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The notion of -valued categorial grammars where a word is associated to at most types is often used in the field of lexicalized grammars as a fruitful constraint for obtaining several properties like the existence of learning algorithms. This principle is relevant only when the classes of -valued grammars correspond to a real hierarchy of languages. This paper establishes the relevance of this notion for two related grammatical systems. In the first part, the classes of -valued non-associative Lambek () grammars without product is proved to define a strict hierarchy of languages. The second part introduces the notion of generalized functor argument for non-associative Lambek () calculus without product but allowing empty antecedent and establishes also that the classes of -valued () grammars without product form a strict hierarchy of languages.

In this paper, we define Dependency Structure Grammars (DSG), which are rewriting rule grammars generating sentences together with their dependency structures, are more expressive than CF-grammars and non-equivalent to mildly context-sensitive grammars.

We show that DSG are weakly equivalent to Categorial Dependency Grammars (CDG) recently introduced in [6,3]. In particular, these dependency grammars naturally express long distance dependencies and enjoy good mathematical properties.

We present two approaches to the task of computing in an inductive compositional way semantic representations of the meaning of a sentence that take into account the principles of Binding Theory. The two algorithms reflect two different interpretations that have been proposed for the principles of Binding Theory as first formulated by Noam Chomsky. We present the two algorithms as additional machinery to enrich well-known bottom-up procedures to compute the logical form of a sentence in a (non intensional) Montagovian style.

We describe a system for automatically translating formal software specifications to natural language. The system produces natural language which is acceptable to a human reader, and it supports by-hand optimization by users who are not experts of our system. The translation system is implemented using the Grammatical Framework, a grammar formalism based on Martin-Löf’s type theory. We show that this grammar-based approach scales well enough to handle a non-trivial case study: translating the Object Constraint Language specifications of the Java Card API into English.

An intermediate logical system in comparison with the non-associative () and the associative Lambek Calculus() is obtained by extending their language by means of a so-called “combining permission”, which is used to regulate the introduction of a product formula in the scope of a derivation and to impose a control on applications of the association structural rules. A cut elimination theorem for such a system, so-called Selective Lambek Calculus, is presented.

This paper is dedicated to the compact representation of Tree Adjoining Grammars. We provide a methodology for grammatical development with eXtensible MetaGrammar (). The provided methodology has been set up together with the development of a large French . Furthermore the grammatical representation language and the assorted development methodology presented can be reused for grammatical development with other strongly lexicalised syntactic formalisms.

In modern approaches to proof-theory (e.g.,[8]) natural-deduction (ND) proof systems are presented with [10], derived from a more general (re)formulation of Prawitz’s [13]. The setting of such enterprises are usually intuitionistic (and occasionally classic), but also [7] propositional calculi.

(LCs) on (unbounded) dependencies have played a major role in the development of generative syntax ever since the seminal work by Ross [22]. Descriptively, they fall into two groups. On the one hand there are often formulated as “minimality constraints” (“minimal link condition,” “minimize chain links”, “shortest move”, “attract closest,” etc.). On the other hand there are typically de.ned in terms of (generalized) grammatical functions (“adjunct island”, “subject island”, “specifier island”, etc.). Research on LCs has been dominated by two very general trends. First, attempts have been made at unifying ILCs and CLCs on the basis of notions such as “government” and “barrier” (e.g. [4]). Secondly, research has often been guided by the intuition that, beyond empirical coverage, LCs somehow contribute to restricting the formal capacity of grammars (cf. [3–p. 125], [6–p. 14f]). Both these issues, we are going to argue, can be fruitfully studied within the framework of as defined by Stabler [25]. In particular, we are going to demonstrate that there is a specic asymmetry between the in.uence of ILCs and CLCs on complexity. Thus, MGs, including an ILC, namely, the have been shown to belong to the grammar formalisms by Michaelis [14]. The same has been shown in [16, 18] for a revised version of MGs introduced in [26], which includes the SMC and an additional CLC, namely, the . In particular [14] and [16, 18] show that, in terms of derivable string languages, both the original MG-type and the revised MG-type constitute a subclass of the class of in the sense of [28, 29], and thus, a series of other formalism classes all generating the same class of string languages as LCFRSs. Here we will demonstrate that removing the SMC from the revised MG-version increases the generative power in such a way that the resulting formalism is not mildly context-sensitive anymore. This suggests that intuitions to the contrary notwithstanding, imposing an LC as such, here the SPIC, does not necessarily reduce formal complexity.

Although Tree Adjoining Grammars (TAG) are widely used for syntactic processing, there is to date no large scale TAG available which also supports semantic construction. In this paper, we present a highly factorised way of implementing a syntax/semantic interface in TAG. We then show how the resulting resource can be used to perform semantic construction either during or after derivation.

In spite of the fact that Arabic offers a well-studied theoretical and historical linguistic knowledge, unfortunately, it has so far received very little computational research and in particular on the level of semantic analysis. The most computational research efforts have been focused on morphological and syntax analysis, whereas research on Arabic computational semantics has been neglected. The main goal of this paper is to characterize the fundamental issues involved in deep logic-based semantic representation of Arabic sentences. The focus of attention of this work is relying on the principle of compositionality for Arabic semantic analysis, utilizing -calculus and type theory analysis of some Arabic syntactical constituents for achieving a semantic construction model for a fragment of ARABIC. Since semantic representation has to be compositional in Natural Language Understanding Systems, this approach offers a central concept for developing more intelligent and robust Arabic NLP systems.