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## Strong Completeness for Markovian Logics

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Citations: | 2 - 1 self |

### Citations

197 | Reasoning about knowledge and probability.
- Fagin, Halpern
- 1994
(Show Context)
Citation Context ...gics Markovian logics are multi-modal logics for semantics based on the three classes of Markov processes introduced in the previous section. They have been introduced and studied in various contexts =-=[1, 2, 14, 12, 19, 9, 4, 15]-=-. In addition to the boolean operators, these logics are equipped with modal operators of type Lr for rational numbers r that are used to approximate the numerical labels of the transitions. Intuitive... |

195 | Labelled Markov processes
- Desharnais
- 1999
(Show Context)
Citation Context ...ilities enter into the modalities. This logic can be stripped down to a very spartan core —just the modalities and finite conjunction— and still characterize bisimulation for labeled Markov processes =-=[5, 6]-=-. It is therefore tempting to understand this logic from a proof theoretic perspective. Recent papers [4, 11, 19] have established complete proof systems and prove finite model properties for similar ... |

114 | Interactive epistemology I: knowledge.
- Aumann
- 1999
(Show Context)
Citation Context ...eteness for Markovian Logics 3 eral case of the measurable polynomial functors on the category of measurable spaces considered in [11], but we do not have such a result yet. 2 Background Let Q0 = Q ∩ =-=[0, 1]-=-, Q + = Q ∩ [0, ∞), R0 = R ∩ [0, 1], and R + = R ∩ [0, ∞). 2.1 Measurable Spaces and Measures In this section we introduce a few concepts and results from measure theory that we will find useful. For ... |

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

40 | Interactive epistemology II: Probability.
- Aumann
- 1999
(Show Context)
Citation Context ...gics Markovian logics are multi-modal logics for semantics based on the three classes of Markov processes introduced in the previous section. They have been introduced and studied in various contexts =-=[1, 2, 14, 12, 19, 9, 4, 15]-=-. In addition to the boolean operators, these logics are equipped with modal operators of type Lr for rational numbers r that are used to approximate the numerical labels of the transitions. Intuitive... |

38 | Labelled Markov Processes - Panangaden - 2009 |

27 |
Stochastic Relations: Foundations for Markov Transition Systems
- Doberkat
- 2007
(Show Context)
Citation Context ...zes the transition from m to a state in N. The condition that θ is measurable is equivalent to the condition that for fixed N ∈ Σ, the function m ↦→ θ(m)(N) is measurable (see e.g. Proposition 2.9 of =-=[7]-=-). 4 Markovian Logics Markovian logics are multi-modal logics for semantics based on the three classes of Markov processes introduced in the previous section. They have been introduced and studied in ... |

21 |
Bisimulation through probablistic testing
- Larsen, Skou
- 1991
(Show Context)
Citation Context ...gics Markovian logics are multi-modal logics for semantics based on the three classes of Markov processes introduced in the previous section. They have been introduced and studied in various contexts =-=[1, 2, 14, 12, 19, 9, 4, 15]-=-. In addition to the boolean operators, these logics are equipped with modal operators of type Lr for rational numbers r that are used to approximate the numerical labels of the transitions. Intuitive... |

16 | Modular algorithms for heterogeneous modal logics
- Schröder, Pattinson
- 2007
(Show Context)
Citation Context ...extend these completeness theorems to the entire class of systems described as coalgebras of polynomial functors described by Goldblatt [11]. It is possible that the results of Pattinson and Schröder =-=[18]-=- will be useful for this. Though the focus of the present paper has been on probabilistic systems and Markovian logics, the techniques may well apply to any non-compact modal logic. We are investigati... |

14 |
A complete deductive system for probability logic.
- Zhou
- 2009
(Show Context)
Citation Context ...es and finite conjunction— and still characterize bisimulation for labeled Markov processes [5, 6]. It is therefore tempting to understand this logic from a proof theoretic perspective. Recent papers =-=[4, 11, 19]-=- have established complete proof systems and prove finite model properties for similar logics. Goldblatt in [11] presents a proof-theoretic analysis of the logic of T-coalgebras, where T is any polyno... |

