Related papers: (Mechanical) Reasoning on Infinite Extensive Games
In this paper, we introduce a system called GamePad that can be used to explore the application of machine learning methods to theorem proving in the Coq proof assistant. Interactive theorem provers such as Coq enable users to construct…
Reasoning about real number expressions in a proof assistant is challenging. Several problems in theorem proving can be solved by using exact real number computation. I have implemented a library for reasoning and computing with complete…
We look at intensionality from the perspective of computation. In particular, we review how game semantics has been used to characterize the sequential functional processes, leading to powerful and flexible methods for constructing fully…
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive…
Game semantics provides an interactive point of view on proofs, which enables one to describe precisely their dynamical behavior during cut elimination, by considering formulas as games on which proofs induce strategies. We are specifically…
We introduce operational semantics into games. And based on the operational semantics, we establish a full algebra of games, including basic algebra of games, algebra of concurrent games, recursion and abstraction. The algebra can be used…
This work presents a requirement analysis for collaborative dialogues among medical experts and an inquiry dialogue game based on this analysis for incorporating explainability into multiagent system design. The game allows experts with…
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…
Dialogue games are a two-player semantics for a variety of logics, including intuitionistic and classical logic. Dialogues can be viewed as a kind of analytic calculus not unlike tableaux. Can dialogue games be an effective foundation for…
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 describe our experience implementing a broad category-theory library in Coq. Category theory and computational performance are not usually mentioned in the same breath, but we have needed substantial engineering effort to teach Coq to…
On grounds of the discussed material, we reason about possible future development of quantum game theory and its impact on information processing and the emerging information society. The idea of quantum artificial intelligence is…
Game Logic is an excellent setting to study proofs-about-programs via the interpretation of those proofs as programs, because constructive proofs for games correspond to effective winning strategies to follow in response to the opponent's…
Quantum games have attracted much attention in recent years due to their ability to solve decision-making dilemmas. The aim of this study is to extend previous work on quantum games by introducing a Mathematica package QEGS (Quantum…
We investigate a family of rule-based logics. The focus is on very expressive languages. We provide a range of characterization results for the expressive powers of the logics and relate them with corresponding game systems.
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…
Main papers on quantum games are written by physicists for physicists, and the inevitable exploitation of physics jargon may create difficulties for mathematicians or economists. Our goal here is to make clear the physical content and to…
This paper studies quantum refereed games, which are quantum interactive proof systems with two competing provers: one that tries to convince the verifier to accept and the other that tries to convince the verifier to reject. We prove that…
Interactive-proof games model the scenario where an honest party interacts with powerful but strategic provers, to elicit from them the correct answer to a computational question. Interactive proofs are increasingly used as a framework to…
We discuss the question of if and how undecidability might be translatable into physics, in particular with respect to prediction and description, as well as to complementarity games.