they answered”, seemingly strengthening the assumption that it indeed is their name. We previously assumed equivalence classes of worlds, where only the relevant proposition are actually considered. But what is the relevant proposition ? Should the relevant proposition contain every single bit of information that could later on be relevant, at the cost of being very clearly too heavy, and losing parallels with the human mind which does not appear to think in gargantuously long propositions, or instead should we only consider the smallest proposition currently relevant, as in that no other rewordings would add any information contradicting or supporting what is already established, at the cost of having to retrospectively change it when new information is added that could interact with a different, previously ignored facet of what was said before ? There is a high level of arbitrariness.
We could also consider the issue of tone, and general suggestion. In our dentist example, the general tone was the setup to the punchline, but how do we characterise tone in logical formulas ? At the very least it would require higher order logic, in a similar way to semantical interpretations of adverbs, which are probably the closest linguistic object we have to tone. The same issue can be said of acting, and in general translating non-linguistic means into proper propositions. Nevertheless this seems even more arbitrary than standard propositions, also given how different people can perceive a same situation under very different lights.
Another limitation is the set amount of people on stage. In our toy examples, we only assumed two (or three) improvisers and one audience for simplicity. Of course, we could have gone for more but more importantly the number of involved agents never changed. However, as was mentioned before, improvisers have the opportunity to exit and enter the stage at any point. This can be treated in two ways, either by considering all improvisers as agents, regardless of whether they are on stage or not, or we could use a system allowing for changing agents, in a similar way as [Singh]. Now, in general both options work, but changing agents could be used to also handle heckling, the practice from one member of the audience to intervene in the show unprompted, by yelling or thankfully more rarely coming on stage. This seems like a proper case where an agent is added, as having the heckler considered an agent from the get-go appears, as a philosophical concern, to have them be a heckler before anything is done. The same thing can be said for shows with audience participation, whether that is suggesting themes, or, this time desirably, coming on stage.

Conclusion

To conclude, let us order the belief changing actions depending on their type of revision, as seen in Table 2, in which we can observe a general tendency for updates to reach as far as possible, and for upgrades to be more lenient with smaller groups.

Update to all	Update to some	Upgrade to all	Upgrade to some
dialogue (out)	time	dialogue (in)	bench-planning
theme		acting	habit
end (individual)			thought
			caucus

Table 2 : Belief revision types

Overall, the study of creation, and a fortiori improvisation, is very new to being studied under the epistemic light, as seems to indicate the extremely narrow scope of relevant papers. It feels however promising, appearing as an interesting entry way into the study of potential factive beliefs and fiction pragmatics. One can only hope that, one day, if deemed worthy enough, it will join other fields of study on the main stage.

References

Fédération d’Improvisation Genevoise / Geneva Improvisation Federation. Official Website. https://www.impro-geneve.ch/limpro/
Daphne Wang, Mehrnoosh Sadrzadeh, Samson Abramsky, and Víctor H. Cervantes. On the Quantum-like Contextuality of Ambiguous Phrases. CoRR, abs/2107.14589, 2021. arXiv:2107.14589
Shahid Rahman and Juan Redmond. A Dialogical Frame for Fictions as Hypothetical Objects. Filosofia Unisinos, 16(1), 2015. HAL
Colin Radford and Michael Weston. How Can We Be Moved by the Fate of Anna Karenina ? Aristotelian Society Supplementary Volume, 49(1), 67–94, 1975. https://doi.org/10.1093/aristoteliansupp/49.1.67
A. L. Thomasson. Fiction and Metaphysics. Cambridge University Press, 1999. Cambridge Studies in Philosophy. ISBN: 9780521640800. Google Books
Shikha Singh, Kamal Lodaya, and Deepak Khemani. Changing Agents and Ascribing Beliefs in Dynamic Epistemic Logic. arXiv:2211.02452, 2023. https://arxiv.org/abs/2211.02452
Alexandru Baltag, Hans P. van Ditmarsch, and Lawrence S. Moss. Epistemic Logic and Information Update. Philosophy of Information, 8, 361–453, 2008.
Alexandru Baltag and Bryan Renne. Dynamic Epistemic Logic. In Edward N. Zalta (Ed.), The Stanford Encyclopedia of Philosophy, Winter 2016 Edition. Metaphysics Research Lab, Stanford University, 2016. Stanford Encyclopedia of Philosophy
Johan van Benthem. Modal Logic for Open Minds. CSLI Publications, Stanford, CA, 2010. CSLI Lecture Notes, Vol. 199. ISBN: 978-1575865980.

