## Heads and Phrases. Type Calculus for Dependency and Constituent Structure (1991)

Venue: | Journal of Language, Logic and Information |

Citations: | 46 - 12 self |

### BibTeX

@INPROCEEDINGS{Moortgat91headsand,

author = {Michael Moortgat and Glyn Morrill},

title = {Heads and Phrases. Type Calculus for Dependency and Constituent Structure},

booktitle = {Journal of Language, Logic and Information},

year = {1991}

}

### Years of Citing Articles

### OpenURL

### Abstract

From a logical perspective, categorial type systems can be situated within a landscape of substructural logics --- logics with a structure-sensitive consequence relation. Research on these logics has shown that the inhabitants of the substructural hierarchy can be systematically related by embedding translations on the basis of structural modalities. The modal operators offer controlled access to stronger logics from within weaker ones by licensing of structural operations. Linguistic material exhibits structure in dimensions not covered by the standard structural rules. The purpose of this paper is to generalize the modalisation and licensing strategy to two such dimensions: phrasal structure and headedness. Phrasal domain-sensitive type systems capture the notion of constituent structure; constituency relaxation can be licensed via an associativity modality. The opposition between heads and non-heads introduces dependency structure, an autonomous dimension of linguistic structure wh...

### Citations

469 |
The mathematics of sentence structure
- Lambek
- 1958
(Show Context)
Citation Context ...sentations signify the same configurations. Different choices of structural rules give rise to different logics even while the logical rules are invariant. 1 The calculus of syntactic types of Lambek =-=[14]-=- (henceforth L) and Intuitionistic Logic (henceforth IL) occupy two extremes of a spectrum: the Lambek calculus has an empty set of structural rules, and thus is sensitive to all aspects of the list r... |

175 |
Labelled Deductive Systems
- Gabbay
- 1996
(Show Context)
Citation Context ...e-sensitivity can be raised without limit: the landscape has no end. A general framework for the study of structure-sensitive consequence relations is provided by Gabbay's Labelled Deductive Systems (=-=[9]-=-, [10]); see also Dunn's Gaggle theory, [8]). Linear logic and its relatives have become the focus of intensive study. Two themes of these investigations are especially relevant for the linguistic app... |

157 |
Logic for Computer Science: Foundations of Automatic Theorem
- Gallier
- 1986
(Show Context)
Citation Context ...ly, irrelevant assumptions are allowed by extending the Axiom sequent A ) A to \Delta; A ) A, under the set interpretation of the database. The structural rule of Weakening thus becomes implicit. See =-=[11]-=- or [21] for some discussion. As it has been described, the substructural landscape materializes by fixing attention on meta-logical notation. Once the basic point is grasped however, it is apparent t... |

136 |
The sound pattern of English. Harper and Row
- Chomsky, Halle
- 1968
(Show Context)
Citation Context ...e defined to be zero. Liberman and Prince actually increment all degrees by one in order to mimic the stress numbering of cyclic transformational treatment of stress assignment, cf. Chomsky and Halle =-=[4]-=-, which counts from one upwards. 11 In the metrical phonology literature the s-head is usually referred to as the distingished terminal element, DTE. A \Theta (B \Theta C) : \Gamma0+ A \Theta (B \Delt... |

120 |
Categorial Investigations: logical and linguistic aspects of the lambek calculus. Foris
- Moortgat
- 1988
(Show Context)
Citation Context ...l in the design of grammar architecture, and represent a challenge to simple monostratality, as in categorial grammar. Prosodically governed forms of restructuring such as that above are discussed in =-=[17]-=- from the perspective of the associative type calculus L, but full associativity of its nature fails to impose a preferred bracketing, being able in principle to resolve any form of mismatch between p... |

