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## Efficient Parsing with the Product-Free Lambek Calculus

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### Citations

714 |
The Syntactic Process
- Steedman
- 2000
(Show Context)
Citation Context ...anguage sentences. The most prominent of these formalisms has been context free grammars (CFGs) but a collection of formalisms known as categorial grammar (CG) (Ajdukiewicz, 1935; Dowty et al., 1981; =-=Steedman, 2000-=-) has received interest because of some significant advantages over CFGs. First, CG is inherently lexicalized due to the fact that all of the variation between grammars is captured by the lexicon. Thi... |

576 | The mathematics of sentence structure
- Lambek
- 1958
(Show Context)
Citation Context ...ic derivation. This leads to a semantical form which is easily extractable from the syntactic parse. A large number of CG formalisms have been introduced including, among others, the Lambek calculus (=-=Lambek, 1958-=-) and Combinatory Categorial Grammar (CCG) (Steedman, 2000). Of these, CCG has received the most zealous computational attention. Impressive results have been achieved culminating in the state-of-the-... |

186 | Parsing the WSJ using CCG and log-linear models - Clark, Curran - 2004 |

150 | The convergence of mildly context-sensitive grammar formalisms
- Joshi, Shanker, et al.
- 1991
(Show Context)
Citation Context ...entry of Bos and Markert (2005). The appeal of CCG can be attributed to the existence of efficient parsing algorithms for it and the fact that it recognizes a mildly context-sensitive language class (=-=Joshi et al., 1989-=-), a language class more powerful than the context free languages (CFLs) that has been argued to be necessary for natural language syntax. The Lambek calculus provides an ideal contrast between CCG an... |

114 |
Die syntaktische KonnexitÃ¤t
- Ajdukiewicz
- 1935
(Show Context)
Citation Context ...lored in the past for parsing natural language sentences. The most prominent of these formalisms has been context free grammars (CFGs) but a collection of formalisms known as categorial grammar (CG) (=-=Ajdukiewicz, 1935-=-; Dowty et al., 1981; Steedman, 2000) has received interest because of some significant advantages over CFGs. First, CG is inherently lexicalized due to the fact that all of the variation between gram... |

88 | Recognising textual entailment with logical inference - Bos, Markert - 2005 |

71 |
Resource Logics. Proof-Theoretical Investigations
- Roorda
- 1991
(Show Context)
Citation Context ... Proof structures correspond to proofs under certain conditions and our conditions will be based on the semantic term of the proof given to us by the Curry-Howard isomorphism for the Lambek calculus (=-=Roorda, 1991-=-). To do this, we interpret left rules as functional application and right rules as functional abstraction of lambda terms. Under this interpretation, the semantic term obtained from the proof structu... |

51 | Multimodal linguistic inference
- Moortgat
- 1995
(Show Context)
Citation Context ... for three reasons. First, it is the foundation of all other non-associative variants of the Lambek calculus including the original Lambek calculus (Lambek, 1958) and the multi-modal Lambek calculus (=-=Moortgat, 1996-=-). Second, the calculus with product is NP-complete (Pentus, 2006), while the sequent derivability in the product-free fragment is still unknown. Finally, the only connectives included are / and \, wh... |

41 |
Formal Philosophy: Selected Papers of
- Montague
- 1974
(Show Context)
Citation Context ...in Montague câ—‹ 2008. Licensed under the Creative Commons Attribution-Noncommercial-Share Alike 3.0 Unported license (http://creativecommons.org/licenses/by-nc-sa/3.0/). Some rights reserved. grammar (=-=Montague, 1974-=-), allowing the semantic derivation to exactly parallel the syntactic derivation. This leads to a semantical form which is easily extractable from the syntactic parse. A large number of CG formalisms ... |

33 | Lambek calculus is NP-complete
- Pentus
- 2006
(Show Context)
Citation Context ...sociative variants of the Lambek calculus including the original Lambek calculus (Lambek, 1958) and the multi-modal Lambek calculus (Moortgat, 1996). Second, the calculus with product is NP-complete (=-=Pentus, 2006-=-), while the sequent derivability in the product-free fragment is still unknown. Finally, the only connectives included are / and \, which are the same connectives as in CCG, providing a corpus for fu... |

24 | Product-free Lambek calculus and context-free grammars
- Pentus
- 1997
(Show Context)
Citation Context ...as been argued to be necessary for natural language syntax. The Lambek calculus provides an ideal contrast between CCG and CFGs by being a CG formalism like CCG but by recognizing the CFLs like CFGs (=-=Pentus, 1997-=-). The primary goal of this paper is to provide an algorithm for parsing with the Lambek calculus and to sketch its correctness. Furthermore, a time bound of O(n 5 ) will be shown for this algorithm w... |

4 | Proving Theorems of the Second Order Lambek Calculus - Aarts - 1994 |

4 | Switch Graphs for parsing Type Logical Grammars - Carpenter, Morrill - 2005 |