Learning regular sets from queries and counterexamples
Information and Computation
On multiple context-free grammars
Theoretical Computer Science
Learnable classes of categorial grammars
Learnable classes of categorial grammars
Inference of Reversible Languages
Journal of the ACM (JACM)
Journal of Automata, Languages and Combinatorics - Special issue: selected papers of the second internaional workshop on Descriptional Complexity of Automata, Grammars and Related Structures (London, Ontario, Canada, July 27-29, 2000)
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Residuated Lattices: An Algebraic Glimpse at Substructural Logics, Volume 151
Grammatical Inference: Learning Automata and Grammars
Grammatical Inference: Learning Automata and Grammars
Efficient, correct, unsupervised learning of context-sensitive languages
CoNLL '10 Proceedings of the Fourteenth Conference on Computational Natural Language Learning
Distributional learning of some context-free languages with a minimally adequate teacher
ICGI'10 Proceedings of the 10th international colloquium conference on Grammatical inference: theoretical results and applications
Learning context free grammars with the syntactic concept lattice
ICGI'10 Proceedings of the 10th international colloquium conference on Grammatical inference: theoretical results and applications
Towards general algorithms for grammatical inference
ALT'10 Proceedings of the 21st international conference on Algorithmic learning theory
Theoretical Computer Science
A learnable representation for syntax using residuated lattices
FG'09 Proceedings of the 14th international conference on Formal grammar
Towards dual approaches for learning context-free grammars based on syntactic concept lattices
DLT'11 Proceedings of the 15th international conference on Developments in language theory
Integration of the dual approaches in the distributional learning of context-free grammars
LATA'12 Proceedings of the 6th international conference on Language and Automata Theory and Applications
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Residuated lattices form one of the theoretical backbones of the Lambek Calculus as the standard free models. They also appear in grammatical inference as the syntactic concept lattice, an algebraic structure canonically defined for every language L based on the lattice of all distributionally definable subsets of strings. Recent results show that it is possible to build representations, such as context-free grammars, based on these lattices, and that these representations will be efficiently learnable using distributional learning. In this paper we discuss the use of these syntactic concept lattices as models of Lambek grammars, and use the tools of algebraic logic to try to link the proof theoretic ideas of the Lambek calculus with the more algebraic approach taken in grammatical inference. We can then reconceive grammars of various types as equational theories of the syntactic concept lattice of the language. We then extend this naturally from models based on concatenation of strings, to ones based on concatenations of discontinuous strings, which takes us from context-free formalisms to mildly context sensitive formalisms (multiple context-free grammars) and Morrill's displacement calculus.