A dynamic logic of agency. II: Deterministic \({\mathcal{DLA}}\), coalition logic, and game theory
type: Item
instance of: scholarly article
title: A dynamic logic of agency. II: Deterministic \({\mathcal{DLA}}\), coalition logic, and game theory
zbMATH Open document ID: 1211.03039
author: Emiliano Lorini
published in: Journal of Logic, Language and Information
publication date: 2010-10-06T00:00:00Z
review text: The author specialises the framework of \(\mathcal{DLA}\), the \textit{Dynamic Logic of Agency}, developed in [\textit{A. Herzig} and \textit{E. Lorini}, ibid. 19, No.~1, 89--121 (2010; Zbl 1189.03025)] to \(\mathcal{DDLA}\), \textit{Deterministic} \(\mathcal{DLA}\). The language is the same and extends that of modal logic with formulas of the form \(\langle i\!:\!a\rangle\varphi\), where \(i\) and \(a\) belong to finite sets whose members denote \textit{agents} and \textit{actions}, respectively. Intuitively, \(\langle i\!:\!a\rangle\varphi\) expresses that ``agent \(i\) performs action \(a\) and \(\varphi\) holds afterwards''. In any given member of a set \(W\) of possible worlds, all agents concurrently perform a unique action, which leads into another possible world. This condition allows one to define a \textit{next time} operator: \(\varphi\) will be true at the next state if, denoting by \(A\) the set of actions and by \(i\) an arbitrary agent, \(\bigwedge_{a\in A}\neg\langle i\!:\!a\rangle\neg\varphi\) holds. An equivalence relation on \(W\) partitions \(W\) into sets of worlds that share a common history\, but might lead later to different worlds depending on the actions performed by all agents in parallel. A key constraint of \(\mathcal{DLA}\) is that, given possible worlds \(w_1\), \dots, \(w_n\) belonging to the same equivalence class, where \(n\) is the number of agents, and given actions \(a_1\), \dots, \(a_n\), where, for all \(j\in\{1,\dots,n\}\), \(a_j\) is the action performed by the \(j\)th agent in world \(w_j\), there exists a possible world \(w\) in the same equivalence class as \(w_1\), \dots, \(w_n\) such that, for all \(j\in\{1,\dots,n\}\), the \(j\)th agent performs action \(a_j\) in \(w\). \(\mathcal{DDLA}\) adds to \(\mathcal{DLA}\) a principle of \textit{joint determinism}, which states that if two distinct worlds \(w\) and \(w'\) are in the same equivalence class, then some agent performs a different action from \(w\) than from \(w'\). …
reviewed by: Éric Martin
Mathematics Subject Classification ID: 03B45
Mathematics Subject Classification ID: 03B42
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T42
Mathematics Subject Classification ID: 91A80
zbMATH DE Number: 5796449
zbMATH Keywords: coalition logic
zbMATH Keywords: reasoning about actions
zbMATH Keywords: joint actions
zbMATH Keywords: coalition capabilities
zbMATH Keywords: agent preferences
zbMATH Keywords: game theory
MaRDI profile type: Publication
full work available at URL: s10849-009-9104-y
OpenAlex ID: W2045282924
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DOI: 10.1007/S10849-009-9104-Y
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description: scientific article; zbMATH DE number 5796449