13 |
A proof of the completeness theorem of Godel.
- Rasiowa, Sikorski
- 1950
(Show Context)
Citation Context ...sses defined on analytic spaces. 2.3 The Baire Category Theorem The Baire category theorem is a topological result with important applications in logic. It is used to prove the Rasiowa-Sikorski lemma =-=[17, 10]-=- which is crucial for this paper. A subset D of a topological space X is dense if its closure D is all of X. Equivalently, a dense set is one intersecting every nonempty open set. A set N ⊆ X is nowhe... |

11 | Deduction systems for coalgebras over measurable spaces.
- Goldblatt
- 2010
(Show Context)
Citation Context ...es and finite conjunction— and still characterize bisimulation for labeled Markov processes [5, 6]. It is therefore tempting to understand this logic from a proof theoretic perspective. Recent papers =-=[4, 11, 19]-=- have established complete proof systems and prove finite model properties for similar logics. Goldblatt in [11] presents a proof-theoretic analysis of the logic of T-coalgebras, where T is any polyno... |

5 |
On the role of the Baire category theorem in the foundations of logic
- Goldblatt
- 1985
(Show Context)
Citation Context ...sses defined on analytic spaces. 2.3 The Baire Category Theorem The Baire category theorem is a topological result with important applications in logic. It is used to prove the Rasiowa-Sikorski lemma =-=[17, 10]-=- which is crucial for this paper. A subset D of a topological space X is dense if its closure D is all of X. Equivalently, a dense set is one intersecting every nonempty open set. A set N ⊆ X is nowhe... |

5 | Stone duality for Markov processes.
- Kozen, Larsen, et al.
- 2013
(Show Context)
Citation Context ...strong completeness for each of the three logics. The contribution of this paper consists in the novelty of the proof method for strong completeness. We have used already these types of techniques in =-=[13]-=-, where we proved a Stone duality for PMPs. That result implies strong completeness for the logic for PMPs but the logical aspects were not spelled out in that paper; there we concentrated on the alge... |

5 | Continuous markovian logics - axiomatization and quantified metatheory
- Mardare, Cardelli, et al.
(Show Context)
Citation Context ...at maximally consistent sets exist for such logics and consequently, in the papers concerned with the strong completeness of the modal logics for Harsanyi type spaces [19, 21] or for Markov processes =-=[4, 15]-=- it had to be assumed that consistent sets can be extended to maximally consistent sets. The completeness theorems cited are contingent on this assumption. In this paper we reconsider the axiomatizati... |

5 |
Approximating markov processes through filtration. Theoretical Computer Science 446: 75–97
- Zhou, Ying
- 2012
(Show Context)
Citation Context ...tisfies Lindenbaum’s lemma. These logics are not compact and for proving the aforementioned results in [11] it is used a powerful infinitary axiom scheme named the Countable Additivity Rule (CAR). In =-=[21]-=- Zhou and Ying prove that such a logic is not strongly-complete in the absence of CAR. A feature of CAR is that it has an uncountable set of instances. This fact makes it difficult to prove that maxim... |

4 |
Radu Mardare. Continuous markovian logic - from complete axiomatization to the metric space of formulas
- Cardelli, Larsen
- 2011
(Show Context)
Citation Context ...es and finite conjunction— and still characterize bisimulation for labeled Markov processes [5, 6]. It is therefore tempting to understand this logic from a proof theoretic perspective. Recent papers =-=[4, 11, 19]-=- have established complete proof systems and prove finite model properties for similar logics. Goldblatt in [11] presents a proof-theoretic analysis of the logic of T-coalgebras, where T is any polyno... |

3 | Probability logic of finitely additive beliefs. - Zhou - 2010 |

1 |
and Mingsheng Ying. Approximating Markov processes through filtration
- Zhou
(Show Context)
Citation Context ...tisfies Lindenbaum’s lemma. These logics are not compact and for proving the aforementioned results in [11] it is used a powerful infinitary axiom scheme named the Countable Additivity Rule (CAR). In =-=[21]-=- Zhou and Ying prove that such a logic is not strongly-complete in the absence of CAR. A feature of CAR is that it has an uncountable set of instances. This fact makes it difficult to prove that maxim... |