## MSc in Logic (2010)

### BibTeX

@MISC{Hamami10mscin,

author = {Yacin Hamami},

title = {MSc in Logic},

year = {2010}

}

### OpenURL

### Abstract

I would like to express my sincere gratitude to my supervisor Johan van Benthem for his guidance during all the period of the master thesis, for his precious comments and suggestions and for teaching the DEL project in January, with Davide Grossi, which provided me with the necessary background on dynamic epistemic logics to carry out this thesis project. I am also extremely grateful to Eric Pacuit, who accepted to co-supervise the master thesis, and who has supported and guided me during all the phases that led to the present thesis. I have enormously benefited from numerous discussions with Stefan Minica and Fernando Velazquez-Quesada on dynamic logics of questions and dynamic logics of inferences, and on the thesis project itself. I am grateful to them for their help and their comments that really contributed to the progression of the thesis project. I would like also to thank Emmanuel Genot who shared with me his expertise on the interrogative model of inquiry. I am thankful to Johan van Benthem, Eric Pacuit, Frank Veltman and Robert van Rooij for accepting to be members of the committee for the master thesis defense. Finally, I would like to thank my family, in particular my mother and Vanessa for all their support during the whole period of the master thesis. i Contents

### Citations

765 |
On the logic of theory change: Partial meet contraction and revision functions
- Alchourrón, Gärdenfors, et al.
- 1985
(Show Context)
Citation Context ... ∼ ⊆ W × W is the epistemic indistinguishability relation of the agent, 3. V : W → P(P) is an atomic valuation function indicating the atomic propositions that are true at each world, 4. P : W → (W ⇀ =-=[0, 1]-=-) 6 is a map such that for all w ∈ W , ∑ v∈dom(P (w)) P (w)(v) = 1, and which assigns a probability function at each world such that its domain is a non-empty subset of the set of possible worlds. The... |

482 |
Modal Logic
- Blackburn, Rijke, et al.
- 2001
(Show Context)
Citation Context ...eness result for EL with respect to the class of epistemic models: Theorem 1.1 (Completeness for EL). EL is strongly complete with respect to the class of epistemic models. Proof. See Blackburn et al =-=[5]-=-. 4 In all this thesis, we make the common assumption that the indistinguishability relation is an equivalence relation.Chapter 1. Introduction 9 1.2.2 Dynamic epistemic logic Epistemic logic describ... |

322 |
Knowledge in Flux
- Gärdenfors
- 1988
(Show Context)
Citation Context ...btained into a dynamic one, we end up with a dynamic partition decomposition of Q w.r.t. to (M, s) in which only occur yes-no questions about immediate subformulas of the answers to Q. 13 See [1] and =-=[9]-=- for a presentation of belief revision theory in the AGM-paradigm. 14 By a compound formula we mean a propositional formula which is not atomic.Chapter 4. Decomposing interrogative inquiry 77 The fol... |

300 |
First-Order Logic
- Smullyan
- 1968
(Show Context)
Citation Context ...leau method. [22, p. 48] We will now provide some background information on the tableau method in the propositional case. The presentation that we adopt is based on Smullyan’s unsigned semantic trees =-=[30]-=- (henceforth, semantic trees). These semantic trees are defined as follows: Definition 2.11 (Semantic tree). A semantic tree for γ ∈ I is a binary tree whose the nodes are labelled with formulas of th... |

254 | The Logic of Public Announcements, Common Knowledge and Private Suspicione
- Baltag, Moss, et al.
- 1998
(Show Context)
Citation Context ... [29] and independently by Gerbrandy and Groenveld [11]. PAL acts as a canonical example of the methodology of dynamic epistemic logics. A more general approach is the one of Baltag, Moss and Solecki =-=[2]-=- which provides a general account of multi-agent update through epistemic events. In this section, we will only present the formal bases of PAL. First of all, the language of public announcement logic... |

