Related papers: Compositionality and String Diagrams for Game Theo…
In work of Fokkinga and Meertens a calculational approach to category theory is developed. The scheme has many merits, but sacrifices useful type information in the move to an equational style of reasoning. By contrast, traditional proofs…
The ability to compose parts to form a more complex whole, and to analyze a whole as a combination of elements, is desirable across disciplines. This workshop bring together researchers applying compositional approaches to physics, NLP,…
Game theory provides a mathematical framework for analysing strategic situations involving at least two players. Normal-form games model situations where the players simultaneously pick their moves. In this thesis we explore the strategic…
We use a reformulation of compositional game theory to reunite game theory with game semantics, by viewing an open game as the System and its choice of contexts as the Environment. Specifically, the system is jointly controlled by $n \geq…
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,…
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…
Quantum game theory is the study of strategic behavior by agents with access to quantum technology. Broadly speaking, this technology can be employed in either of two ways: As part of a randomization device or as part of a communications…
Inductions and game semantics are two useful extensions to traditional logic programming. To be specific, inductions can capture a wider class of provable formulas in logic programming. Adopting game semantics can make logic programming…
In category theory, the use of string diagrams is well known to aid in the intuitive understanding of certain concepts, particularly when dealing with adjunctions and monoidal categories. We show that string diagrams are also useful in…
This is a draft of the textbook/monograph that presents computability theory using string diagrams. The introductory chapters have been taught as graduate and undergraduate courses and evolved through 8 years of lecture notes. The later…
This essay gives a self-contained introduction to quantum game theory, and is primarily oriented to economists with little or no acquaintance with quantum mechanics. It assumes little more than a basic knowledge of vector algebra. Quantum…
Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical…
Semantic composition remains an open problem for vector space models of semantics. In this paper, we explain how the probabilistic graphical model used in the framework of Functional Distributional Semantics can be interpreted as a…
Causality and game theory are two influential fields that contribute significantly to decision-making in various domains. Causality defines and models causal relationships in complex policy problems, while game theory provides insights into…
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…
Following our recent development of a compositional model checking algorithm for Markov decision processes, we present a compositional framework for solving mean payoff games (MPGs). The framework is derived from category theory,…
Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic…
A communication game consists of distributed parties attempting to jointly complete a task with restricted communication. Such games are useful tools for studying limitations of physical theories. A theory exhibits preparation contextuality…
Game theoretical techniques have recently become prevalent in many engineering applications, notably in communications. With the emergence of cooperation as a new communication paradigm, and the need for self-organizing, decentralized, and…
The present paper introduces a novel notion of `(effective) computability', called viability, of strategies in game semantics in an intrinsic (i.e., without recourse to the standard Church-Turing computability), non-inductive and…