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k-valued non-associative Lambek categorial grammars are not learnable from strings

Denis Béchet, Annie Foret
2003 Proceedings of the 41st Annual Meeting on Association for Computational Linguistics - ACL '03  
Another interest of our construction is that it provides limit points for the whole hierarchy of Lambek grammars, including the recent pregroup grammars.  ...  We show that the class of rigid and kvalued NL grammars is unlearnable from strings, for each k; this result is obtained by a specific construction of a limit point in the considered class, that does not  ...  G 1 is a rigid (or 1-valued) grammar. Learning and Limit Points We now recall some useful definitions and known properties on learning.  ... 
doi:10.3115/1075096.1075141 dblp:conf/acl/BechetF03 fatcat:prsxfrccqnbfhc463ic5jsjuni

Some Classes of Regular Languages Identifiable in the Limit from Positive Data [chapter]

François Denis, Aurélien Lemay, Alain Terlutte
2002 Lecture Notes in Computer Science  
from Positive Data p. 63 Learning Probabilistic Residual Finite State Automata p. 77 Fragmentation: Enhancing Identifiability p. 92 On Limit Points for Some Variants of Rigid Lambek Grammars  ...  Used with permission. p. 28 Beyond EDSM p. 37 Consistent Identification in the Limit of Rigid Grammars from Strings Is NP-hard p. 49 Some Classes of Regular Languages Identifiable in the Limit  ... 
doi:10.1007/3-540-45790-9_6 fatcat:nmlknwqoyfbybhb6rpomqrn7qy

Learning Lambek Grammars from Proof Frames [chapter]

Roberto Bonato, Christian Retoré
2014 Lecture Notes in Computer Science  
We do so for 1-valued also known as rigid Lambek grammars with product, since standard techniques can extend our result to k-valued grammars.  ...  Because of the correspondence between cut-free proof nets and normal natural deductions, our initial result on product free Lambek grammars can be recovered.  ...  The algorithm RG for learning rigid Lambek grammars converges in the sense of Gold. Proof.  ... 
doi:10.1007/978-3-642-54789-8_7 fatcat:nooacismt5euhb2skhgtjxzmqm

Learning Lambek grammars from proof frames [article]

Roberto Bonato, Christian Retoré
2013 arXiv   pre-print
We do so for 1-valued also known as rigid Lambek grammars with product, since standard techniques can extend our result to k-valued grammars.  ...  Because of the correspondence between cut-free proof nets and normal natural deductions, our initial result on product free Lambek grammars can be recovered.  ...  The algorithm RG for learning rigid Lambek grammars converges in the sense of Gold. Proof.  ... 
arXiv:1310.0576v1 fatcat:swun4qxqlndc5f5kfo7he2qvde

Natural Language Semantics and Computability [article]

Richard Moot
2016 arXiv   pre-print
This paper is a reflexion on the computability of natural language semantics.  ...  We argue that as long as possible world semantics is left out, one can compute the semantic representation(s) of a given statement, including aspects of lexical meaning.  ...  Although richer variants of categorial grammars are possible, and used in practice, we give here an example with Lambek grammars, and briefly comment on variants later.  ... 
arXiv:1605.04122v1 fatcat:6ir6tt2i2zh3jl2kbxtng3pjmi

Natural Language Semantics and Computability

Richard Moot, Christian Retoré
2019 Journal of Logic, Language and Information  
This paper is a reflexion on the computability of natural language semantics.  ...  We argue that as long as possible world semantics is left out, one can compute the semantic representation(s) of a given statement, including aspects of lexical meaning.  ...  Although richer variants of categorial grammars are possible, and used in practice, we give here an example with Lambek grammars, and briefly comment on variants later.  ... 
doi:10.1007/s10849-019-09290-7 fatcat:xnkyltzmrngbdkuo73m5dcptqi

A note on the strong and weak generative powers of formal systems

Aravind K. Joshi
2003 Theoretical Computer Science  
Our main goal of this note is to comment on the strong generative power of context-free grammars, lexicalized tree-adjoining grammars (and some of their variants) and Lambek grammars, especially in the  ...  This paper is a note on some relationships between the strong and weak generative powers of formal systems, in particular, from the point of view of squeezing more strong power out of a formal system without  ...  Acknowledgements I would like to thank the two reviewers of this paper whose valuable comments helped to improve the presentation of this paper.  ... 
doi:10.1016/s0304-3975(01)00347-4 fatcat:b36jdym4enhzlkbg4h3vy3jdii

k-Valued non-associative Lambek grammars are learnable from generalized functor-argument structures

