Related papers: The Qualitative Collapse of Concurrent Games
Combinatorial games are widely used in finite model theory, constraint satisfaction, modal logic and concurrency theory to characterize logical equivalences between structures. In particular, Ehrenfeucht-Fraisse games, pebble games, and…
We present syntactic characterisations for the union closed fragments of existential second-order logic and of logics with team semantics. Since union closure is a semantical and undecidable property, the normal form we introduce enables…
Game comonads offer a categorical view of a number of model-comparison games central to model theory, such as pebble and Ehrenfeucht-Fra\"iss\'e games. Remarkably, the categories of coalgebras for these comonads capture preservation of…
We provide an overview of the hybrid compositional distributional model of meaning, developed in Coecke et al. (arXiv:1003.4394v1 [cs.CL]), which is based on the categorical methods also applied to the analysis of information flow in…
Categorical semantics of type theories are often characterized as structure-preserving functors. This is because in category theory both the syntax and the domain of interpretation are uniformly treated as structured categories, so that we…
We define game semantics for the constructive $\mu$-calculus and prove its equivalence to bi-relational semantics. As an application, we use the game semantics to prove that the $\mu$-calculus collapses to modal logic over the modal logic…
Combinatorial Game Theory(CGT)is a branch of Game Theory that has developed largely independently of Economic Game Theory (EGT), and is concerned with deep mathematical properties of two-player zero-sum games recursively defined over…
It has been shown that a functional interpretation of proofs in mathematical analysis can be given by the product of selection functions, a mode of recursion that has an intuitive reading in terms of the computation of optimal strategies in…
We apply ideas from abstract argumentation theory to study cooperative game theory. Building on Dung's results in his seminal paper, we further the correspondence between Dung's four argumentation semantics and solution concepts in…
Theory of Mind benchmarks for large language models typically produce aggregate scores without theoretical grounding, making it unclear whether high performance reflects strategic reasoning or surface-level heuristics. We introduce a…
We propose a simple yet rich model to extend the notions of Nash equilibria and correlated equilibria of strategic games to the quantum setting, in which we then study the relations between classical and quantum equilibria. Unlike the…
Sequential equilibrium is one of the most fundamental refinements of Nash equilibrium for games in extensive form. However, it is not defined for extensive-form games in which a player can choose among a continuum of actions. We define a…
We investigate quantitative extensions of modal logic and the modal mu-calculus, and study the question whether the tight connection between logic and games can be lifted from the qualitative logics to their quantitative counterparts. It…
We define solution concepts appropriate for computationally bounded players playing a fixed finite game. To do so, we need to define what it means for a \emph{computational game}, which is a sequence of games that get larger in some…
The overall aim of our research is to develop techniques to reason about the equilibrium properties of multi-agent systems. We model multi-agent systems as concurrent games, in which each player is a process that is assumed to act…
We present a unifying representation of computation as a two-player game between an \emph{Algorithm} and \emph{Nature}, grounded in domain theory and game theory. The Algorithm produces progressively refined approximations within a Scott…
Despite the impressive feats demonstrated by Reinforcement Learning (RL), these algorithms have seen little adoption in high-risk, real-world applications due to current difficulties in explaining RL agent actions and building user trust.…
In this paper we introduce a typed, concurrent $\lambda$-calculus with references featuring explicit substitutions for variables and references. Alongside usual safety properties, we recover strong normalization. The proof is based on a…
In the context of multi-player, general-sum games, there is an increasing interest in solution concepts modeling some form of communication among players, since they can lead to socially better outcomes with respect to Nash equilibria, and…
Using Sperner's lemma for modified partition of a simplex we will constructively prove the existence of a Nash equilibrium in a finite strategic game with sequentially locally non-constant payoff functions. We follow the Bishop style…