Games can be analyzed at many levels, leading to different designs for matching logics: from very detailed to very global. I discuss several concrete examples to show the existing variety. This proliferation of logics raises an issue of finding one coherent overall logical perspective on games, which I will discuss in terms of translations and tracking. 

Here are the slides of the talk.

Given a Markov decision process (MDP) M and a formula Phi, the strategy synthesis problem asks if there exists a strategy sigma such that the resulting Markov chain M[sigma] satisfies Phi. This problem is known to be undecidable for the probabilistic temporal logic PCTL. We study a class of formulae that can be seen as a fragment of PCTL where a local, bounded horizon property is enforced all along an execution. Moreover, we allow for linear expressions in the probabilistic inequalities. This logic is at the frontier of decidability, depending on the type of strategies considered. In particular, strategy synthesis is shown to be decidable when strategies are deterministic while the problem is undecidable for arbitrary strategies.

Joint work with Benjamin Bordais, Damien Busatto-Gaston, and Jean-François Raskin.

Here are the slides of the talk.

Polarization has been intensifying in recent years and manifested in various facets of individuals' daily lives around the world. What was initially a phenomenon on the ideological political spectrum ("ideological polarization'') has since become a strongly emotional one based on one's social ties ("social'' or "affective polarization''), influencing individual and group actions largely based on their group identity ("social polarization''). We first investigate population-level network formation mechanisms that closely model the polarization seen empirically, notably in the United States, Canada, and many European countries. In doing so, we pay a particular close attention to how polarization undergoes a phase change from ideological to affective. We then introduce bipolar exogenous shocks to the ideologies of  a select few balanced numbers of individuals, denoted as the "political elites'', and allow ideologies of agents to evolve over time through social interactions. As a result, we find that in equilibrium, given that individuals place sufficient weight on the behaviors of their peers when optimizing their actions (the affective polarization parameter), disparate network communities emerge that partition the network and action space. 

Here are the slides of the talk.

Cops and Robbers is a popular graph game studied in both computer science and mathematics. In this talk, we examine scenarios where players must reason about uncertainties during gameplay. I will present a formal logical framework to model players' reasoning about the ever-changing situations and their knowledge updates. This framework also provides valuable insights into the dynamics of gameplay. This is joint work with Dazhu Li and Sujata Ghosh. 

Here are the slides of the talk.

Broadly speaking, the game of Hide and Seek serves as a concise model for interactions in pursuit-evasion environments. It has been extensively studied from a computational perspective, and in this talk, we will explore it from a logical perspective. Specifically, we will introduce several logics that are used to reason about the game at different levels and show how seemingly simple designs can significantly impact logical properties. Additionally, we will discuss the application of the logics to the game and of the techniques to relevant fields in logic. This talk is based on joint papers with Qian Chen, Sujata Ghosh, Fenrong Liu, Katsuhiko Sano and Yaxin Tu. 

Here are the slides of the talk.

First Order Modal Logic (FOML) extends First Order Logic (FO) with modal operators. FOML is suitable for many applications including planning, predicate epistemic logics among others. However, FOML is computationally unfriendly. Most of the decidable fragments of FO that are decidable (like the two variable fragment, guarded fragment, restriction to unary predicates) become undecidable when extended with modal operators. Until recently, the only known decidable fragment of FOML was the monodic fragment.  In this talk we will discuss some recent developments in identifying some decidable fragments of FOML. 

Here are the slides of the talk.

Artemov and Protopopescu (2016) introduced a Brouwer-Heyting-Kolmogorov (BHK) interpretation of the knowledge operator to define the intuitionistic epistemic logic IEL, where the axiom A -> KA is accepted but the axiom KA -> A is rejected. Under this umbrella of IEL, this talk investigates how we can interpret the notion of distributed knowledge in the literature on epistemic logic. Based on an interpretation, we provide a BHK interpretation of the distributed knowledge operator to define the intuitionistic epistemic logic with distributed knowledge DIEL. We construct a Hilbert system and a cut-free sequent calculus for DIEL and show that they are sound and complete for the intended Kripke semantics.

Here are the slides of the talk.