## Partial realization in dynamic justification logic

Venue: | Logic, Language, Information and Computation, 18th International Workshop, WoLLIC 2011 |

Citations: | 5 - 4 self |

### BibTeX

@INPROCEEDINGS{Bucheli_partialrealization,

author = {Samuel Bucheli and Roman Kuznets and Thomas Studer},

title = {Partial realization in dynamic justification logic},

booktitle = {Logic, Language, Information and Computation, 18th International Workshop, WoLLIC 2011},

year = {},

pages = {35--51},

publisher = {Springer}

}

### OpenURL

### Abstract

Abstract. Justification logic is an epistemic framework that provides a way to express explicit justifications for the agent’s belief. In this paper, we present OPAL, a dynamic justification logic that includes term operators to reflect public announcements on the level of justifications. We create dynamic epistemic semantics for OPAL. We also elaborate on the relationship of dynamic justification logics to Gerbrandy–Groeneveld’s PAL by providing a partial realization theorem. 1

### Citations

181 |
Bisimulations on Planet Kripke
- Gerbrandy
- 1999
(Show Context)
Citation Context ...w ⊩ [p] ⇑(c1 · c2) : p. ⊓⊔ 4 Modal Public Announcement Logic In this section, we recall some of the basic definitions and facts concerning the Gerbrandy–Groeneveld modal logic of public announcements =-=[12, 13, 18]-=-. Definition 15 (PAL Language). The language of PAL consists of the formulas A ∈ Fml □,[·] formed by the grammar A ::= p | ¬A | (A → A) | □A | [A]A p ∈ Prop The language Fml □ of modal formulas withou... |

166 |
Logics of public communications
- Plaza
- 1989
(Show Context)
Citation Context ...tics for OPAL. We also elaborate on the relationship of dynamic justification logics to Gerbrandy–Groeneveld’s PAL by providing a partial realization theorem. 1 Introduction Public announcement logic =-=[14, 13]-=- describes how public announcements affect an agent’s belief (knowledge). It is a subarea of dynamic epistemic logic [18], which studies the relationship between belief (knowledge) and communication i... |

108 | Reasoning about information change
- Gerbrandy, Groeneveld
- 1997
(Show Context)
Citation Context ...tics for OPAL. We also elaborate on the relationship of dynamic justification logics to Gerbrandy–Groeneveld’s PAL by providing a partial realization theorem. 1 Introduction Public announcement logic =-=[14, 13]-=- describes how public announcements affect an agent’s belief (knowledge). It is a subarea of dynamic epistemic logic [18], which studies the relationship between belief (knowledge) and communication i... |

58 | The logic of proofs, semantically
- Fitting
- 2005
(Show Context)
Citation Context ...lary 8 (Constructive Necessitation). For any formula A, if ⊢ A, then there is a ground term t such that ⊢ t : A. 3 Semantics We adapt the Kripke-style semantics for Justification Logic due to Fitting =-=[9]-=-. A similar semantics for JPAL was presented in [7]. Our semantics uses Kripke models augmented by an evidence function that relates each world–term pair (w, t) to a set of formulas E(w, t) that the t... |

56 |
Dynamic Epistemic Logic, volume 337 of Synthese Library
- Ditmarsch, Hoek, et al.
- 2007
(Show Context)
Citation Context ...ng a partial realization theorem. 1 Introduction Public announcement logic [14, 13] describes how public announcements affect an agent’s belief (knowledge). It is a subarea of dynamic epistemic logic =-=[18]-=-, which studies the relationship between belief (knowledge) and communication in general. The effect of a public announcement of statement A is represented by a formula [A]B that means B holds after t... |

46 | Justified common knowledge
- Artemov
(Show Context)
Citation Context ... formal epistemology. Justifications can be employed, for instance, to tackle the logical omniscience problem [4], to analyze several classical epistemic puzzles [2, 3], and to study common knowledge =-=[1, 8]-=-. It is natural to ask how public announcements factor into the reasoning of the agent. Public announcement logic describes how the beliefs change, but not why. The aim of this paper is to suggest way... |

32 | The logic of justification
- Artemov
- 2008
(Show Context)
Citation Context ...y not be an option unless the agent is omniscient. In this paper, we consider beliefs rather than knowledge, hence we concentrate on Gerbrandy– Groeneveld’s logic PAL. The idea of justification logic =-=[2]-=- is to formalize reasons for the agent’s belief. Instead of □A used in the modal language to state that the agent believes A, in justification logic, a specific reason for belief is given—t : A says t... |

