Skip to main content

Elementary Action Systems

  • Chapter
  • First Online:
Freedom and Enforcement in Action

Part of the book series: Trends in Logic ((TREN,volume 42))

  • 583 Accesses

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.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD 54.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Notes

  1. 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.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Janusz Czelakowski .

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer Science+Business Media Dordrecht

About this chapter

Cite this chapter

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

Download citation

Publish with us

Policies and ethics