204 |
Knowledge and belief: an introduction to the logic of two notions
- Hintikka
- 1962
(Show Context)
Citation Context ...ogic. 1.2.1 Epistemic logic The emergence of epistemic logic is generally traced back to the seminal work of Hintikka in his book Knowledge and Belief: An Introduction to the Logic of the Two Notions =-=[15]-=-. In this book, Hintikka, combining ideas from von Wright with the newly developed possible world semantics, proposes for the first time a semantics for the notions of knowledge and belief. The main i... |

163 | Reasoning about knowledge and probability
- Fagin, Halpern
- 1994
(Show Context)
Citation Context ... [32, 33]. 1.2.3 Probabilistic epistemic logic Probabilistic epistemic logic (PEL for short) results from the encounter of epistemic logic and probability theory and originates from Fagin and Halpern =-=[8]-=- and Halpern and Tuttle [14]. The main idea is to provide the epistemic agent with degrees of belief or subjective probabilities. To this end, the language of epistemic logic is enriched in such a way... |

154 |
Studies on the Semantics of Questions and the Pragmatics of Answers
- Groenendijk, Stokhof
- 1984
(Show Context)
Citation Context ... has already been carried out in the study of questions and answers from the point of view of the semantics and pragmatics of natural language. In particular, Groenendijk and Stokhof have proposed in =-=[12]-=- an analysis of questions in terms of partitions which allows to define a notion of entailment for questions. This work has then been extended by Robert van Rooij in [39] and [40] who proposes an anal... |

108 | Reasoning about information change
- Gerbrandy, Groeneveld
- 1997
(Show Context)
Citation Context ...mplest one is the modification due to a public announcement represented in the so-called public announcement logic (PAL for short) developed by Plaza [29] and independently by Gerbrandy and Groenveld =-=[11]-=-. PAL acts as a canonical example of the methodology of dynamic epistemic logics. A more general approach is the one of Baltag, Moss and Solecki [2] which provides a general account of multi-agent upd... |

76 | Knowledge, probability, and adversaries
- Halpern, Tuttle
- 1993
(Show Context)
Citation Context ...tic epistemic logic Probabilistic epistemic logic (PEL for short) results from the encounter of epistemic logic and probability theory and originates from Fagin and Halpern [8] and Halpern and Tuttle =-=[14]-=-. The main idea is to provide the epistemic agent with degrees of belief or subjective probabilities. To this end, the language of epistemic logic is enriched in such a way that it can express the pro... |

74 |
Semantic Information
- Bar-Hillel, Carnap
- 1958
(Show Context)
Citation Context ...ied by van Benthem and Martinez [36] as information as range. In the quantitative approach, the notion of information that we consider is the one defined by Bar-Hillel and Carnap’s information theory =-=[4]-=-. 3.2.1 The semantic approach According to van Benthem and Martinez [36], the intuitive understanding of the notion of information as range can be summarized as follows: “The greater one’s range of op... |

41 | Merging frameworks for interaction
- Benthem, Gerbrandy, et al.
(Show Context)
Citation Context ...nquiring agent. Hintikka strongly suggests that game theory provides such a framework, but learning theory or framework merging temporal logic and dynamic epistemic logic such as the one developed in =-=[34]-=- might also be possible candidates.Chapter 3. Entailment, informativity and relevance 59 Decomposition of interrogative inquiries. In the following chapter, we will investigate how one can decompose ... |

28 |
Inquiry as Inquiry: A Logic of Scientific Discovery
- Hintikka
- 1999
(Show Context)
Citation Context ...ed to be observations and experiments. [22, pp. 161-162] 1 The two main references on the IMI are the volume 5 of Hintikka’s selected papers entitled Inquiry as Inquiry: a Logic of Scientific Inquiry =-=[22]-=- and Hintikka’s recent book (2007) entitled Socratic Epistemology, Explorations of Knowledge-Seeking by Questioning [25]. 1Chapter 1. Introduction 2 Thus, the general conceptual structure of the IMI ... |

