## MSc in Logic (2010)

Citations: | 1 - 0 self |

### BibTeX

@MISC{Wampler-doty10mscin,

author = {Matthew P. Wampler-doty and Prof Jan Van Eijck and Prof Frank and Veltman Contents},

title = {MSc in Logic},

year = {2010}

}

### OpenURL

### Abstract

under the supervision of Prof.dr J. F. A. K. van Benthem, and submitted to the Board of

### Citations

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Citation Context ...(b, B) ( ϕ 1 While this paper is considered seminal, it should be remarked that research into this subject began prior to it. Specifically, the phrase “explicit belief” appears to have its origins in =-=[Lev84]-=-. 2 In the proceeding discussion, we shall refer to noninferentially justified beliefs as basic beliefs or premises. 4We now provide motivation for the above definition. In the semantics presented, i... |

257 | The logic of public announcements, common knowledge and private suspicions
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Citation Context ...tions and easy to describe dynamics. We will focus on single agent DAL, however multi-agent DAL is also introduced in [vBV09]. 99Likewise, DAL also accommodates action model updates as introduced in =-=[BMS98]-=-. Since our purpose in investigating this framework is to understand how it accommodates explicit inference, we have chosen not to pursue these topics here. We begin by reviewing the grammars employed... |

190 | Modal Logic - Chagrov, Zakharyaschev - 1997 |

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123 | Dynamic Epistemic Logic - Ditmarsch, Hoek, et al. - 2007 |

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Citation Context ... however in this case evidently it would have to be M ⊆ ℘Φ×℘LK(Φ)×℘M, so apparently it would have to be a non-wellfounded set. This is somewhat natural, given a modal logic setting - see for instance =-=[BM96]-=- for an elaboration on these connections. Definition 1.0.154. Define by recursion the following two truth relations: First relation: M, w ⊩ p ⇐⇒ p ∈ V (w) M, w ⊩ ϕ ∧ ψ ⇐⇒ both M, w ⊩ ϕ and M, w ⊩ ψ M,... |

59 | The logic of proofs, semantically - FITTING - 2005 |

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15 |
Mastering Regular Expressions. O’Reilly
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Citation Context ...by casting assumptions into doubt only once: ( � + ϕ → �ϕ (2.1.12) Here + is taken from the syntax for regular expressions commonly used in computer science and UNIX programming to mean “one or more” =-=[Fri06]-=-. Similarly, we have assumed that discarding no assumptions is, in a way, vacuously casting assumptions into doubt. In light of this EviL also makes true the following: ( ϕ → �ϕ (2.1.13) Furthermore, ... |

14 |
Logics for resource-bounded agents
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- 2006
(Show Context)
Citation Context ...thor notes himself how his work compares to other awareness based approaches. Notably, his work is related to Ho Ngoc Duc’s logic [Duc95, Duc97, Duc01], Jago’s logic for agents with bounded resources =-=[Jag06]-=-, and van Benthem’s acts of realization [vB08]. V QL Kripke structures have two awareness relations. The first relation establishes whether the agent is aware of a particular fact, while the second es... |

12 | Logical omniscience vs. logical ignorance on a dilemma of epistemic logic - Duc |

11 |
Reflections on epistemic logic
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(Show Context)
Citation Context ... Justification In this document, we shall propose a logic that enforces a form of explicit justification of propositions agents believe. The hunt for logics of explicit justification was initiated in =-=[vB91]-=- 1 . One framework which has been proposed to achieve this is Justification Logic [AN05, Art07, Fit04, Fit05]. Alternative frameworks for reasoning about implicit/explicit information have also been p... |

8 | Inference and update
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Citation Context ...h has been proposed to achieve this is Justification Logic [AN05, Art07, Fit04, Fit05]. Alternative frameworks for reasoning about implicit/explicit information have also been proposed in [vBV09] and =-=[Vel09]-=-. We will discuss these other approaches in §5. To model beliefs with justifications, we shall modify the semantics of modal logic to incorporate certain basic beliefs, which we should interpret as no... |