Footnotes

We will be using the words “scene” and “play” interchangeably. ↩
We here assume for structural purposes that time indications are discreetly signaled, and thus not perceived by the audience. We also assume that improvisers are not identically familiar with the styles of all other players, and that some habits might not be known to all. This is typically where the “match” nature of the show comes into play, as teams train amongst themselves, not with other teams. In reality, the world of improvisation is small enough that anyone will get to know all other players, but probably not to the same level as one might know their own teammates. ↩
Note however that, in our rhyming example, the presence of the constraint helps players guess which words are about to be said in a much easier way than normally (as there are trivially less words riming with the previous sentence than there are words in general), and that, in our western example, cliches of genres and stories greatly help anticipating development of the scene. We choose to ignore this canal to avoid delving into both semantics and general story structure, keeping the scope of future examples focused enough yet not too minute. Adding constraints to the framework is a task we leave for future works. ↩
There are some interesting discussions on what fiction creates, and whether or not fictitious entities must be assumed outside of their original work. Some say that “Once created, [...] a fictional character can go on existing without its author or his or her creative acts, for it is preserved in literary works that may long outlive their author”[Thomasson]. This however assumes the existence of a tangible source material, which will never exist for improvisation, as it is usually not recorded nor transcribed. ↩
Note that, ironically, this complete trust and acceptance in what is being said could be seen as the baseline for the “yes and” principle of improvisation, probably its most famous one, which claims that improvisers should always accept the newly given information and build on top of it, effectively making it a trusted source by assumption. ↩
I am by far not claiming that this is the very first paper to talk about this, rather that it seems at first counterintuitive. ↩
This is just for simplicity, in reality timing is a crucial aspect of improvisation, as the same actions with a different rhythm would be perceived in different ways by the audience (long silences showing awkwardness, a fast pace showing excitement, etc.). ↩
One could argue that “the character’s name is Alice” and “the character’s name is Bob” are also not contradictory in a logical sense. Then, use instead “Your one and only name is Bob”. It was simply more digest to treat a simpler case. ↩
This is how we write both statements for conciseness, but in reality it would make more sense to treat them as “character 1 does not lie”, “character 2 does not lie”, etc., to avoid one character’s behaviour to prevent all others from making the same mistake. ↩
Fundamentally, there is nothing preventing a scene from having characters with inconsistent names, or contradictory beliefs (liberties that can be found in more contemporary absurdist theater). Yet we still seem to rely on what we are used to from the real world. ↩
In actuality, this rarely ever happens. Despite improvisation’s central point being not knowing what is about to be played out, most improvisers come up on stage with some intent (maybe a joke they thought of that morning, or a desire to play a certain type of scene), and as such there more often than not is some kind of starting belief, causing some asymmetry between the players mental states. We choose to ignore this for simplicity. ↩
In general, we always assume cooperative agents that do not attempt to sabotage the scene. ↩
The reason we do not treat these cases is that it is actually a bit more complex than this. Doing improvisation usually means building on what others have said, and this includes building on little details in their phrases. It is actually completely possible for I1 to say something carrying both $\varphi$ and $\psi$ , but only intending to say $\varphi$ , and have I2 build on $\psi$ instead. Then, we would have a case where what was said by an improviser is not necessarily known by themselves, demultiplying the amount of edge cases to consider. ↩
We will come back to this in the limitations, but the wording of the propositions is very arbitrary and sometimes hard to fully translate into formal logic. ↩
This can be very much contested ontologically, but given our belief revision system only accounts for discrete states, it would involve adding an extra system representing those cognitive differences. ↩