The scientific literature provides substantial evidence that a considerable part of face-to-face communication depends on non-verbal cues. The emergence of Online Social Networks has altered the way individuals interact, promoting Computer-Mediated Communication (CMC). However, it is important to note that CMC does not completely capture the richness of in-person conversations. This is a major issue, especially when users engage in communication through instant messaging platforms. In this work, we conceptualize this kind of communication as a multi-agent game in which the winning conditions are expressed by means of ATL formulas. These winning conditions may express diferent conversational objectives, such as the group wanting a particular agent to reach a certain emotional state.
The advent of Online Social Networks [
On the other hand, this digital revolution has also introduced challenges, such as privacy
concerns, the spread of misinformation, and the potential for addiction. Additionally, the brevity
and informality of online communication took the place of deep and meaningful exchanges.
Indeed, we are in the Computer-mediated communication [
Unlike face-to-face interactions, where non-verbal cues like facial expressions, tone of voice, and body language play a significant role in expressing and interpreting emotions, helping us discern between sarcasm and sincerity, empathy and indiference, excitement and apathy, CMC relies predominantly on text-based messages, emojis, and gifs. While these tools can help share some emotional aspects, they often fall short in capturing the full spectrum of human feelings. Written words alone may lack the context and the precision needed to accurately bring emotions. As a result, messages can be misread or misjudged, leading to misunderstandings and conflict. In instant messaging platforms, that enable us to connect with friends, family, and colleagues from anywhere in the world at the touch of a button, emojis, and emoticons attempt to bridge this emotional gap by providing users with a set of visual symbols to express their feelings. However, people have diferent interpretations of them, and this lack of standardized emotional expression can lead to miscommunication and even conflict in online interactions.
There are several existent techniques to obtain information about user’s emotions, from
machine learning approaches to lexicon-based ones, but still not enough has been done on
employing these emotions to improve the quality of the services ofered by instant messaging
platforms. This work constitutes an important step forward in this direction, since it allows
reasoning on strategic aspects of instant messaging framework formally. Indeed, we do not just
observe the user’s feelings, but we modify them to reach some goal, relying on the expressive
power of the Alternate-Time Temporal Logic [
Related Work Social networks and strategic reasoning have been already used in literature, among the others [16, 17, 18]. We here present the state of the art on sentiment analysis, in particular on solutions using logic approaches, as we do. The authors of [19] propose an abstract model of the communication scenario in OSN containing a Virtual Counselor to help the interpretation of the messages and of the emotional state, by providing an implementation of it in [20].
In [21], the authors used a fuzzy-rough sets based sentiment analysis classifier for analyzing political Twitter data, while in [22] the authors provide a fuzzy natural logic for sentiment analysis to evaluate linguistic expressions.
theauthors of [23], instead, propose a new semantic and fuzzy aware content recommendation system for retrieving the suitable content for the users, while in [24] the authors present two models of opinion difusion on a network, where the agents try to achieve their individual goals by deciding to enforce or not their opinions over the agents they can influence.
Sentiment analysis [25] is a natural language processing technique used to determine the emotional tone or sentiment expressed in a piece of text, such as a tweet, review, comment, or article. Its primary goal is to understand and classify the sentiment of the text as positive, negative, or neutral emotions like joy, anger, sadness. It has three main approaches:[25]: • Lexicon Based Approach [26, 27]: it typically does not require training data and it relies on predefined dictionaries associated with specific sentiments (positive, negative, neutral). Each word or phrase in the text is assigned to a sentiment score. This approach can be computationally eficient but may struggle with handling sarcasm, context, or new words not present in the lexicon. • Machine Learning Approach [28, 29]: it involves training a model on labeled data to learn patterns and relationships between words and sentiment labels. Common machine learning algorithms used for sentiment analysis include Support Vector Machines (SVM), Naive Bayes, Random Forests, and more recently, deep learning models like Recurrent Neural Networks (RNNs). These models can capture complex linguistic and contextual information and adapt to diferent domains and languages with suficient training data. • Hybrid Approach: it combines both lexicon-based and machine learning-based techniques to leverage their respective strengths. It can be more robust and flexible in handling diverse text sources but may require more computational resources.
There are also biometrics approaches based on wearable devices, such as EmotiBit, that do not rely on words analysis, but rather it can wirelessly stream and locally record data from a multimodal constellation of sensors, including electrodermal activity, a medical-grade temperature sensor, and a growing list of derivative metrics [30].
Without lack of generality, in this work we get rid of the way emotions are discovered, and we assume that, by applying one of the existent approaches, it is possible to know how users feel.
