## Definites and the Proper Treatment of Rabbits (1999)

Venue: | in Proceedings of Inference in Computational Semantics, eds., Christof Monz and Maarten de Rijke |

Citations: | 4 - 1 self |

### BibTeX

@INPROCEEDINGS{Gardent99definitesand,

author = {Claire Gardent and Karsten Konrad},

title = {Definites and the Proper Treatment of Rabbits},

booktitle = {in Proceedings of Inference in Computational Semantics, eds., Christof Monz and Maarten de Rijke},

year = {1999},

pages = {53--69},

publisher = {ILLC}

}

### OpenURL

### Abstract

We argue that model generation programs, i.e., deduction systems that automatically compute the interpretations satisfying a given formula, can provide a procedural interpretation for semantic theories of natural language. We illustrate this claim by describing how the higher-order model generator Kimba interprets definite descriptions. 1 Introduction The concept of a Discourse Model has repeatedly been advocated as an essential component of natural language understanding. In cognitive psychology, discourse models have been used to explain inferences that people draw in understanding text [3]. In artificial intelligence, Webber proposes them as describing the situation/state which the speaker is talking about [21]. The understanding task then consists in an attempt by the listener to synthesize the appropriate discourse model. In the dynamic/DRT (Discourse Representation Theory [10]) trend of natural language semantics, it represents the context created by previous discourse and ...

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Citation Context ...goes back to Lewis [13] and refers to the process by which the listener adjust her assumptions by adding just enough information to remedy the violation of some felicity condition. 3 Second (cf. e.g. =-=[7]-=-), quantifiers may weaken and even annihilate uniqueness. Thus in (3a), the definite description the carrot is unique only per rabbit: there is one carrot per rabbit but there may be many rabbits and ... |

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Citation Context ...he speaker is talking about [21]. The understanding task then consists in an attempt by the listener to synthesize the appropriate discourse model. In the dynamic/DRT (Discourse Representation Theory =-=[10]-=-) trend of natural language semantics, it represents the context created by previous discourse and against which subsequent utterances will be interpreted [10, 11]. The crucial observation underlying ... |

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Citation Context ...tisfies the input specification. There is no post-processing of the semantic representation (as needed for instance in [2]) and no need for post-hoc consistency checking (as in the abductive approach =-=[8]-=-). Another crucial asset of the logical approach is that variables and quantifier scope are built-in notions. As we saw, this permits a straightforward treatment of such notoriously difficult cases as... |

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Citation Context ...s, although its constraint-based decision procedure makes it unsuitable for applications in finite mathematics where standard propositional methods such as the Davis-Putnam-Loveland-Logeman procedure =-=[DLL62]-=- are still among the best. 2.2.3 Minimal Model Generation For many applications, Kimba must restrict generation to models that fulfill certain conditions. A locally minimal model M is a model that has... |

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Citation Context ...o unique rabbit available. Intuitively, one would rather either find the sentence odd, or accommodate 1 the existence of a rabbit. (2) The rabbit sleeps. 1 The term "accommodation" goes back=-= to Lewis [13]-=- and refers to the process by which the listener adjust her assumptions by adding just enough information to remedy the violation of some felicity condition. 3 Second (cf. e.g. [7]), quantifiers may w... |

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Citation Context ...f definites The semantics of definite descriptions (e.g. the rabbit) is still an open question and there does not seem to be one accepted theory of definiteness. Here we will follow Russel's approach =-=[17]-=- and assume that the main characteristics of definites is (a restricted form of) uniqueness. Roughly (we will give a more precise analysis at the end of the section), a definite description supplies a... |

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Citation Context ...mic/DRT (Discourse Representation Theory [10]) trend of natural language semantics, it represents the context created by previous discourse and against which subsequent utterances will be interpreted =-=[10, 11]-=-. The crucial observation underlying the concept of a discourse model is (i) that discourse is about a limited/finite situation in the real, or in some hypothetical world and (ii) that this finite sit... |

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Citation Context ...efficient decision procedures for propositional logics. In recent years, the automated deduction community has developed a score of very efficient techniques for deciding propositional satisfiability =-=[JW90]-=-. As a result, finite model generators that use these techniques can solve certain combinatorial problems that are beyond the capabilities even of high-speed first-order theorem provers. Programs such... |

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Citation Context ...whereas (1b) is odd. (1) a. Jon has a rabbit. The rabbit is cute. b. Jon has two rabbits. The rabbit is cute. (*) As is well-known however, the Russellian approach is not without problems. First (cf. =-=[20]-=-), it asserts rather than presupposes uniqueness and as a result, declares a sentence such as (2) false in a context where there is no unique rabbit available. Intuitively, one would rather either fin... |

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Citation Context ... have been used to explain inferences that people draw in understanding text [3]. In artificial intelligence, Webber proposes them as describing the situation/state which the speaker is talking about =-=[21]-=-. The understanding task then consists in an attempt by the listener to synthesize the appropriate discourse model. In the dynamic/DRT (Discourse Representation Theory [10]) trend of natural language ... |

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Citation Context ...ng evidence, it might seem best to give up uniqueness. There are a number of proposals however which manage to reconcile uniqueness with reality and on which we shall base our computational treatment =-=[4, 5, 9]-=-. In such proposals, uniqueness is not solely determined by the property denoted by the common noun occurring in the definite description. Additional contextual information also plays a role. In Coope... |