28 |
Logical Dynamics of Information and Interaction
- Benthem
- 2011
(Show Context)
Citation Context ...t to the class of epistemic models: Theorem 1.2 (Completeness for PAL). The logic PAL is strongly complete with respect to the class of epistemic models. Proof. See Blackburn et al [5] or van Benthem =-=[32, 33]-=-. 1.2.3 Probabilistic epistemic logic Probabilistic epistemic logic (PEL for short) results from the encounter of epistemic logic and probability theory and originates from Fagin and Halpern [8] and H... |

22 | An Examination of Information Theory - Bar-Hillel - 1955 |

19 | What Is Abduction? The Fundamental Problem of Contemporary Epistemology - Hintikka - 1998 |

18 |
Logics of public announcements
- Plaza
- 1989
(Show Context)
Citation Context ...e modified in a lots of various ways. Maybe the simplest one is the modification due to a public announcement represented in the so-called public announcement logic (PAL for short) developed by Plaza =-=[29]-=- and independently by Gerbrandy and Groenveld [11]. PAL acts as a canonical example of the methodology of dynamic epistemic logics. A more general approach is the one of Baltag, Moss and Solecki [2] w... |

18 | Dynamic update with probabilities
- Benthem, Gerbrandy, et al.
- 2006
(Show Context)
Citation Context ...emic models explicit and formally precise. Such an enterprise is sometimes quiet difficult, witness for instance the definition of probabilistic update developed by van Benthem, Gerbrandy and Kooi in =-=[35]-=-. Thus, in such situations, it might be necessary to have these model operations precisely defined in order to investigate notions of informativity and relevance for questions and answers. 11 It will ... |

15 |
Benthem (Eds.), Handbook of Modal Logics
- Blackburn, Wolter, et al.
- 2006
(Show Context)
Citation Context ...emic range. 17 Here again it is crucial, for the same reason as for local explicit knowledge, to give up the coherence property for the sets of semantic trees entertained by the agent. 18 See [5] and =-=[6]-=- for a presentation of hybrid logic.Chapter 2. The IMI as a dynamic logic of questions and inferences 37 creation and elimination, into hybrid dynamic operators. To this end, we first need to transfo... |

15 | The stories of logic and information
- Benthem, Mart́ınez
- 2008
(Show Context)
Citation Context ...g notion of information considered. In the semantic approach, the notion of information that we adopt is the one lying at the heart of dynamic epistemic logics, identified by van Benthem and Martinez =-=[36]-=- as information as range. In the quantitative approach, the notion of information that we consider is the one defined by Bar-Hillel and Carnap’s information theory [4]. 3.2.1 The semantic approach Acc... |

13 |
Interrogative logic as a general theory of reasoning
- Hintikka, Halonen, et al.
- 2002
(Show Context)
Citation Context ... as questions, then the task amounts to provide a logical theory of inferences and questions. This is exactly what Hintikka and colleagues have done by developing the so-called interrogative logic in =-=[26]-=-. This interrogative logic is based on the tableau method for representing inferences, and on Hintikka’s own theory of questions and answers for representing questions: One kind of logic we clearly ne... |

8 |
Twelve Angry Men: A study on the fine-grain of announcements
- Grossi, Velázquez-Quesada
- 2009
(Show Context)
Citation Context ... the treatment of questions for non-logically omniscient agents. In this third section, we will 1 For recent developments on dynamic logics of questions see [37], for dynamic logics of inferences see =-=[13, 38, 41]-=-. 14Chapter 2. The IMI as a dynamic logic of questions and inferences 15 then try to precisely locate this problem and to propose an alternative treatment of questions in the case of non-logical omni... |

8 | Inference and update - Velazquez-Quesada - 2008 |

7 | Toward a dynamic logic of questions
- Benthem, Minică
- 2009
(Show Context)
Citation Context ...n inquiry. The main problem seems to lie in the treatment of questions for non-logically omniscient agents. In this third section, we will 1 For recent developments on dynamic logics of questions see =-=[37]-=-, for dynamic logics of inferences see [13, 38, 41]. 14Chapter 2. The IMI as a dynamic logic of questions and inferences 15 then try to precisely locate this problem and to propose an alternative tre... |

