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Lambek calculus is NPcomplete
 THEORETICAL COMPUTER SCIENCE
, 2003
"... We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete. ..."
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Cited by 32 (0 self)
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We prove that for both the Lambek calculus L and the Lambek calculus allowing empty premises L ∗ the derivability problem is NPcomplete. It follows that also for the multiplicative fragments of cyclic linear logic and noncommutative linear logic the derivability problem is NPcomplete.
Lambek Calculus with Nonlogical Axioms
 Language and Grammar, Studies in Mathematical Linguistics and Natural Language
, 2002
"... We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions of Associa ..."
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Cited by 14 (11 self)
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We study Nonassociative Lambek Calculus and Associative Lambek Calculus enriched with nitely many nonlogical axioms. We prove that the nonassociative systems are decidable in polynomial time and generate contextfree languages. In [1] it has been shown that nite axiomatic extensions
Parsing CCGbank with the Lambek Calculus
, 2009
"... This paper will analyze CCGbank, a corpus of CCG derivations, for use with the Lambek calculus. We also present a Java implementation of the parsing algorithm for the Lambek calculus presented in Fowler (2009) and the results of experiments using that algorithm to parse the categories in CCGbank. We ..."
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Cited by 1 (0 self)
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This paper will analyze CCGbank, a corpus of CCG derivations, for use with the Lambek calculus. We also present a Java implementation of the parsing algorithm for the Lambek calculus presented in Fowler (2009) and the results of experiments using that algorithm to parse the categories in CCGbank
LC Graphs for the Lambek calculus with product
, 2007
"... The Lambek calculus, introduced in Lambek (1958), is a categorial grammar having two variants which will be considered in this paper: the Lambek calculus ..."
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The Lambek calculus, introduced in Lambek (1958), is a categorial grammar having two variants which will be considered in this paper: the Lambek calculus
Preliminaries to the Lambek Calculus
"... Summary. Some preliminary facts concerning completeness and decidability problems for the Lambek calculus [13] are proved as well as some theses and derived rules of the calculus itself. MML Identifier: PRELAMB. ..."
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Summary. Some preliminary facts concerning completeness and decidability problems for the Lambek calculus [13] are proved as well as some theses and derived rules of the calculus itself. MML Identifier: PRELAMB.
Models for the Lambek calculus
 Annals of Pure and Applied Logic
, 1995
"... We prove that the Lambek calculus is complete w.r.t. Lmodels, i.e., free semigroup models. We also prove the completeness w.r.t. relativized relational models over the natural linear order of integers. ..."
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Cited by 7 (1 self)
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We prove that the Lambek calculus is complete w.r.t. Lmodels, i.e., free semigroup models. We also prove the completeness w.r.t. relativized relational models over the natural linear order of integers.
Lambek Calculus and Formal Grammars
, 1997
"... Contents Introduction 1 1. Preliminaries 4 2. Free group interpretation 7 3. Thin sequents 9 4. Interpolation 10 5. Main theorem 14 6. Interpolation in fragments 18 7. Construction of a contextfree grammar for a productfree Lambek grammar 23 8. Conjoinable types in the Lambek calculus 24 9. Multi ..."
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Cited by 2 (0 self)
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Contents Introduction 1 1. Preliminaries 4 2. Free group interpretation 7 3. Thin sequents 9 4. Interpolation 10 5. Main theorem 14 6. Interpolation in fragments 18 7. Construction of a contextfree grammar for a productfree Lambek grammar 23 8. Conjoinable types in the Lambek calculus 24 9
Lambek calculus: recognizing power and complexity
 Essays Dedicated to Johan van Benthem on the Occasion of his 50th Birthday
, 1998
"... I survey known results and results that easily follow from known results about the recognizing power and complexity of various fragments of the Lambek calculus. Contents ..."
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Cited by 2 (0 self)
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I survey known results and results that easily follow from known results about the recognizing power and complexity of various fragments of the Lambek calculus. Contents
A lambdaCalculus for the Lambek Calculus
, 1996
"... :The Lambek Calculus was introduced by Lambek [2] in order to obtain effective rules to allow forming sentences and distinguishing sentences from nonsentences. Two primitives types are defined in this calculus and from these types is allowed to construct compound types to the words of the sentence. ..."
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:The Lambek Calculus was introduced by Lambek [2] in order to obtain effective rules to allow forming sentences and distinguishing sentences from nonsentences. Two primitives types are defined in this calculus and from these types is allowed to construct compound types to the words of the sentence
Lambek Calculus: Recognizing Power and Complexity
"... I survey known results and results that easily follow from known results about the recognizing power and complexity of various fragments of the Lambek calculus. Contents 1 Complexity and recognizing power of logics 2 2 Lambek calculus 3 3 Multiplicativeexponential Lambek calculus 5 4 Multiplicativ ..."
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I survey known results and results that easily follow from known results about the recognizing power and complexity of various fragments of the Lambek calculus. Contents 1 Complexity and recognizing power of logics 2 2 Lambek calculus 3 3 Multiplicativeexponential Lambek calculus 5 4
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