In this section, we demonstrate how a (very simple) example of communicative interaction
among multiple agents, in which they traverse diferent emotional states, can be modeled using
Concurrent Game Structures[
Definition 1 (Concurrent Game Structure [
Given a CGS a path is an infinite sequence of states of the CGS, = 1, 2, . . . for which the following holds: for any ∈ N+ there is a joint action a ∈ such that +1 = ( , a). We will denote paths by the letters , , , and . If is a path, then ≤ denotes the finite prefix of , ≤ = 1, . . . , ≤. A finite sequence of states ℎ is a history if there is a path such that ℎ = ≤ for some positive natural number . We will denote by the set of all histories over a given model , and if ℎ is a history, then (ℎ) denotes its last element. Given a state of the model , we denote by () the set of joint actions that defines a transition from , that is () = {a ∈ ⋃︀ (, a) = ′ for some ′ ∈ }. If is a coalition, (a subset of agents) a -action available at is a function ∶ → such that () ∈ (, ) for each ∈ . If and are actions available at for the coalitions and we say that extends , if ⊆ and () = () for each ∈ . We write ⪯ if extends . (, ) denotes the set of -actions available at and (, ) is ⋃∈ (, ).
Definition 2 (Strategy). Given a CGS and a coalition , a strategy for (or simply strategy) is a function Σ ∶ → that maps each history ℎ to an -action such that ∈ (, (ℎ)). An -strategy Σ is memoryless if ℎ = ℎ′ implies Σ (ℎ) = Σ (ℎ′) for every pair of histories ℎ and ℎ′.
As usual, we can see a memoryless strategy for an agent as a function whose domain is the set of states of the CGS and whose co-domain is the set of agents actions. A path is compatible with A-strategy Σ for the coalition (Σ compatible for short) if for every ≥ 1, we have that +1 = ( , a) implies Σ ( ≤) ⪯ a. We denote with Out(Σ , ) the set of all Σ -compatible paths whose first state is .
To define our multi-agent game, we need to represent emotions as discrete values. To this aim, we mention the Plutchik’s Model [31], that consists of eight primary emotions, arranged in a circular pattern, and various combinations and intensities of these primary emotions result in a wide range of complex emotion. For this work, it is enough to consider the set of the eight primary emotions, namely: Joy Sadness, Anger, Fear, Trust, Disgust, Surprise, Anticipation. To simplify our model we assume that for each of the participant of our game, there is an atomic proposition for each primitive emotion considered. The intended meaning of is “the agent feels the emotion ". More formally, if is the set of emotions and Ag is the set of agents, then Ap = ⋃ ∈Ag
{ ⋃︀ ∈ }
We here define our Game Model as a CGS over Ap and Ag having the following characteristics.
︀⋃ ⋃︀ = ⋃︀ ⋃︀ Ag⋃︀
︀⋃ player.
States : A state of our model will be a description of the emotions that each of the agents feels at a given moment of a conversational exchange. More precisely, a state will be identified with a set of atomic propositions containing exactly one atomic proposition for each agent . Thus, if ⋃︀ ︀⋃ is the cardinality of the set of emotions and ⋃︀ Ag⋃︀ is those of Ag, then Actions : An action will be identified with a message that one of the player can send to another Labeling : the labeling function will be simply the identity function on each state. This definition makes sense since each state of the model is a subset of Ap .
To enhance the understanding of our approach, we provide a minimal toy example. Let’s assume
that our set of agents consists solely of Bob and Alice. Furthermore, let’s assume that the set of
emotions is { , }, and that our set of actions is {1, 2}. Let’s assume that the content
of 1 brings joy to its recipient, and conversely, let’s assume that the content of 2 makes
its recipient feel fearful. A concurrent game structure specifying a possible communication
pattern between Alice and Bob and the evolution of their emotional state is showed in Figure 1.
In the figure, in a tuple ∐︀ , ̃︀ labeling an edge from one state to another, the first component
represents the output of the joint action for Alice, while the second represent the output of the
joint action for Bob. The protocol function can be easily retrieved. The intended meaning of
dialogue state in which Alice became joyful and Bob stays joyful1.
a joint action ∐︀ , ̃︀ starting from a certain state is “Alice sends the message to Bob,
and Bob sends the message to Alice". According to our assumption that 1 brings joy to
his (or her) receiver and that 2 makes its recipient fear fearful, if e.g., from a state in which
Alice is fearful and Bob is joyful, both Alice and Bob send 1 to each other, they will arrive at a
5. ATL
The advantage of modeling a communicative exchange between agents through a CGS is that
we can use Alternate-timeTemporal Logic [
The set of ATL formulae is specified inductively by the following grammar:
∶∶= ⋃︀ ⊺ ⋃︀ ¬ ⋃︀ ∧ ⋃︀ ∐︀ ∐︀ ︀̃ ̃︀ X ⋃︀ ∐︀ ∐︀ ︀̃ (̃︀ U ) ⋃︀ ∐︀ ∐︀ ︀̃ (̃︀ R ) where is any atomic proposition and is any subset of Ag. We define ∐︀ ∐︀ ︀̃ ̃︀ F as︀∐ ∐︀ ︀̃ (̃︀ ⊺ U ) and ∐︀ ∐︀ ︀̃ ̃︀ G as ∐︀ ∐︀ ︀̃ (̃︀ ¬⊺ R ).