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Citation Context ...ng evidence, it might seem best to give up uniqueness. There are a number of proposals however which manage to reconcile uniqueness with reality and on which we shall base our computational treatment =-=[4, 5, 9]-=-. In such proposals, uniqueness is not solely determined by the property denoted by the common noun occurring in the definite description. Additional contextual information also plays a role. In Coope... |

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Citation Context ...logical specifications. In recent years, finite model generators for classical first-order logics such as Finder [18] or Maze [15] have been used to answer several open problems in finite mathematics =-=[19]-=-. Model generation is considered one of the most successful areas of automated theorem proving. For our natural language application we use the finite model generator Kimba [12], a model generator for... |

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Citation Context ...is determined by the context of use. Kadmon [9] asserts that it can be "accommodated, implicated or contextually supplied". Other approaches identify the property with the context set of the=-= definite [5, 22]. In what -=-follows, we adopt a combination of these analyses and assume that the definite article the is assigned the following semantic representation: The j P 1 P 2 P 3 : j P 1 " P 2 j= 1sP 1 " P 2 `... |

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Citation Context ...-efficiently enumerates locally minimal models by employing a combination of model generation and theorem proving originally developed by Niemela for a form of propositional circumscriptive reasoning =-=[16]-=-. Unlike all other existing systems, Kimba does not expect its input in a standard first-order form, but generates models for type-logical specifications. This means that Kimba accepts semantic repres... |

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Citation Context ...tedly been advocated as an essential component of natural language understanding. In cognitive psychology, discourse models have been used to explain inferences that people draw in understanding text =-=[3]-=-. In artificial intelligence, Webber proposes them as describing the situation/state which the speaker is talking about [21]. The understanding task then consists in an attempt by the listener to synt... |

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Citation Context ...ation Model generators are programs that automatically generate models for satisfiable logical specifications. In recent years, finite model generators for classical first-order logics such as Finder =-=[18]-=- or Maze [15] have been used to answer several open problems in finite mathematics [19]. Model generation is considered one of the most successful areas of automated theorem proving. For our natural l... |

23 | Automatic Proofs and Counterexamples for Some Ortholattice
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Citation Context ...enerators are programs that automatically generate models for satisfiable logical specifications. In recent years, finite model generators for classical first-order logics such as Finder [18] or Maze =-=[15]-=- have been used to answer several open problems in finite mathematics [19]. Model generation is considered one of the most successful areas of automated theorem proving. For our natural language appli... |

18 | Inference and computational semantics
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Citation Context ... a locally minimal model results in a preference for bridging over accommodation. In the general case at least, this seems correct. Third, Kimba is higher-order. Hobbs et al. [8] and Blackburn et al. =-=[1]-=- also use a logic-based approach to computational semantics, but they remain first-order. The higher-order approach has the advantage that it permits a straightforward implementation of semantic theor... |

18 |
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Citation Context ...bbit was Welch. Fourth, the uniquely identifying property may not be given by the definite description itself, but might have to be somehow inferred from the surrounding context. In (5a) from Haddock =-=[6]-=-, there is no unique hat in the context but the definite description the hat refers successfully to the hat that contains a rabbit. In (5b), the rabbit actually refers to the rabbit in the hat (becaus... |

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Citation Context ...o a penalty in efficiency. 9 More generally, it is well known in the automated-reasoning community that higher-order specifications often allow more efficient forms of inference than first-order ones =-=[14]-=-. In particular, Kimba is able to quickly compute solutions for combinatorial problems whose standard first-order formalizations are not solvable within a reasonable time limit by many state-of-the-ar... |

10 |
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Citation Context ... logic formula, a model is directly generated which (i) is consistent and (ii) satisfies the input specification. There is no post-processing of the semantic representation (as needed for instance in =-=[2]-=-) and no need for post-hoc consistency checking (as in the abductive approach [8]). Another crucial asset of the logical approach is that variables and quantifier scope are built-in notions. As we saw... |

5 |
Presupposition and accomodation in update semantics
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Citation Context ... other implementation which could deal with the range of cases discussed in this paper. Three features of Kimba are here crucial. 4 Thanks to Bonnie Webber for this particular version of the example. =-=[23] prop-=-oses a similar example namely: "A man died in a car accident last night. The Amsterdam father of four had been drinking. 5 see http://www.ags.uni-sb.de/~konrad/kimba.html 8 First, model generatio... |

4 | A new translation from deduction into integer programming - HĂ¤hnle - 1992 |

3 |
What Can We Talk about Now
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Citation Context ...n used to explain inferences that people draw in understanding text [CBL78,JL83]. In artificial intelligence, Webber proposes them as describing the situation/state which the speaker is talking about =-=[Web82]-=-. The understanding task then consists in an attempt by the listener to synthesize the appropriate discourse model. In the dynamic/DRT (Discourse Representation Theory [Kam81]) trend of natural langua... |

1 |
a model generator for many-valued first-order logics
- Kimba
- 1999
(Show Context)
Citation Context ... in finite mathematics [19]. Model generation is considered one of the most successful areas of automated theorem proving. For our natural language application we use the finite model generator Kimba =-=[12]-=-, a model generator for a higher-order logical specification language. Given a specification OE and an initial signature \Sigma of first-order and higher-order constants, Kimba translates OE into a co... |