## Guarded actions (2004)

Citations: | 4 - 3 self |

### BibTeX

@MISC{Eijck04guardedactions,

author = {Jan Van Eijck},

title = {Guarded actions},

year = {2004}

}

### OpenURL

### Abstract

Guarded actions are changes with preconditions acting as a guard. Guarded action models are multimodal Kripke models with the valuations replaced by guarded actions. Call guarded action logic the result of adding product updates with guarded action models to PDL (propositional dynamic logic). We show that guarded action logic reduces to PDL. 1

### Citations

358 |
Propositional dynamic logic of regular programs
- Fischer, Ladner
- 1979
(Show Context)
Citation Context ...ction, using the program transformation lemma for the translation of [A, si][π]ϕ formulas. The translation points the way to appropriate reduction axioms, as follows. Take all axioms and rules of PDL =-=[8, 4, 7]-=-, plus the following reduction axioms: [A, s]⊤ ↔ ⊤ [A, s]p ↔ (pre(s) → p subA(s) ) [A, s]¬ϕ ↔ (pre(s) → ¬[A, s]ϕ) [A, s](ϕ1 ∧ ϕ2) ↔ ([A, s]ϕ1 ∧ [A, s]ϕ2) [A, si][π]ϕ ↔ n−1 � j=0 [T A ij (π)][A, sj]ϕ. ... |

237 | The logic of public announcements, common knowledge, and private suspicions
- Baltag, Moss, et al.
- 1998
(Show Context)
Citation Context ...Ag formulas σ, all LP,Ag programs π, all LP,Ag substitutions σ: M |=w ϕ σ iff M σ |=w ϕ. (w, w ′ ) ∈ [π σ ] M iff (w, w ′ M σ ) ∈ [π ] . 2sProof. Simultaneous induction on the structure of ϕ and π. ✷ =-=[1]-=- proposes to model epistemic actions as epistemic models, with valuations replaced by preconditions. Here, we extend this to guarded action models. Guarded action models for LP,Ag A guarded action mod... |

52 |
A completeness theorem in the modal logic of programs
- Segerberg
- 1977
(Show Context)
Citation Context ...ction, using the program transformation lemma for the translation of [A, si][π]ϕ formulas. The translation points the way to appropriate reduction axioms, as follows. Take all axioms and rules of PDL =-=[8, 4, 7]-=-, plus the following reduction axioms: [A, s]⊤ ↔ ⊤ [A, s]p ↔ (pre(s) → p subA(s) ) [A, s]¬ϕ ↔ (pre(s) → ¬[A, s]ϕ) [A, s](ϕ1 ∧ ϕ2) ↔ ([A, s]ϕ1 ∧ [A, s]ϕ2) [A, si][π]ϕ ↔ n−1 � j=0 [T A ij (π)][A, sj]ϕ. ... |

39 | Dynamic Logic. Foundations of Computing - Harel, Kozen, et al. - 2000 |

30 |
Benthem. Reduction Axioms for Epistemic Actions
- Kooi, van
- 2004
(Show Context)
Citation Context ...ded action logic the result of adding product updates with guarded action models to PDL (propositional dynamic logic). We show that guarded action logic reduces to PDL. 1 Introduction It was shown in =-=[6]-=- how generic updating with finite epistemic actions can be axiomatized in automata PDL [5, Chapter 10.3], and in [2] how generic updating with finite epistemic actions can be axiomatized in PDL. Below... |

20 |
The Completeness of Propositional Dynamic Logic
- Parikh
- 1978
(Show Context)
Citation Context ...ction, using the program transformation lemma for the translation of [A, si][π]ϕ formulas. The translation points the way to appropriate reduction axioms, as follows. Take all axioms and rules of PDL =-=[8, 4, 7]-=-, plus the following reduction axioms: [A, s]⊤ ↔ ⊤ [A, s]p ↔ (pre(s) → p subA(s) ) [A, s]¬ϕ ↔ (pre(s) → ¬[A, s]ϕ) [A, s](ϕ1 ∧ ϕ2) ↔ ([A, s]ϕ1 ∧ [A, s]ϕ2) [A, si][π]ϕ ↔ n−1 � j=0 [T A ij (π)][A, sj]ϕ. ... |

14 | Action emulation
- Eijck, Ruan
- 2004
(Show Context)
Citation Context ...date: Now suppose the update is the exchange of the cards that Alice and Bob are holding, but without showing the cards to Carol. The result of this update in the initial situation: 6 Further Work In =-=[3]-=-, action emulation was identified as the appropriate structural equivalence on action models for capturing the relation of having the same update effect. What is the appropriate structural equivalence... |

6 |
Reducing dynamic epistemic logic to PDL by program transformation
- Eijck
- 2004
(Show Context)
Citation Context ...). We show that guarded action logic reduces to PDL. 1 Introduction It was shown in [6] how generic updating with finite epistemic actions can be axiomatized in automata PDL [5, Chapter 10.3], and in =-=[2]-=- how generic updating with finite epistemic actions can be axiomatized in PDL. Below we give a reduction of generic updating with finite guarded action models to PDL. 2 PDL and Guarded Action Models L... |