115 | On stress and linguistic rhythm
- Liberman, Prince
- 1977
(Show Context)
Citation Context ...endency It has already been pointed out that the Hoeksema interpretation of metrical trees assigns all distinct trees a distinct prosodic value. In the original interpretation of Liberman and Prince (=-=[16]-=-, p259) each leaf is assigned a degree of stress subordination equal to the depth of its lowest dominating w-node. 10 Under such an interpretation there are equations such as the following: a. (a + l ... |

109 |
On the calculus of syntactic types
- Lambek
- 1961
(Show Context)
Citation Context ...ly, we include a dimension of associativity. The associative type system L of [14] is ignorant of any notion of constituency. Withdrawal of the associativity assumption as for the type calculus NL of =-=[15]-=- introduces sensitivity to constituent domains. Instead of strings the well-formed inhabitants of types become hierarchically structured bracketed strings, i.e. trees. The regain of this constituent s... |

48 |
Gaggle theory: An abstraction of galois connections and residuations with applications to various logical operations
- Dunn
- 1991
(Show Context)
Citation Context ...the landscape has no end. A general framework for the study of structure-sensitive consequence relations is provided by Gabbay's Labelled Deductive Systems ([9], [10]); see also Dunn's Gaggle theory, =-=[8]-=-). Linear logic and its relatives have become the focus of intensive study. Two themes of these investigations are especially relevant for the linguistic application of type systems: (i) the decomposi... |

25 |
Categorial deductions and structural operations
- Morrill, Leslie, et al.
- 1990
(Show Context)
Citation Context ... 2 i A. 2 2 Notice that the ' !' modality (in our notation 2 ! ) of Linear Logic is in fact a combination of Reuse and Waste of resources, which in principle could be considered apart, as is done in (=-=[18]-=-, [1]) on linguistic grounds. ffl Reusability of resources [2 ! C] \Gamma; 2 ! A; 2 ! A; \Delta ) B \Gamma; 2 ! A; \Delta ) B (7) ffl Waste of resources \Gamma; \Delta ) B \Gamma; 2 ! A; \Delta ) B [2... |

21 |
Proof Figures and Structural Operators for Categorial Grammar
- Barry, Hepple, et al.
(Show Context)
Citation Context .... 2 2 Notice that the ' !' modality (in our notation 2 ! ) of Linear Logic is in fact a combination of Reuse and Waste of resources, which in principle could be considered apart, as is done in ([18], =-=[1]-=-) on linguistic grounds. ffl Reusability of resources [2 ! C] \Gamma; 2 ! A; 2 ! A; \Delta ) B \Gamma; 2 ! A; \Delta ) B (7) ffl Waste of resources \Gamma; \Delta ) B \Gamma; 2 ! A; \Delta ) B [2 ! W]... |

17 |
Sequent systems and groupoid models I
- Došen
- 1988
(Show Context)
Citation Context ...symbol, we have practically determined the future behaviour of the logical operations". The character of the various points in this landscape has already been quite well explored; see for example=-= [3] [5]-=-, [6], [22] [23]. The sequent presentation given above shows characterisation of a structuresensitive consequence relation by taking seriously the representation of a sequent antecedent and being full... |

15 |
Formulas-as-types for a hierarchy of sublogics of Intuistionistic Propositional Logic.' ms. Institut fur Philosophie
- Wansing
- 1990
(Show Context)
Citation Context ... have practically determined the future behaviour of the logical operations". The character of the various points in this landscape has already been quite well explored; see for example [3] [5], =-=[6], [22]-=- [23]. The sequent presentation given above shows characterisation of a structuresensitive consequence relation by taking seriously the representation of a sequent antecedent and being fully explicit ... |

10 |
Axiomatizability of Ajdukiewicz-Lambek Calculus by Means of Cancellation Schemes. Zeitschrift für mathematische Logik und Grundlagen der Mathematik
- Zielonka
- 1981
(Show Context)
Citation Context ... appr : A=B ffl B ! A appl : B ffl BnA ! A (21) appr \Gamma1 : A ! (A ffl B)=B appl \Gamma1 : B ! An(A ffl B) (22) The reader may recognize in (19), (20) and (21), (22) a slight variant of Zielonka's =-=[24]-=- axiomatization of Lambek's type calculus, which has the application arrows (21) and type lifting ((23) instead of (22)) as the characteristic axioms. The associative system L is obtained by adding th... |

