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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
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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]
2002
Lecture Notes in Computer Science
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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]
2014
Lecture Notes in Computer Science
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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]
2013
arXiv
pre-print
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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]
2016
arXiv
pre-print
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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
2019
Journal of Logic, Language and Information
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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
2003
Theoretical Computer Science
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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
2006
Theoretical Computer Science
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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]
2003
Trends in Logic
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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
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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]
2012
Lecture Notes in Computer Science
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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
1997
Proceedings of the 35th annual meeting on Association for Computational Linguistics -
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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]
2011
Lecture Notes in Computer Science
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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
2012
Theoretical Computer Science
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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]
2011
Handbook of Logic and Language
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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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