4 | Resurrecting old-fashioned foundationalism - DePaul, ed - 2001 |

2 |
Continuous fragment of the mu-calculus
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Citation Context ... = ϕ and (ψ A ) B = ψ. Moreover, we have the following validities: ( ¬(ϕ B ) ↔ ϕ and ( ¬(ψ A ) ↔ ψ. 1 We were inspired to look at the fragment LA(Φ) by thinking about the continuous fragment of µ PML =-=[Fon08]-=-. 18The above duality is convenient, since it can be leveraged to transfer results proven for the fragment LA(Φ) to LB(Φ) and vice versa. With the above machinery in place, we can observe a natural c... |

2 |
Bisimulations on Planet Kripke. ILLC Dissertation Series
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Citation Context ...ems are discussed in [Vel09]. The semantics for V QL also supports modeling inference. The author chose to model inference using model updates, in the style of dynamic epistemic logic as pioneered in =-=[Ger98]-=-. Definition 5.2.142 (Model Deduction Update). For a V QL Kripke structure V = 〈W, R, V, Y, Z〉, and let ρ ∈ R(Φ) be a rule. Let Γ be the premises of ρ and let γ be the conclusion. Define Vρ := 〈W, R, ... |

2 | The information in intuitionistic logic. Synthese, 167(2):251–270, 2009. 110 Johan van Benthem. Modal Logic for Open Minds. Center for the Study of Language and Information - Benthem - 2010 |

2 |
Inference, promotion, and the dynamics of awareness. ILLC
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Citation Context ...amework which has been proposed to achieve this is Justification Logic [AN05, Art07, Fit04, Fit05]. Alternative frameworks for reasoning about implicit/explicit information have also been proposed in =-=[vBV09]-=- and [Vel09]. We will discuss these other approaches in §5. To model beliefs with justifications, we shall modify the semantics of modal logic to incorporate certain basic beliefs, which we should int... |

1 | Atiyah and Ian Grant Macdonald. Introduction to commutative algebra - Francis - 1994 |

1 |
Modal logic. Cambridge Univ Pr
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Citation Context ...so we shall focus on right to left. Assume that �K ϕ, then we know from completeness and the finite model property that there’s some finite model M = 〈W, V, R〉 and world w ∈ W such that M, w � ϕ (see =-=[BRV01]-=-, chapters 2 & 4 for details of these facts). Now let L(ϕ) be the proposition letters that occur as subformulae of ϕ, and let p : W ↩→ Φ\L(ϕ) be an injection. In other words p assigns fresh letters to... |

1 |
limited reasoning* 1
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(Show Context)
Citation Context ...re is more than one system that claims to model explicit and implicit knowledge. The idea behind the semantics of V QL is to equip Kripke structures with special awareness relations, as introduced in =-=[FH87]-=-. In [Vel09], the author notes himself how his work compares to other awareness based approaches. Notably, his work is related to Ho Ngoc Duc’s logic [Duc95, Duc97, Duc01], Jago’s logic for agents wit... |

1 | A logic of explicit knowledge. Logica Yearbook - Fitting - 2004 |

1 |
A problem about reference
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- 1981
(Show Context)
Citation Context ... logic may be seen found. This corresponds to a well known proposal for constructive semantics extended by Hilary Putnam, who suggests “To claim a statement is true is to claim it could be justified” =-=[Put81]-=-. Since our proposed Theorem Theorem (Theorem 2.1.12 from §2.1) equates �-boxed formulae with justification, we may leverage Putnam’s philosophical insight into a formal observation in EviL. The rest ... |

1 |
Merging observation and access in dynamic epistemic logic
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- 2008
(Show Context)
Citation Context ...er awareness based approaches. Notably, his work is related to Ho Ngoc Duc’s logic [Duc95, Duc97, Duc01], Jago’s logic for agents with bounded resources [Jag06], and van Benthem’s acts of realization =-=[vB08]-=-. V QL Kripke structures have two awareness relations. The first relation establishes whether the agent is aware of a particular fact, while the second establishes whether the agent is aware of a rule... |

1 | René Descartes. Descartes’ meditations. http://www.wright.edu/cola/descartes - Vietch, Manley, et al. - 2005 |