## Action emulation (2004)

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Venue: | CWI and ILLC, Amsterdam & Department of Economics |

Citations: | 14 - 6 self |

### BibTeX

@INPROCEEDINGS{Eijck04actionemulation,

author = {Jan Van Eijck and Ji Ruan and Tomasz Sadzik},

title = {Action emulation},

booktitle = {CWI and ILLC, Amsterdam & Department of Economics},

year = {2004}

}

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### Abstract

Abstract. The effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models [3], now in widespread use (see [10] for a textbook treatment). There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models gives the same result (modulo bisimulation). But the converse turns out to be false: update models may have the same update effects without being bisimilar. We propose action emulation as a notion of structural equivalence more appropriate for action models, and generalizing standard bisimulation. It is proved that action emulation provides a full characterization of update effect, provided we confine attention to ‘smooth ’ action models. We also give a recipe for turning any action model into a smooth one with the same update effect. Together, this yields a simplification procedure for action models, and it gives designers of multi-agent systems a useful tool for comparing different ways of representing a particular communicative action. 1.

### Citations

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Citation Context ...eason about the effects of such communicative actions one needs a powerful logic that can (at least) express common knowledge, and the effects of communication on common knowledge. In epistemic logic =-=[12]-=- knowledge is represented with multi-agent Kripke models (or possible world models) that contain for each agent an accessibility relation pointing at the situations that the agent considers possible. ... |

360 |
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Citation Context ...gic the construction is based on the set of all sub-formulas of φ, but in PDL we have to be careful in the handling of formulas with complex modalities α, so we need so-called Fischer/Ladner closures =-=[13]-=-. DEFINITION 29. Let Σ be a set of LANG0 formulas. Then FL(Σ), the Fischer/Ladner closure of Σ, is the smallest set of formulas X that has Σ ⊆ X, that is closed under taking sub-formulas, and that sat... |

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Citation Context ...tion procedure can loop), extended with the (rather obvious) treatment of the modal operators. Since the case of both true and false is not excluded, we have in fact a Belnap-style four valued system =-=[4]-=-. For convenience, we work out the verification and falsification rules for ∨ and 〈i〉 from the definitions: A |=s φ1 ∨ φ2 if A |=s φ1 or A |=s φ2 A =| s φ1 ∨ φ2 if A =| s φ1 and A =| s φ2 A |=s 〈i〉φ i... |

238 | The logic of public announcements, common knowledge, and private suspicions
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Citation Context ...e effects of public announcements, private communications, deceptive messages to groups, and so on, can all be captured by a general mechanism of updating multi-agent models with update action models =-=[3]-=-, now in widespread use (see [10] for a textbook treatment). There is a natural extension of the definition of a bisimulation to action models. Surely enough, updating with bisimilar action models giv... |

164 |
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Citation Context ...mic Epistemic Logic (DEL) does: it introduces the representation of actions, and a method of updating a situation with these actions. For an overview of developments in these areas, consult Gerbrandy =-=[14]-=-, van Ditmarsch [9], van Benthem [5, 6], and Baltag, Moss and coworkers [3, 1, 2]. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is th... |

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Citation Context ... and a method of updating a situation with these actions. For an overview of developments in these areas, consult Gerbrandy [14], van Ditmarsch [9], van Benthem [5, 6], and Baltag, Moss and coworkers =-=[3, 1, 2]-=-. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic lo... |

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Citation Context ...t Gerbrandy [14], van Ditmarsch [9], van Benthem [5, 6], and Baltag, Moss and coworkers [3, 1, 2]. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of =-=[7]-=-, which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic logic [17, 16] with the programs interpreted as composite epistemic modalities, and with modal operators add... |

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Citation Context ...ifies φ in A”. Note that the clauses for truth and falsity of p and of [i]φ use the concept of logical consequence for the logic of Σ. The evaluation uses the strong Kleene scheme (invented by Kleene =-=[15]-=- to describe the behaviour of partial recursive functions, where the evaluation procedure can loop), extended with the (rather obvious) treatment of the modal operators. Since the case of both true an... |

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Citation Context ...rhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic logic =-=[17, 16]-=- with the programs interpreted as composite epistemic modalities, and with modal operators added for describing the effects of communicative actions (epistemic PDL with action modalities). The basic i... |