6 |
Dynamic epistemic logic
- Ditmarsch, Hoek, et al.
- 2007
(Show Context)
Citation Context ...(Logic PAL). The logic PAL is obtained by adding to the axiom system EL the following reduction axioms: 1. [!ψ]p ↔ ψ → p 2. [!ψ]¬ϕ ↔ ψ → ¬[!ψ]ϕ 5 For a recent textbook on dynamic epistemic logics see =-=[7]-=-.Chapter 1. Introduction 10 3. [!ψ](ϕ1 ∧ ϕ2) ↔ [!ψ]ϕ1 and [!ψ]ϕ2 4. [!ψ]Kiϕ ↔ ψ → Ki(ψ → [!ψ]ϕ). Then, we have the following completeness result for PAL with respect to the class of epistemic models:... |

6 |
Modal Logic for Open Minds. Center for the Study of Language and Information
- Benthem
- 2010
(Show Context)
Citation Context ...of epistemic model: Definition 1.2 (Epistemic models). Let P be a countable set of atomic propositions and N be a finite set of agents. An epistemic model is a tuple M = 〈W, {∼i}i∈N, V 〉 where: 3 See =-=[32]-=- for an up-to-date textbook on modal logic and epistemic logic.Chapter 1. Introduction 8 • W is a non-empty set of worlds, • ∼i ⊆ W ×W is a binary equivalence relation representing the epistemic indi... |

6 |
informativity and protocols
- Utility
(Show Context)
Citation Context ... and Stokhof have proposed in [12] an analysis of questions in terms of partitions which allows to define a notion of entailment for questions. This work has then been extended by Robert van Rooij in =-=[39]-=- and [40] who proposes an analysis of the notions of informativity and relevance for questions and answers using tools from information and decision theory. Thus, even if these works have been carried... |

5 | Is logic the key to all good reasoning - Hintikka - 1999 |

5 |
On the role of the research agenda in epistemic change
- Olsson, Westlund
- 2006
(Show Context)
Citation Context ... ′ Q . We are touching an important issue here which concerns the modification of an inquiry plan, or dynamic decomposition, during an inquiry. This issue has been investigated by Olsson and Westlund =-=[28]-=- in the AGM-paradigm of belief revision theory 13 . According to their perspective, a research agenda is a set of questions entertained by the inquirer. Then, their objective is to formalize how a res... |

4 | The Role of Logic in Argumentation - Hintikka - 1989 |

4 |
Erotetic Implications
- Wiśniewski
- 1994
(Show Context)
Citation Context ...lment and multiple-conclusion entailment: Definition 4.24 (Entailment). A set of d-wffs X entails a d-wff A if and only if A is true under each valuation in which all the d-wffs in X are true. 15 See =-=[42]-=- for detailed on the notion of erotetic implication and [43] for a presentation of the general program of erotetic logic.Chapter 4. Decomposing interrogative inquiry 80 Definition 4.25 (Multiple-conc... |

4 |
The Posing of Questions
- Wisniewski
- 1995
(Show Context)
Citation Context ...ntailment). A set of d-wffs X entails a d-wff A if and only if A is true under each valuation in which all the d-wffs in X are true. 15 See [42] for detailed on the notion of erotetic implication and =-=[43]-=- for a presentation of the general program of erotetic logic.Chapter 4. Decomposing interrogative inquiry 80 Definition 4.25 (Multiple-conclusion entailment). A set of d-wffs X multiple-conclusion en... |

3 |
Socratic Epistemology: Explorations of Knowledge Seeking by Questions
- Hintikka
- 2007
(Show Context)
Citation Context ...ka’s selected papers entitled Inquiry as Inquiry: a Logic of Scientific Inquiry [22] and Hintikka’s recent book (2007) entitled Socratic Epistemology, Explorations of Knowledge-Seeking by Questioning =-=[25]-=-. 1Chapter 1. Introduction 2 Thus, the general conceptual structure of the IMI is pretty simple: the inquirer aims to establish a certain conclusion C by making deductive and interrogative moves. 2 N... |

