Related papers: Game semantics of universes
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…
Absolute Universes of combinatorial games, as defined in a recent paper by the same authors, include many standard short normal- mis\`ere- and scoring-play monoids. In this note we show that the class is categorical, by extending Joyal's…
We develop methods to formally describe and compare games, in order to probe questions of game structure and design, and as a stepping stone to predicting player behavior from design patterns. We define a grammar-like formalism to describe…
We introduce versions of game-theoretic semantics (GTS) for Alternating-Time Temporal Logic (ATL). In GTS, truth is defined in terms of existence of a winning strategy in a semantic evaluation game, and thus the game-theoretic perspective…
Combinatorial games lead to several interesting, clean problems in algorithms and complexity theory, many of which remain open. The purpose of this paper is to provide an overview of the area to encourage further research. In particular, we…
Quantum game theory offers a lot of interesting questions, and it is relevant to use the quantum information theory to resolve or improve games with lack of information : how to use the power of quantum entanglement to show the superiority…
The framework of graded semantics uses graded monads to capture behavioural equivalences of varying granularity, for example as found on the linear-time/branching-time spectrum, over general system types. We describe a generic…
This paper addresses several significant gaps in the theory of restricted mis\`ere play (Plambeck, Siegel 2008), primarily in the well-studied universe of dead-ending games, $\mathcal{E}$ (Milley, Renault 2013); if a player run out of moves…
Logic programming with fixed-point definitions is a useful extension of traditional logic programming. Fixed-point definitions can capture simple model checking problems and closed-world assumptions. Its operational semantics is typically…
Large language models (LLMs) offer a new empirical setting in which long-standing theories of linguistic meaning can be examined. This paper contrasts two broad approaches: social constructivist accounts associated with language games, and…
We present abstract complexity results about Coquand and Hyland-Ong game semantics, that will lead to new bounds on the length of first-order cut-elimination, normalization, interaction between expansion trees and any other dialogical…
A description of the environment cognition process by intelligent systems with a fixed set of system goals is suggested. Such a system is represented by the set of its goals only without any models of the system elements or the environment.…
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…
Interpretability has arisen as a key desideratum of machine learning models alongside performance. Approaches so far have been primarily concerned with fixed dimensional inputs emphasizing feature relevance or selection. In contrast, we…
Axioms are presented which encapsulate the properties satisfied by categories of games which form the basis of results on full abstraction for PCF and other programming languages, and on full completeness for various logics and type…
As a contribution to the challenge of building game-playing AI systems, we develop and analyse a formal language for representing and reasoning about strategies. Our logical language builds on the existing general Game Description Language…
Game semantics has proven to be a robust method to give compositional semantics for a variety of higher-order programming languages. However, due to the complexity of most game models, game semantics has remained unapproachable for…
Game theory is a powerful framework for reasoning about strategic interactions, with applications in domains ranging from day-to-day life to international politics. However, applying formal reasoning tools in such contexts is challenging,…
A framework for discussing relationships between different types of games is proposed. Within the framework, quantum simultaneous games, finite quantum simultaneous games, quantum sequential games, and finite quantum sequential games are…
Number games play a central role in alternating normal play combinatorial game theory due to their real-number-like properties (Conway 1976). Here we undertake a critical re-examination: we begin with integer and dyadic games and identify…