Game logic and its applications. II
type: Item
instance of: scholarly article
title: Game logic and its applications. II
zbMATH Open document ID: 0871.03030
DOI: 10.1023/A:1004975724824
author: Mamoru Kaneko
author: Takashi Nagashima
published in: Studia Logica
publication date: 1997-09-29T00:00:00Z
review text: This is a sequel to our development of the game logic framework. In Part I [the authors, ibid. 57, No. 2-3, 325-354 (1996; Zbl 0858.03035)] of this paper, we presented the framework in the Hilbert style formulation and showed some applications of the framework to game theory -- the epistemic axiomatization of Nash equilibrium and the undecidability on the playability of a game. To obtain the undecidability results (Theorems 6.2 and 6.3 of Part I), we used a result called term existence theorem. This is a metatheorem stating an evaluation of provability on an existential formula. The Hilbert style formulation is convenient in presentation, but is difficult in managing an evaluation of such provability. In general, it would be better to reformulate the Hilbert style formulation into a Gentzen style sequent calculus for the purpose of evaluating provability. This paper provides a Gentzen style formulation of the game logic framework, and proves the cut-elimination theorem. As its application, we prove the term existence theorem used in Part I.
Mathematics Subject Classification ID: 03C75
Mathematics Subject Classification ID: 03F05
Mathematics Subject Classification ID: 91A99
Mathematics Subject Classification ID: 03B45
zbMATH DE Number: 1019354
zbMATH Keywords: infinitary predicate KD4
zbMATH Keywords: common knowledge
zbMATH Keywords: undecidability of playability
zbMATH Keywords: game logic
zbMATH Keywords: Nash equilibrium
zbMATH Keywords: evaluation of provability
zbMATH Keywords: Gentzen style sequent calculus
zbMATH Keywords: cut-elimination
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1019354