Abstract
This chapter expounds basic notions. An elementary action system is a triple consisting of the set of states, the transition relation between states, and a family of binary relations defined on the set of states. The elements of this family are called atomic actions. Each pair of states belonging to an atomic action is a possible performance of this action. This purely extensional understanding of atomic actions is close to dynamic logic. Compound actions are defined as sets of finite sequences of atomic actions. Thus compound actions are regarded as languages over the alphabet whose elements are atomic actions. This chapter is concerned with the problem of performability of actions and the algebraic structure of the set of compound actions of the system. The theory of probabilistic action systems is also outlined.
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- 1.
Strictly speaking, the adopted set-theoretic formalism represents everyday situations in which actions and states of affairs are involved in much the same way as probabilistic spaces model random events.
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© 2015 Springer Science+Business Media Dordrecht
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Czelakowski, J. (2015). Elementary Action Systems. In: Freedom and Enforcement in Action. Trends in Logic, vol 42. Springer, Dordrecht. https://doi.org/10.1007/978-94-017-9855-6_1
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DOI: https://doi.org/10.1007/978-94-017-9855-6_1
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Publisher Name: Springer, Dordrecht
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Online ISBN: 978-94-017-9855-6
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