Denis Béchet, Annie Foret
2006 Theoretical Computer Science  
We first show that (ii) for each k and each bound on arity the class of FA-arity bounded k-valued NL languages of FA structures is finite and (iii) that FA-arity bounded k-valued NL grammars are learnable  ...  We show that (i) rigid and k-valued non-associative Lambek (NL without product) grammars are learnable from generalized functor-argument structured sentences.  ...  In fact, as shown in [5, 7] by limit points, each class of k-valued non-associative Lambek grammar is unlearnable from strings and even from wellbracketed strings.  ... 
doi:10.1016/j.tcs.2006.01.006 fatcat:lf7vgytgunbnjmubxx6in2tefe

Type Logics in Grammar [chapter]

W. Buszkowski
2003 Trends in Logic  
Recently, Foret has shown that string languages of rigid grammars based on Associative Lambek Calculus (see section 3) admit a limit point, hence this class of grammars is not learnable from strings.  ...  Consequently, no Lambek grammar is esentially rigid (or k−valued), and grammars of that kind seem to require some different notion of learnability.  ... 
doi:10.1007/978-94-017-3598-8_12 fatcat:mfpscmkdffhkzkzvuju4uj3qxa

Encyclopedia of cognitive science

2003 ChoiceReviews  
A categorial lexicon assigns one or more types to the atomic elements of a language; the assembly of form and meaning is accounted for in terms of the rules of inference for these types seen as formulas  ...  of a grammar logic.  ...  Variants and alternatives Pregroup grammars. An interesting variation on the categorial theme has been developed by Jim Lambek in a number of recent papers (Lambek 1999; Lambek 2001) .  ... 
doi:10.5860/choice.41-0046 fatcat:tpjsphfjqrebdnp7bt4zrng46y

The Non-associative Lambek Calculus [chapter]

Richard Moot, Christian Retoré
2012 Lecture Notes in Computer Science  
For example, given a grammar G based on D = Q, NL , for some structural package Q, the extension of G to G based on D = Q ∪ Q, NL for some set of postulates Q , may allow G to derive sentences that were  ...  , and an actual parsing module, operating on the simplified categories and implementing (some variant of) some traditional context-free parsing algorithm.  ...  This question has been previously addressed in [van Benthem, 1991] and [Tiede, 1999] and represents an important issue for proof theoretic grammar.  ... 
doi:10.1007/978-3-642-31555-8_4 fatcat:z6zssyjuprhjxow4rhwwewq6ga

Maximal incrementality in linear categorial deduction

Mark Hepple
1997 Proceedings of the 35th annual meeting on Association for Computational Linguistics -  
Recent work has seen the emergence of a common framework for parsing categorial grammar (CG) formalisms that fall within the 'type-logical' tradition (such as the Lambek calculus and related systems),  ...  whereby some method of linear logic theorem proving is used in combination with a system of labelling that ensures only deductions appropriate to the relevant grammatical logic are allowed.  ...  The non-associative Lambek calculus (Lambek, 1961) sets the further requirement that types combine under some fixed initial bracketting.  ... 
doi:10.3115/976909.979661 dblp:conf/acl/Hepple97 fatcat:r4qmhpfbdnd2razl4h4ndd7ugq

Categorial Grammars with Iterated Types form a Strict Hierarchy of k-Valued Languages [chapter]

Denis Béchet, Alexandre Dikovsky, Annie Foret
2011 Lecture Notes in Computer Science  
The notion of k-valued categorial grammars in which every word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining interesting properties  ...  Such a hierarchy has been established earlier for the classical categorial grammars.  ...  Overview We first sum up some previous work for classical categorial grammars (AB) and non-associative Lambek grammars (NL). AB.  ... 
doi:10.1007/978-3-642-22256-6_5 fatcat:ubwaqz34ubfnjjeegxc6b65aby

Categorial grammars with iterated types form a strict hierarchy of k-valued languages

Denis Béchet, Alexandre Dikovsky, Annie Foret
2012 Theoretical Computer Science  
The notion of k-valued categorial grammars in which every word is associated to at most k types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining interesting properties  ...  Such a hierarchy has been established earlier for the classical categorial grammars.  ...  Introduction The field of natural language processing includes lexicalized grammars such as classical categorial grammars (AB grammars) [1] , the different variants of Lambek calculus [2] , lexicalized  ... 
doi:10.1016/j.tcs.2012.04.024 fatcat:h6enqz7pefekxigaeo2mv65rru

Categorial Type Logics [chapter]

Michael Moortgat
2011 Handbook of Logic and Language  
SBR-9510706, and on research conducted in the context of the Esprit BRA project 6852 'Dynamic interpretation of natural language'.  ...  I thank the editors, Gosse Bouma and Martin Emms for comments on preliminary versions.  ...  An essential limitation of the pure residuation logic is its rigid concept of constituency -a property which NL shares with conventional phrase structure grammars.  ... 
doi:10.1016/b978-0-444-53726-3.00002-5 fatcat:mg4b3coyyfhgrcztbtkglsigry
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