相关论文: On the Recognizing Power of the Lambek Calculus wi…
Lambek calculus is a logical foundation of categorial grammar, a linguistic paradigm of grammar as logic and parsing as deduction. Pentus (2010) gave a polynomial-time algorithm for determ- ining provability of bounded depth formulas in the…
We present a translation of the Lambek calculus with brackets and the unit constant, $\mathbf{Lb}^{\boldsymbol{*}}_{\mathbf{1}}$, into the Lambek calculus with brackets allowing empty antecedents, but without the unit constant,…
The Lambek calculus is a well-known logical formalism for modelling natural language syntax. The original calculus covered a substantial number of intricate natural language phenomena, but only those restricted to the context-free setting.…
Lambeks Syntactic Calculus, commonly referred to as the Lambek calculus, was innovative in many ways, notably as a precursor of linear logic. But it also showed that we could treat our grammatical framework as a logic (as opposed to a…
The Lambek calculus can be considered as a version of non-commutative intuitionistic linear logic. One of the interesting features of the Lambek calculus is the so-called "Lambek's restriction," that is, the antecedent of any provable…
In this paper, we introduce a variant of the Lambek calculus allowing empty antecedents. This variant uses two connecives: the left division and a unary modality that occurs only with negative polarity and allows weakening in antecedents of…
We consider relational semantics (R-models) for the Lambek calculus extended with intersection and explicit constants for zero and unit. For its variant without constants and a restriction which disallows empty antecedents, Andreka and…
In (Van Benthem, 1991) it is proved that all permutation closures of context-free languages can be generated by grammars over the Lambek calculus with the permutation rule (LP-grammars); however, to our best knowledge, it is not established…
We consider the Lambek calculus, or non-commutative multiplicative intuitionistic linear logic, extended with iteration, or Kleene star, axiomatised by means of an $\omega$-rule, and prove that the derivability problem in this calculus is…
Extended versions of the Lambek Calculus currently used in computational linguistics rely on unary modalities to allow for the controlled application of structural rules affecting word order and phrase structure. These controlled structural…
We investigate language interpretations of two extensions of the Lambek calculus: with additive conjunction and disjunction and with additive conjunction and the unit constant. For extensions with additive connectives, we show that…
We explore the consequences of layering a Lambek proof system over an arbitrary (constraint) logic. A simple model-theoretic semantics for our hybrid language is provided for which a particularly simple combination of Lambek's and the proof…
A new family of categorial grammars is proposed, defined by enriching basic categorial grammars with a conjunction operation. It is proved that the formalism obtained in this way has the same expressive power as conjunctive grammars, that…
We enrich the Lambek calculus with the cyclic shift operation, which is expected to model the closure operator of formal languages with respect to cyclic shifts. We introduce a Gentzen-style calculus and prove cut elimination. Secondly, we…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement…
We present new descriptive complexity characterisations of classes REG (regular languages), LCFL (linear context-free languages) and CFL (context-free languages) as restrictions on inference rules, size of formulae and permitted connectives…
We study the computational complexity of the parsing problem of a variant of Lambek Categorial Grammar that we call {\em semidirectional}. In semidirectional Lambek calculus $\SDL$ there is an additional non-directional abstraction rule…
The syntactic calculus of Lambek is a deductive system for the multiplicative fragment of intuitionistic non-commutative linear logic. As a fine-grained calculus of resources, it has many applications, mostly in formal computational…
While context-free grammars are characterized by a simple proof-theoretic grammatical formalism namely categorial grammar and its logic the Lambek calculus, no such characterizations were known for tree-adjoining grammars, and even for any…
In this paper we study some fragments without implications of the (Hilbert) full Lambek logic $\mathbf{HFL}$ and also some fragments without implications of some of the substructural extensions of that logic. To do this, we perform an…