3 | Tell it like it is: Information flow in logic
- Benthem
(Show Context)
Citation Context ...ions of implicit and explicit knowledge. To this end, we will adopt the same approach as the one of dynamic logics of inferences, i.e., we will use the two-level semantic-syntactic format proposed in =-=[31]-=-. According to this approach, implicit knowledge is represented in the same way knowledge is traditionally represented in epistemic logic using possible-worlds semantics, and explicit knowledge is rep... |

3 | Comparing Questions and Answers: A Bit of Logic, a Bit of Language and Some Bits of Information. Available online: http://staff.science.uva.nl/ vanrooy/Sources.pdf (accessed on 8
- Rooij
- 2014
(Show Context)
Citation Context ...hof have proposed in [12] an analysis of questions in terms of partitions which allows to define a notion of entailment for questions. This work has then been extended by Robert van Rooij in [39] and =-=[40]-=- who proposes an analysis of the notions of informativity and relevance for questions and answers using tools from information and decision theory. Thus, even if these works have been carried out in o... |

2 |
Socratic Questioning, Logic and Rhetoric', Revue Internationale de Philosophie
- Hintikka
- 1993
(Show Context)
Citation Context ...ic presentation of the Socratic method. We will not discuss further Hintikka’s historical view on the interrogative method of reasoning and we invite the reader interested in these aspects to look at =-=[20]-=- and the volume 6 of Hintikka’s selected papers [24]. 1.2 Dynamic epistemic logics Dynamic epistemic logics is a generic term to denote a family of logics dealing with information change and resulting... |

2 |
Inference, promotion, and the dynamics of awareness. ILLC
- Benthem, Velázquez-Quesada
- 2009
(Show Context)
Citation Context ... the treatment of questions for non-logically omniscient agents. In this third section, we will 1 For recent developments on dynamic logics of questions see [37], for dynamic logics of inferences see =-=[13, 38, 41]-=-. 14Chapter 2. The IMI as a dynamic logic of questions and inferences 15 then try to precisely locate this problem and to propose an alternative treatment of questions in the case of non-logical omni... |

1 | The game of inquiry: the interrogative approach to inquiry and belief revision theory - Genot |

1 |
The logic of science as a model-oriented logic
- Hintikka
- 1984
(Show Context)
Citation Context ...ositional formulas. Such a question Q = (γ1, . . . , γk) is read as “Is it the case that γ1, or is it the case that γ2,. . . , or is it the case that γk?” 4 Among propositional questions, yes-no 2 In =-=[16]-=-, Hintikka explains what he means by model-oriented logic and argues that the logic of science shall be seen as a model-oriented logic. 3 We refer to this theory as Hintikka’s theory of questions. 4 N... |

1 | What is the logic of experimental inquiry - Hintikka - 1988 |

1 | Theory-ladenness of observations as a test case of kuhn’s approach to scientific inquiry - Hintikka - 1992 |

1 |
Analyses of Aristotle
- Hintikka
- 2004
(Show Context)
Citation Context ...discuss further Hintikka’s historical view on the interrogative method of reasoning and we invite the reader interested in these aspects to look at [20] and the volume 6 of Hintikka’s selected papers =-=[24]-=-. 1.2 Dynamic epistemic logics Dynamic epistemic logics is a generic term to denote a family of logics dealing with information change and resulting from the encounter of epistemic logic and dynamic m... |

1 |
Erotetic search scenarios
- Wiśniewski
(Show Context)
Citation Context ... on erotetic search scenarios in order to make a comparison with the notion of dynamic decomposition of questions. 4.4 Erotetic search scenarios In his 2003 paper entitled ‘Erotetic search scenarios’ =-=[44]-=-, Andrzej Wiśniewski investigates the mechanism of question decomposition, consisting in answering a principal question by asking small or operational questions, from the point of view of erotetic log... |