The satisfaction relation , ⊧ is inductively defined on the structure of by the following clauses: • , ⊧ if ∈ ℒ () • , ⊧ ∐︀ ∐︀ ︀̃ ̃︀ X 1 if there is an A-strategy Σ such that , 2 ⊧ 1 for each ∈ Out(Σ , ); • , ⊧ ∐︀ ∐︀ ︀̃ (̃︀ 1 U 2) if there is an A-strategy Σ such that for every ∈ Out(Σ , ) there is a ≥ 1 such that , ⊧ 2 and , ⊧ 1 for each 1 ≤ < ; • , ⊧ ∐︀ ∐︀ ︀̃ (̃︀ 1 R 2) if there is an A-strategy Σ such that for every ∈ Out(Σ , ) either there is a ≥ 1 such that , ⊧ 1 and , ⊧ 2 for each 1 ≤ ≤ or , ⊧ 2 for every ≥ 1.
The clauses for the boolean connectives are immediate and thus omitted.
Using ATL formulas, we can reason about the objectives of the agents in our communication games. For instance, In the example of Figure 1, we can express the fact that, by cooperating, Alice and Bob can reach a state in which Alice is joyful i.e., ∐︀ {∐︀ , }̃︀ ̃︀ F or that Bob can always keep Alice in a state of fear ∐︀ {∐︀ }̃︀ ̃︀ G .
In this paper, we have defined a conversational game between multiple agents in which their emotional state evolves according to message exchange among them.
Our modeling is basic and relies on strong assumptions. For instance, we assume precise knowledge of an agent’s emotional state and treat emotions as binary. These assumptions can be relaxed for a more realistic approach. We could consider emotions as fuzzy and message exchanges as probabilistic, leading to a variant of ATL logic. This variant could address questions like, “Can coalition A, with a probability exceeding X, reach a state where player Y is at happiness level Z?". This work provides an overview of a long-term project, whose main characters are sentiment analysis and strategic reasoning. Indeed, we plan to keep following this research line, by relaxing the assumption made in this work, and by letting the model more realistic with the introduction of fuzziness aspects. strategies, in: Proceedings of the 11th conference on Theoretical aspects of rationality and knowledge, 2007, pp. 15–24. [9] F. Mogavero, A. Murano, G. Perelli, M. Y. Vardi, What makes atl* decidable? a decidable fragment of strategy logic, in: CONCUR 2012–Concurrency Theory: 23rd International Conference, CONCUR 2012, Newcastle upon Tyne, UK, September 4-7, 2012. Proceedings 23, Springer, 2012, pp. 193–208. [10] D. Della Monica, M. Napoli, M. Parente, On a logic for coalitional games with pricedresource agents, Electronic Notes in Theoretical Computer Science 278 (2011) 215–228. [11] W. Jamroga, V. Malvone, A. Murano, Natural strategic ability, Artificial Intelligence 277 (2019) 103170. [12] F. Belardinelli, A. Lomuscio, V. Malvone, E. Yu, Approximating perfect recall when model checking strategic abilities: theory and applications, Journal of Artificial Intelligence Research 73 (2022) 897–932. [13] W. Jamroga, W. van der Hoek, Agents that know how to play, Fundamenta Informaticae 63 (2004) 185–219. [14] A. Lomuscio, H. Qu, F. Raimondi, Mcmas: an open-source model checker for the verification of multi-agent systems, International Journal on Software Tools for Technology Transfer 19 (2017) 9–30. [15] A. Ferrando, V. Malvone, Strategy RV: A tool to approximate ATL model checking under imperfect information and perfect recall, in: F. Dignum, A. Lomuscio, U. Endriss, A. Nowé (Eds.), AAMAS ’21: 20th International Conference on Autonomous Agents and Multiagent Systems, Virtual Event, United Kingdom, May 3-7, 2021, ACM, 2021, pp. 1764–1766. URL: https://www.ifaamas.org/Proceedings/aamas2021/pdfs/p1764.pdf. doi:10.5555/3463952.3464230. [16] R. Niyogi, A. Milani, Modeling agents’ knowledge in collective evolutionary systems, in: International Conference on Computational Science and Its Applications, Springer, 2009, pp. 924–936. [17] W. Ji, F. Wang, P. Wu, Synthesizing coalitions for multi-agent games, in: International
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