## Computing Presuppositions and Implicatures in Mathematical Discourse

Citations: | 1 - 1 self |

### BibTeX

@MISC{Zinn_computingpresuppositions,

author = {Claus Zinn},

title = {Computing Presuppositions and Implicatures in Mathematical Discourse},

year = {}

}

### OpenURL

### Abstract

In any well-written mathematical discourse a certain amount of mathematical and meta-mathematical knowledge is presupposed and implied. We give an account on presuppositions and implicatures in mathematical discourse and describe an architecture that allows to e ectively interpret them. Our approach heavily relies on proof methods that capture common patterns of argumentation in mathematical discourse. This pragmatic information provides a high-level strategic discourse understanding and allows to compute the presupposed and implied information.

### Citations

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(Show Context)
Citation Context ...ly the Gricean conversational principles making his argument \such as is required, at the stage at which it occurs, by the accepted purpose or direction of the talk exchange in which you are engaged&q=-=uot; [Gri68-=-]. Now, how do the Gricean maxims of quantity, quality, relation and manner instantiate for mathematical discourse? Quality. Of course, a dening cornerstone of mathematics is to respect the Gricean ma... |

788 |
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(Show Context)
Citation Context ...contains indeed a proof for (2a) is completely ignored. Interpretation within the DRT Framework. In [vdS92], an approach for handling implicit information within Discourse Representation Theory (DRT) =-=[KR93]-=- is presented. Presuppositions are considered as anaphoric entities with semantic content. The cancelling of presuppositions (vide (1b)) is realised by binding it to its antecedent. If no suitable ant... |

608 | Interpretation as Abduction
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(Show Context)
Citation Context ... to the work of Hobbs et al., van der Sandt, and Asher and Lascarides. Then, we shortly discuss Lamport's proof presentation style and the technique of proof planning. Interpretation as Abduction. In =-=[HSAM90-=-], to interpret a natural language sentence its logical form has to be derived. The logical form comes from an assumed syntax /semantics interface, and will, in general, be semantically under-specied.... |

331 |
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(Show Context)
Citation Context ...rhetorically relate to prior discourse | into account. Asher and Lascarides aim to properly handle presuppositions within their SDRT framework (a considerable extension of DRT oering more structure) [=-=Ash93-=-]. They argue that their SDRT discourse update mechanism allows to eectively interface semantics with pragmatics. The discourse update procedure consists of relating a sentence to its prior discourse ... |

295 |
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(Show Context)
Citation Context ...less obscure without compromising their qualities. 3 2 Examples Before analysing mathematical discourse for its implicit content, have a look at the following example (taken from [AL98], adapted from =-=[vdS92]-=-): (1) a. If baldness is hereditary, then Jack's son is bald. b. If Jack has a son, then Jack's son is bald. The presupposition that Jack has a son (triggered by Jack's son) is entailed by (1a), but n... |

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(Show Context)
Citation Context ...orem or assumption used to logically derive the truth of some statement is relevant | informativeness depends on the proof reader and must be computed in function of his knowledge and interests. 2 In =-=[Lam93]-=-, Lamport gives the following example illustrating how the use of new syntactic constructions allowed for more brief and precise statements. The sentence There do not exist four positive integers, the... |

60 |
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(Show Context)
Citation Context ...ppeal to a wide audience of potential readers most of which are not experts in the subject being introduced. Here, the common ground 1 As the mathematician and Fields Medal recipient Thurston says in =-=[Thu94-=-]: \Within a subeld, people develop a body of common knowledge and known techniques. By informal contact, people learn to understand and copy each other's way of thinking, so that ideas can be explain... |

53 | The semantics and pragmatics of presupposition
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(Show Context)
Citation Context ... more expressive and less obscure without compromising their qualities. 3 2 Examples Before analysing mathematical discourse for its implicit content, have a look at the following example (taken from =-=[AL98]-=-, adapted from [vdS92]): (1) a. If baldness is hereditary, then Jack's son is bald. b. If Jack has a son, then Jack's son is bald. The presupposition that Jack has a son (triggered by Jack's son) is e... |

23 |
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(Show Context)
Citation Context ...en in the special purpose language of mathematics), and to leave much of a mathematical argument unsaid lead Frege to his Begrisschrift [Fre67] and Hilbert to his logischen Grundlagen der Mathematik [=-=Hil-=-22]: mathematics has to be expressed in a well-dened formal language using a well-dened set of formal reasoning schemes. In formal mathematical discourse, there is, by denition, no room for ambiguity.... |

15 | XBarnacle: Making theorem provers more accessible - Lowe, Duncan - 1997 |

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8 |
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(Show Context)
Citation Context ...goal-oriented, thus constraining the search space of possible inferences. Proof plans are an enabling technology for generating high-level proofs. The technique of proof planning has been invented by =-=[Bun88-=-]. This requires the analysis of families of related proofs, the identication of common patterns in them (called proof plans) and the use of these proof plans to guide future proofs from the same fami... |

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3 | How to Write a Proof
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(Show Context)
Citation Context ...calculi (although one can easily identify some of them). That is, steps are only justied by other steps without citing the inference rules being involved in the reasoning. For similar criticism, see [=-=RT96-=-]. 16 A selection of linguistic phenomena in mathematical discourse is discussed in [Zin99a, Zin99b]. 13 The Nature of Mathematical Discourse and Proof Planning. Mathematical discourse is dierent from... |

2 |
Elementary theory of numbers. Series in introductory mathematics
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(Show Context)
Citation Context ...sitions and implicatures. Depending on the context, Jack's son can both give rise to presuppositions and implicatures. The next discourse is taken from a standard textbook on elementary number theory =-=[LeV65]-=-; (2a) is the theorem to be proven, (2b-2f) its proof. (2) a. Every integer a > 1 can be represented as a product of one or more primes. b. The theorem is true for a = 2. c. Assume it to be true for 2... |

1 | On proof and progress in mathematics. Bulletin (New Series) of the American - Thurston - 1994 |