Freedom and enforcement in action. A study in formal action theory
type: Item
instance of: scholarly article
title: Freedom and enforcement in action. A study in formal action theory
zbMATH Open document ID: 1401.68007
DOI: 10.1007/978-94-017-9855-6
author: Janusz Czelakowski
published in: Trends in Logic -- Studia Logica Library
publication date: 2015-04-13T00:00:00Z
review text: Chapter 1 defines the notion of an \textit{elementary action system} as a triple of the form \((W,R,{\mathcal{A}})\) where \(R\) is a binary relation on \(W\), the set of \textit{states}, and \({\mathcal{A}}\) is a nonempty set of binary relations on \(W\) each of whose members is called an \textit{atomic action}. A number of examples are provided, one of which is washing a bed linen in an automatic washing machine (the following description is slightly adapted from the one provided). Let \(\alpha\), \(\beta\) and \(\gamma\) denote the sentences ``the bed linen is washed'', ``the linen is in the machine'', and ``the machine is turned on'', respectively. For all members \(\sigma\) of \(\{0,1\}^3\) of the form \(abc\), let \(w_\sigma\) be the state denoting the situation where \(\alpha\), \(\beta\), \(\gamma\) holds iff \(a\), \(b\), \(c\) are equal to 1, respectively. Then \(W\) is set to \(\bigl\{w_\sigma\mid\sigma\in\{0,1\}^3\bigr\}\). The relation \(R\) is meant to capture all transitions from one state to another that are not ruled out (because they are physically impossible, or unwanted, \dots). With this example, \(R\) is defined as a set of 14 elements, containing in particular \((w_{000},w_{010})\) -- if the bed linen is not washed, it is not in the machine and the machine is turned off, then one can put the bed linen in the machine -- and \((w_{011},w_{111})\) -- if the bed linen is not washed, it is in the machine and the machine is turned on, then the bed linen can get washed. As for \({\mathcal{A}}\), it is defined as the set consisting of the 5 actions meant to capture the actions of putting the bed linen into the machine, taking the bed linen out of the machine, turning the machine on, turning the machine off, and washing the bed linen, respectively, with for instance turning the machine on defined as the set consisting of the 4 pairs of the form \((w_{ab0},w_{ab1})\). A number of properties of elementary action systems are defined, in particular: {\par…
reviewed by: Éric Martin
Mathematics Subject Classification ID: 68-02
Mathematics Subject Classification ID: 68T01
Mathematics Subject Classification ID: 68T27
Mathematics Subject Classification ID: 68T30
zbMATH DE Number: 6424440
zbMATH Keywords: elementary action systems
zbMATH Keywords: situational action systems
zbMATH Keywords: ordered action systems
zbMATH Keywords: action and deontology
zbMATH Keywords: stit frames
zbMATH Keywords: knowledge models
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1007/978-94-017-9855-6
OpenAlex ID: W2483658324
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description: scientific article; zbMATH DE number 6424440