DS-1993-05:
Hendriks, Herman
(1993)
*Studied Flexibility.*
Doctoral thesis, University of Amsterdam.

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## Abstract

In theories of formal grammar it has become customary to assume that

linguistic expressions belong to syntactic {\em categories}, whereas their

interpretations inhabit semantic {\em types}. {\em Studied Flexibility} is

an exploration of the consequences of this twofold assumption. Its starting

point are the basic ideas of logical syntax and semantics as they are found

in categorial grammar and lambda calculus, and it focuses on their

convergence in theories of linguistic syntax and semantics.

In Chapter 1, `Flexible Montague Grammar', it is argued that adoption of

flexible type assignment in Montuage grammar leads to an elegant account of

natural language scope ambiguities which arise in the pesence of

quantifying and coordinating expressions. Whereas Montague's original

fragments resort to the syntactic device of quantifying-in for representing

quantifier scope ambiguities, Cooper's alternative mechanism of

semantically storing quantifiers avoids the `unintuitive' syntactic aspects

of Montague's proposal -- at the expense, however, of complicating the

semantic component. Hence Cooper's conclusion that `wide scope quantification

seems to involve somewhat unpalatable principles either in the syntax or in

the semantics.' Flexible interpretation is an alternative which avoids the

unintuitive syntactic and semantic features of quantifying-in and storage.

This alternative involves giving up Montague's strategy of uniformly

assigning {\em all} members of a certain category the most complicated type

that is needed for {\em some} expression in that category. This strategy of

generalizing to the worst case fails, not because the worst case cannot

always be generalized to, but simply because there {\em is} no such case.

Instead, a reverse strategy is proposed which generalizes to the `best case'

on the lexical level. Generalized syntactic/semantic rules permit the

compounding of all `mutually fitting' translations, type-shifting rules

produce derived translations out of lexical and compound ones, and the

recursive nature of these rules reflects the empirical fact that there is no

worst case. The proposal is formalized as a fully explicit fragment of

flexible Montague grammar, which is shown to allow one to represent scope

ambiguities without special syntactic or semantic devices and, thus, to

involve a more adequate division of labour between the syntactic and semantic

component.

Chapter 2, `Compositionality and Flexibility', is concerned with determining

whether the flexible Montague grammar of Chapter 1 observes the principle of

compositionality. A detailed consideration of the implications of the

principle of compositionaliy for the organization of grammar fragments in

general leads to a formalization of the principle which differs from the one

presented by Janssen. It is argued that this formalization can be motivated

and applied more easily, and that it avoids some technical complications

inherent in Janssen's approach. The flexible Montague grammar of Chapter 1

turns out to be compositional under the `most intuitive' interpretation of

the principle, provided that the type-shifting derivation of translations is

explicitly incorporated into the grammar.

Chapter 3, `Lambek Semantics', deals with semantic interpretation in the

Lambek calculus {\bf L}, of which Lambek established the syntactic

decidability. It presents and motivates an alternative, equivalent

formulation of the Van Benthem/Moortgat semantics for {\bf L}. In this

semantics, the interpretations of a grammatical expression are directly

determined by the proofs of its validity in the syntactic calculus. The

alternative formulation is used in a straightforward semantic version of

Lambek's {\em Cut} elimination theorem which entails that {\bf L} is

semantically decidable as well: the result of applying Lambek's {\em Cut}

elimination algorithm is a derivation which is semantically equivalent to

the original derivation. Moreover, it is shown that the calculus {\bf L} can

be further normalized to a calculus {\bf L*} that offers a solution to the

so-called `spurious ambiguity problem' -- the problem that different proofs

of a given sequent may yield one and the same semantic interpretation. In

{\bf L*}, each interpretation of a sequent corresponds to exactly one proof.

This solution is compared with (an explicit elaboration of) proposals by

Moortgat and Roorda, and applied in an extension of an encoding result of

Ponse.

Item Type: | Thesis (Doctoral) |
---|---|

Report Nr: | DS-1993-05 |

Series Name: | ILLC Dissertation (DS) Series |

Year: | 1993 |

Subjects: | Language Logic |

Depositing User: | Dr Marco Vervoort |

Date Deposited: | 14 Jun 2022 15:16 |

Last Modified: | 14 Jun 2022 15:16 |

URI: | https://eprints.illc.uva.nl/id/eprint/1962 |

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