9 |
A general theory of structured consequence relations
- Gabbay
- 1993
(Show Context)
Citation Context ...sitivity can be raised without limit: the landscape has no end. A general framework for the study of structure-sensitive consequence relations is provided by Gabbay's Labelled Deductive Systems ([9], =-=[10]-=-); see also Dunn's Gaggle theory, [8]). Linear logic and its relatives have become the focus of intensive study. Two themes of these investigations are especially relevant for the linguistic applicati... |

8 |
Resource Logics
- Roorda
- 1991
(Show Context)
Citation Context ...t proof search, one can move to a proof-net presentation as an optimal datastructure for sequent deductions. The relation between sequent calculus and proof nets for occurrence logics is discussed in =-=[20]-=-. We obtain proof nets with digital labelling from the sequent presentation above by adding a polarity label which distinguishes antecedent (`1') from succedent (`0') occurrences of types. [Ax] hA; 1;... |

5 |
Modal Logic as Metalogic
- Dosen
- 1992
(Show Context)
Citation Context ...l modalities or exponentials. The `of course' modality (`!') in Linear Logic does this for Contraction and Weakening. Kosta Dosen has investigated the modalization strategy in its generality, cf. his =-=[7]-=-. The common logical pattern of the modalities is outlined below. As to notation: we use a general modal operator 2, subscripted for specific structural operations, or unsubscripted for rules which ap... |

5 |
Sources and structures of linguistic prominence in English
- Oehrle
- 1988
(Show Context)
Citation Context ...\GammafflR] [ r sffi\Gamman; n] ) s [ffi\GammaL] n ) n id s ) s id [ r n; n\Gammaffls] ) s [\GammafflL] n ) n id s ) s id (60) Not all transitive verbs have the same neutral prosodic context. Oehrle (=-=[19]-=-) notes that (61) again has the object strongest, but the verb and not the subject is weakest. John passed Mary. (61) From figure 2, we see that the following lexical assignment is required. passed :=... |

2 |
Dependency and Constituency
- Barry, Piekering
- 1990
(Show Context)
Citation Context ... to root. The prominence assignments (which are in fact always total orderings) defined by this procedure are illustrated in Figure 1. That 8 Examples of such a derived notion of head can be found in =-=[2]-=-. A \Theta (B \Theta C) : 120 A \Theta (B \Delta C) : 102 A \Delta (B \Theta C) : 031 A \Delta (B \Delta C) : 013 R A \Theta (B \Theta C) A w 1sC C C C C s B \Theta C B w 10sC C C C C s C 00 R A \Thet... |

2 |
Formal properties of stress representations
- Hoeksema
- 1985
(Show Context)
Citation Context ...other as weak (w). It is thus a headed tree in our sense. Metrical trees specify a hierarchical organisation of localised stress assignments interpreted as prosodic prominence contours. The Hoeksema (=-=[13]-=-) interpretation that we shall now assume interprets each path in a metrical tree as a degree of stress subordination equal to the value of the binary numeral obtained by reading w as 1 and s as 0 fro... |

1 |
Functional completeness for subsystems of intuitionistic propositional logic'. Berichte der Gruppe Logik, Wissenstheorie und Information 10/90
- Wansing
- 1990
(Show Context)
Citation Context ... practically determined the future behaviour of the logical operations". The character of the various points in this landscape has already been quite well explored; see for example [3] [5], [6], =-=[22] [23]-=-. The sequent presentation given above shows characterisation of a structuresensitive consequence relation by taking seriously the representation of a sequent antecedent and being fully explicit about... |