Related papers: Game Comonads & Generalised Quantifiers
Homomorphisms between relational structures play a central role in finite model theory, constraint satisfaction and database theory. A central theme in quantum computation is to show how quantum resources can be used to gain advantage in…
This paper presents equational-based logics for proving first order properties of programming languages involving effects. We propose two dual inference system patterns that can be instanciated with monads or comonads in order to be used…
In this paper we will discuss scoring play games. We will give the basic definitions for scoring play games, and show that they form a well defined set, with clear and distinct outcome classes under these definitions. We will also show that…
We consider the class of "well-tempered" integer-valued scoring games, which have the property that the parity of the length of the game is independent of the line of play. We consider disjunctive sums of these games, and develop a theory…
This paper has two parts. The first is concerned with a variant of a family of games introduced by Holy and Schlicht, that we call \emph{Welch games}. Player II having a winning strategy in the Welch game of length $\omega$ on $\kappa$ is…
In this paper, we introduce a notion of generalized potential games that is inspired by a newly developed theory on generalized gradient flows. More precisely, a game is called generalized potential if the simultaneous gradient of the loss…
In 1901, Bouton proved that a winning strategy of the game of Nim is given by the bitwise XOR, called the nim-sum. But, why does such a weird binary operation work? Led by this question, this paper introduces a categorical reinterpretation…
A large branch of explainable machine learning is grounded in cooperative game theory. However, research indicates that game-theoretic explanations may mislead or be hard to interpret. We argue that often there is a critical mismatch…
We generalize Banica's construction of the quantum isometry group of a metric space to the class of quantum metric spaces in the sense of Kuperberg and Weaver. We also introduce quantum isometries between two quantum metric spaces, and we…
Candogan et al. (2011) provide an orthogonal direct-sum decomposition of finite games into potential, harmonic and nonstrategic components. In this paper we study the issue of decomposing games that are strategically equivalent from a…
Finite games in normal form and their mixed extensions are a corner stone of noncooperative game theory. Often generic finite games and their mixed extensions are considered. But the properties which one expects in generic games and the…
We study the class of potential games that are also graphical games with respect to a given graph $G$ of connections between the players. We show that, up to strategic equivalence, this class of games can be identified with the set of…
The use of Extended Logics to replace ordinary second order definability in Kleene's {\em Ramified Analytical Hierarchy} is investigated. This mirrors a similar investigation of Kennedy, Magidor and V\"a\"an\"anen \cite{KeMaVa2016} where…
Arboreal categories, introduced by Abramsky and Reggio, axiomatise categories with tree-shaped objects. These categories provide a categorical language for formalising behavioural notions such as simulation, bisimulation, and…
Game semantics and winning strategies offer a potential conceptual bridge between semantics and proof systems of logics. We illustrate this link for hybrid logic -- an extension of modal logic that allows for explicit reference to worlds…
The aim of this work is to put together two novel concepts from the theory of integrable billiards: billiard ordered games and confocal billiard books. Billiard books appeared recently in the work of Fomenko's school, in particular of V.…
In the present paper, based on the previous work (Part I), we present a game semantics for the intensional variant of intuitionistic type theory that refutes the principle of uniqueness of identity proofs and validates the univalence axiom,…
We consider graphical games as introduced by Kearns et al. (2001). First we analyse the interaction of graphicality with a notion of strategic equivalence of games, providing a minimal complexity graphical description for games. Then we…
For any abstract elementary class (AEC) ${\bf K}$ with $\lambda=LS({\bf K})$, the following holds: 1. $K$ has an axiomatization in $L_{(2^\lambda)^+,\lambda^+}$, allowing game quantification. If ${\bf K}$ has arbitrarily large models, the…
We look at substructural calculi from a game semantic point of view, guided by certain intuitions about resource conscious and, more specifically, cost conscious reasoning. To this aim, we start with a game, where player I defends a claim…