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Citation Context ... and a method of updating a situation with these actions. For an overview of developments in these areas, consult Gerbrandy [14], van Ditmarsch [9], van Benthem [5, 6], and Baltag, Moss and coworkers =-=[3, 1, 2]-=-. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic lo... |

28 |
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Citation Context ...rhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic logic =-=[17, 16]-=- with the programs interpreted as composite epistemic modalities, and with modal operators added for describing the effects of communicative actions (epistemic PDL with action modalities). The basic i... |

22 |
Logics for epistemic programs, Synthese 139
- Baltag, Moss
- 2004
(Show Context)
Citation Context ...f the appropriate notion of equivalence for action models. It may seem that generalizing bisimulations to action models in the obvious way to ‘precondition preserving bisimulation’, as is proposed in =-=[2]-=-, is the way to go. Definition 1.5 (Action bisimulation). Let A, B be L action models. Let ≡L be the appropriate equivalence notion for L. Then relation C ⊆ WA×WB is a L bisimulation if whenever mCn t... |

14 |
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Citation Context ...iple. Computation may be costly, for it involves satisfiability checks for conjunctions of preconditions, and the satisfiability problem for our language is the same as that for PDL: it is in EXPTIME =-=[8]-=-. Computation of minimal action models is important for epistemic model checking. In fact, the initial motivation ae.tex; 19/03/2008; 9:25; p.2of our quest was the need for a means to simplify action... |

13 |
Knowledge Games
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(Show Context)
Citation Context ...s a multiple pointed epistemic model, indicating that the actual world is among U. 1[4] proposes to model epistemic actions as epistemic models, with valuations replaced by preconditions. (See also: =-=[1, 2, 3, 5, 6, 7, 8, 9, 10]-=-.) Definition 2 (Action models for a given language L) Let a finite set of agents Ag and an epistemic language L be given. An action model for L is a triple A = (W, pre, R) where W is a set of action ... |

11 |
Language, logic, and communication
- Benthem
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(Show Context)
Citation Context ...troduces the representation of actions, and a method of updating a situation with these actions. For an overview of developments in these areas, consult Gerbrandy [14], van Ditmarsch [9], van Benthem =-=[5, 6]-=-, and Baltag, Moss and coworkers [3, 1, 2]. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt her... |

10 |
One is a lonely number: on the logic of communication
- Benthem
- 2002
(Show Context)
Citation Context ...troduces the representation of actions, and a method of updating a situation with these actions. For an overview of developments in these areas, consult Gerbrandy [14], van Ditmarsch [9], van Benthem =-=[5, 6]-=-, and Baltag, Moss and coworkers [3, 1, 2]. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of [7], which is the version of DEL that we will adopt her... |

8 | Logics of communication and change
- Benthem, Eijck, et al.
(Show Context)
Citation Context ...t Gerbrandy [13], van Ditmarsch [8], van Benthem [4, 5], and Baltag, Moss and coworkers [3, 1, 2]. Perhaps the most streamlined version of DEL so far is the logic of communication and change (LCC) of =-=[6]-=-, which is the version of DEL that we will adopt here. LCC is in fact propositional dynamic logic [15, 14] with the programs interpreted as composite epistemic modalities, and with modal operators add... |

6 |
a demo of epistemic modelling
- Eijck
- 2007
(Show Context)
Citation Context ...t for epistemic model checking. In fact, the initial motivation ae.tex; 19/03/2008; 9:25; p.2of our quest was the need for a means to simplify action models in the epistemic model checking tool DEMO =-=[11]-=-. The structure of the paper is as follows. In Section 2, we review the version of Dynamic Epistemic Logic we work with, motivate our choice, and define our basic notions. Section 3 gives a definition... |

1 |
Three partition refinement algorithms
- Kooi, Chance, et al.
- 2003
(Show Context)
Citation Context ...s a multiple pointed epistemic model, indicating that the actual world is among U. 1[4] proposes to model epistemic actions as epistemic models, with valuations replaced by preconditions. (See also: =-=[1, 2, 3, 5, 6, 7, 8, 9, 10]-=-.) Definition 2 (Action models for a given language L) Let a finite set of agents Ag and an epistemic language L be given. An action model for L is a triple A = (W, pre, R) where W is a set of action ... |