## Towards Dynamic Probabilistic Logics: A Survey and a Proposal (2002)

### BibTeX

@MISC{Ogata02towardsdynamic,

author = {Norihiro Ogata},

title = {Towards Dynamic Probabilistic Logics: A Survey and a Proposal},

year = {2002}

}

### OpenURL

### Abstract

In this paper, I will briefly survey probabilistic logics and investigate logics of probabilistic epistemic change, conjectures, and discovery of chances by resourcebounded agents in the sense of the limitation of the available data and its temporal instability, called dynamic probabilistic logic (DP rL), based on probabilistic dynamic logics and probabilistic Kripke systems, of which equivalence is defined by probabilistic bisimulation.

### Citations

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Citation Context ...a ϕ is a chance of achieving ψ. Formula 2 expresses that getting data ϕ must be a chance of achieving ψ. Formula 3 can also be regarded as expressing a Hidden Markov Model (HMM)(Rabiner & Juang 1986; =-=Rabiner 1989-=-; Charniak 1993). Probabilistic Kripke Systems (PKS) A P KS is an extension of a Kripke System, which is a reformulation of a Kripke model by using coalgebras, defined as follows. Definition 1 Let W b... |

894 | An Introduction to Hidden Markov Models
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Citation Context ...esses that getting data ϕ is a chance of achieving ψ. Formula 2 expresses that getting data ϕ must be a chance of achieving ψ. Formula 3 can also be regarded as expressing a Hidden Markov Model (HMM)(=-=Rabiner & Juang 1986-=-; Rabiner 1989; Charniak 1993). Probabilistic Kripke Systems (PKS) A P KS is an extension of a Kripke System, which is a reformulation of a Kripke model by using coalgebras, defined as follows. Defini... |

870 | Dynamic Logic
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(Show Context)
Citation Context ... rather I mean a kind of special situation that plays a role of a key of agents’ decision of thier future actions. In section 5, I will define this term more explicitly. dynamic logics (Feldman 1984; =-=Feldman & Harel 1984-=-; Kozen 1985) of probabilistic programs and probabilistic processes. Unfortunately, however, these probabilistic logics are not proposed for modeling the epistemic dynamics in terms of probability. In... |

582 |
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(Show Context)
Citation Context ...e of achieving ψ. Formula 2 expresses that getting data ϕ must be a chance of achieving ψ. Formula 3 can also be regarded as expressing a Hidden Markov Model (HMM)(Rabiner & Juang 1986; Rabiner 1989; =-=Charniak 1993-=-). Probabilistic Kripke Systems (PKS) A P KS is an extension of a Kripke System, which is a reformulation of a Kripke model by using coalgebras, defined as follows. Definition 1 Let W be a set, Φ a se... |

348 |
Measure theory
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Citation Context ...ution (or probability measure) on measurable space 〈X, A〉, written 2 A is a σ-algebra of X if (i) ø ∈ A, (ii) Xi ∈ A ⇒ ¯Xi(= X − Xi) ∈ A (complement), (iii) Xi ∈ A (n ≥ 1) ⇒ Ai ∈ A (countable union) (=-=Halmos 1950-=-). S∞ i=1µ ∈ D(X) or D(X, A), if it is a mesurable space, i.e., pair 〈X, A〉, satisfying the following conditions: (a) it is countably additive, i.e., if for every disjoint sequence {Xi}i∈I of sets su... |

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Citation Context ...reasoning in computer science logics, modal logic (Desharnais, Edalat, & Panangaden 1998; Jonsson, Larsen, & Yi 2001), epistemic logic (Halpern & Tuttle 1993), temporal logics (Lehmann & Shelah 1982; =-=Segala & Lynch 1994-=-; Bianco & de Alfaro 1995), and Copyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1 I do not intend that this term mean (objective) probability, ... |

225 | Model checking of probabilistic and nondeterministic systems - Bianco, Alfaro - 1995 |

104 |
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(Show Context)
Citation Context ...of special situation that plays a role of a key of agents’ decision of thier future actions. In section 5, I will define this term more explicitly. dynamic logics (Feldman 1984; Feldman & Harel 1984; =-=Kozen 1985-=-) of probabilistic programs and probabilistic processes. Unfortunately, however, these probabilistic logics are not proposed for modeling the epistemic dynamics in terms of probability. In this paper,... |

78 | Bisimulation for probabilistic transition systems: a coalgebraic approach, Theoretical Computer Science 221 - Vink, Rutten - 1999 |

73 | Knowledge, probability, and adversaries
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(Show Context)
Citation Context ...uthors (cf. (Adams 1998)) propose many systems of probabilistic reasoning in computer science logics, modal logic (Desharnais, Edalat, & Panangaden 1998; Jonsson, Larsen, & Yi 2001), epistemic logic (=-=Halpern & Tuttle 1993-=-), temporal logics (Lehmann & Shelah 1982; Segala & Lynch 1994; Bianco & de Alfaro 1995), and Copyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1... |

67 | W.: Probabilistic extensions of process algebras - Jonsson, Larsen, et al. - 2001 |

38 |
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(Show Context)
Citation Context ...gic have been one of the main tasks of logic. In mathematical logics or model theory, Keisler (Keisler 1985) proposes a logic of probability, in philosophical logics, since Carnap, many authors (cf. (=-=Adams 1998-=-)) propose many systems of probabilistic reasoning in computer science logics, modal logic (Desharnais, Edalat, & Panangaden 1998; Jonsson, Larsen, & Yi 2001), epistemic logic (Halpern & Tuttle 1993),... |

37 | A logical characterization of bisimulation for labeled Markov processes - Desharnais, Edalat, et al. - 1998 |

22 | Probability quantifiers - Keisler |

12 |
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(Show Context)
Citation Context ...ϕ?)(w, w) = . 0 otherwise The class of Γ-probabilistic Kripke models is denoted by P KS(Γ). As well as Kripke Systems, an equivalence among PKSs is characterized by bisimulation. Since Larsen & Skou (=-=Larsen & Skou 1991-=-), some authors have proposed the notion of probabilistic bisimulations. 10 The probabilistic bisimulation among PKSs is defined as follows. Definition 2 Let P = 〈W, e, ρ〉, Q = 〈U, f, σ〉 ∈ P KS(Γ), w ... |

10 |
A decidable propositional dynamic logic with explicit probabilities
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(Show Context)
Citation Context ...obability, but rather I mean a kind of special situation that plays a role of a key of agents’ decision of thier future actions. In section 5, I will define this term more explicitly. dynamic logics (=-=Feldman 1984-=-; Feldman & Harel 1984; Kozen 1985) of probabilistic programs and probabilistic processes. Unfortunately, however, these probabilistic logics are not proposed for modeling the epistemic dynamics in te... |

1 |
Reasoning with time and chance. Information and Control 53:165–198
- Lehmann, Shelah
- 1982
(Show Context)
Citation Context ...stems of probabilistic reasoning in computer science logics, modal logic (Desharnais, Edalat, & Panangaden 1998; Jonsson, Larsen, & Yi 2001), epistemic logic (Halpern & Tuttle 1993), temporal logics (=-=Lehmann & Shelah 1982-=-; Segala & Lynch 1994; Bianco & de Alfaro 1995), and Copyright c○ 2002, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 1 I do not intend that this term mean (obj... |