22 |
On explicit counterparts of modal logics
- Brezhnev
- 2000
(Show Context)
Citation Context ...ed in the term !t either. Remark 5. The announcement-free fragment of OPAL (the first four axioms with σ = ε, rule MP, and rule AN, restricted to cn : C) is the well-known justification logic J4 (see =-=[5]-=-). We will consider not only OPAL but also JPAL (see [7] for details), which does not include the two term operations ⇑ and ⇓. Definition 6 (JPAL Deductive System). The axioms of JPAL are the axioms o... |

17 | Logical omniscience as a computational complexity problem
- Artemov, Kuznets
- 2009
(Show Context)
Citation Context ...he agent’s belief provides a novel approach to several problems of multi-agent systems and formal epistemology. Justifications can be employed, for instance, to tackle the logical omniscience problem =-=[4]-=-, to analyze several classical epistemic puzzles [2, 3], and to study common knowledge [1, 8]. It is natural to ask how public announcements factor into the reasoning of the agent. Public announcement... |

9 | Dynamic Epistemic Logic with Justification
- Renne
- 2008
(Show Context)
Citation Context ...t from the already mentioned [7], not much work has been done so far to combine justification logic and dynamic epistemic logic. A notable exception is Renne’s research about introducing new evidence =-=[15]-=- and eliminating unreliable evidence [16] in the framework of justification logic. He also studied the effect certain announcements have on the expressivity of justification logic [17]. However, the m... |

8 | Justified belief change
- Bucheli, Kuznets, et al.
- 2010
(Show Context)
Citation Context ... mentions both regulations t and the demonstration of Ann’s elite card A. In principle, any of the three options can be used to model the situation. In our joint work with Bryan Renne and Joshua Sack =-=[7]-=-, we developed the logic JPAL based on option (A). In this paper, we will present a new logic OPAL based on option (B). We should, therefore, start by explaining why the simplicity of JPAL may not alw... |

7 | A syntactic realization theorem for justification logics
- Brünnler, Goetschi, et al.
- 2010
(Show Context)
Citation Context ... = xi does not occur in r(B). The following realization result for the logic K4 is due to Brezhnev [5]; the additional result about non-self-referentiality can be read off from the proof presented in =-=[6]-=-. Theorem 32 (Realization for K4). If A is a theorem of K4, then for any properly annotated version B of A, there is a realization function r such that r(B) is provable in J4. Additionally, r is non-s... |

7 | Justifications for common knowledge - Bucheli, Kuznets, et al. |

6 |
Realizations and LP
- Fitting
- 2007
(Show Context)
Citation Context ...se the standard realization method for the latter, and finally reverse the performed reduction on the justification side. This reversal process employs the replacement techniques developed by Fitting =-=[11]-=-. The closest analog of this method can be found in [10], where Fitting realizes S5 by reducing it to K45. However, there the reversal of the reduction is trivial. Extending this method to OPAL presen... |

5 | Tracking evidence
- Artemov
- 2010
(Show Context)
Citation Context ...al problems of multi-agent systems and formal epistemology. Justifications can be employed, for instance, to tackle the logical omniscience problem [4], to analyze several classical epistemic puzzles =-=[2, 3]-=-, and to study common knowledge [1, 8]. It is natural to ask how public announcements factor into the reasoning of the agent. Public announcement logic describes how the beliefs change, but not why. T... |

5 | The Realization Theorem for S5 A Simple, Constructive Proof
- Fitting
- 2011
(Show Context)
Citation Context ...inally reverse the performed reduction on the justification side. This reversal process employs the replacement techniques developed by Fitting [11]. The closest analog of this method can be found in =-=[10]-=-, where Fitting realizes S5 by reducing it to K45. However, there the reversal of the reduction is trivial. Extending this method to OPAL presented unexpected challenges, which we also discuss at the ... |

4 | Public communication in justification logic
- Renne
- 2011
(Show Context)
Citation Context ...ng new evidence [15] and eliminating unreliable evidence [16] in the framework of justification logic. He also studied the effect certain announcements have on the expressivity of justification logic =-=[17]-=-. However, the modal logic counterparts of those systems do not correspond to any traditional public announcement logic. Both JPAL from [7] and OPAL introduced here are intended as justification logic... |