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

2003
*
Proceedings of the 41st Annual Meeting on Association for Computational Linguistics - ACL '03
*

Another interest

doi:10.3115/1075096.1075141
dblp:conf/acl/BechetF03
fatcat:prsxfrccqnbfhc463ic5jsjuni
*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. ...##
###
Some Classes of Regular Languages Identifiable in the Limit from Positive Data
[chapter]

2002
*
Lecture Notes in Computer Science
*

from Positive Data
p. 63
Learning Probabilistic Residual Finite State Automata
p. 77
Fragmentation: Enhancing Identifiability
p. 92

doi:10.1007/3-540-45790-9_6
fatcat:nmlknwqoyfbybhb6rpomqrn7qy
*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*...##
###
Learning Lambek Grammars from Proof Frames
[chapter]

2014
*
Lecture Notes in Computer Science
*

We do so

doi:10.1007/978-3-642-54789-8_7
fatcat:nooacismt5euhb2skhgtjxzmqm
*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. ...##
###
Learning Lambek grammars from proof frames
[article]

2013
*
arXiv
*
pre-print

We do so

arXiv:1310.0576v1
fatcat:swun4qxqlndc5f5kfo7he2qvde
*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. ...##
###
Natural Language Semantics and Computability
[article]

2016
*
arXiv
*
pre-print

This paper is a reflexion

arXiv:1605.04122v1
fatcat:6ir6tt2i2zh3jl2kbxtng3pjmi
*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. ...##
###
Natural Language Semantics and Computability

2019
*
Journal of Logic, Language and Information
*

This paper is a reflexion

doi:10.1007/s10849-019-09290-7
fatcat:xnkyltzmrngbdkuo73m5dcptqi
*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. ...##
###
A note on the strong and weak generative powers of formal systems

2003
*
Theoretical Computer Science
*

Our main goal

doi:10.1016/s0304-3975(01)00347-4
fatcat:b36jdym4enhzlkbg4h3vy3jdii
*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. ...##
###
k-Valued non-associative Lambek grammars are learnable from generalized functor-argument structures

2006
*
Theoretical Computer Science
*

We first show that (ii)

doi:10.1016/j.tcs.2006.01.006
fatcat:lf7vgytgunbnjmubxx6in2tefe
*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. ...##
###
Type Logics in Grammar
[chapter]

2003
*
Trends in Logic
*

Recently, Foret has shown that string languages

doi:10.1007/978-94-017-3598-8_12
fatcat:mfpscmkdffhkzkzvuju4uj3qxa
*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. ...##
###
Encyclopedia of cognitive science

2003
*
ChoiceReviews
*

A categorial lexicon assigns

doi:10.5860/choice.41-0046
fatcat:tpjsphfjqrebdnp7bt4zrng46y
*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) . ...##
###
The Non-associative Lambek Calculus
[chapter]

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*. ...

##
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Maximal incrementality in linear categorial deduction

1997
*
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
*

Recent work has seen the emergence

doi:10.3115/976909.979661
dblp:conf/acl/Hepple97
fatcat:r4qmhpfbdnd2razl4h4ndd7ugq
*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. ...##
###
Categorial Grammars with Iterated Types form a Strict Hierarchy of k-Valued Languages
[chapter]

2011
*
Lecture Notes in Computer Science
*

The notion

doi:10.1007/978-3-642-22256-6_5
fatcat:ubwaqz34ubfnjjeegxc6b65aby
*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. ...##
###
Categorial grammars with iterated types form a strict hierarchy of k-valued languages

2012
*
Theoretical Computer Science
*

The notion

doi:10.1016/j.tcs.2012.04.024
fatcat:h6enqz7pefekxigaeo2mv65rru
*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 ...##
###
Categorial Type Logics
[chapter]

2011
*
Handbook of Logic and Language
*

SBR-9510706, and

doi:10.1016/b978-0-444-53726-3.00002-5
fatcat:mg4b3coyyfhgrcztbtkglsigry
*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*. ...
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