Studia Logica

, Volume 104, Issue 4, pp 705–739

Progression and Verification of Situation Calculus Agents with Bounded Beliefs

  • Giuseppe De Giacomo
  • Yves Lespérance
  • Fabio Patrizi
  • Stavros Vassos
Open Access

DOI: 10.1007/s11225-015-9626-z

Cite this article as:
De Giacomo, G., Lespérance, Y., Patrizi, F. et al. Stud Logica (2016) 104: 705. doi:10.1007/s11225-015-9626-z


We investigate agents that have incomplete information and make decisions based on their beliefs expressed as situation calculus bounded action theories. Such theories have an infinite object domain, but the number of objects that belong to fluents at each time point is bounded by a given constant. Recently, it has been shown that verifying temporal properties over such theories is decidable. We take a first-person view and use the theory to capture what the agent believes about the domain of interest and the actions affecting it. In this paper, we study verification of temporal properties over online executions. These are executions resulting from agents performing only actions that are feasible according to their beliefs. To do so, we first examine progression, which captures belief state update resulting from actions in the situation calculus. We show that, for bounded action theories, progression, and hence belief states, can always be represented as a bounded first-order logic theory. Then, based on this result, we prove decidability of temporal verification over online executions for bounded action theories.


Reasoning about actions Situation calculus Progression Online execution Verification of agent behaviors Mu-Calculus 

Funding information

Funder NameGrant NumberFunding Note
Ripartizione Diritto allo Studio, Università e Ricerca Scientifica of Provincia Autonoma di Bolzano-Alto Adige
  • VeryiSyncopated
European Commission
  • FP7-318338
Università La Sapienza di Roma
  • Spiritlets

Copyright information

© The Author(s) 2015

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (, which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Giuseppe De Giacomo
    • 1
  • Yves Lespérance
    • 2
  • Fabio Patrizi
    • 3
  • Stavros Vassos
    • 1
  1. 1.Sapienza University of RomeRomeItaly
  2. 2.York UniversityTorontoCanada
  3. 3.Free University of Bozen-BolzanoBozen-BolzanoItaly

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