Online research in philosophy

Various restrictions on transformational grammars have been investigated in order to reduce their generative power from recursively enumerable languages to recursive languages.It will be shown that any restriction on transformational grammars defining a recursively enumerable subset of the set of all transformational grammars, is either too weak (in the sense that there does not exist a general decision procedure for all languages generated under such a restriction) or too strong (in the sense that there exists a recursive language that cannot be generated by any transformational grammar thus restricted). In addition, some related problems will be discussed.

The equivalence of leaf languages of tree adjoining grammars and monadic linear context-free grammars was shown about a decade ago. This paper presents a proof of the strong equivalence of these grammar formalisms. Non-strict tree adjoining grammars and monadic linear context-free grammars define the same class of tree languages. We also present a logical characterisation of this tree language class showing that a tree language is a member of this class iff it is the two-dimensional yield of an MSO-definable three-dimensional tree language.

This paper defines the grammar class of sequentially indexed grammars. Sequentially indexed grammars are the result of a change in the index stack handling mechanism of indexed grammars [Aho68, Aho69]. Sequentially indexed grammars are different from linear indexed grammars [Gaz88]. Like indexed languages, sequentially indexed languages are a fully abstract language class. Unlike indexed languages, sequentially indexed languages allow polynomial parsing algorithms. We give a polynomial algorithm for parsing with sequentially indexed gramamrs that is an extension of the Earley algorithm for parsing with context free grammars.

Pregroup grammars have a cubic recognition algorithm. Here, we define a correct and complete recognition and parsing algorithm and give sufficient conditions for the algorithm to run in linear time. These conditions are satisfied by a large class of pregroup grammars, including grammars that handle coordinate structures and distant constituents.

The paper presents a way to transform pregroup grammars into contextfree grammars using functional composition. The same technique can also be used for the proof-nets of multiplicative cyclic linear logic and for Lambek calculus allowing empty premises.

This paper investigates the learnability by positive examples in the sense of Gold of Pregroup Grammars. In a first part, Pregroup Grammars are presented and a new parsing strategy is proposed. Then, theoretical learnability and non-learnability results for subclasses of Pregroup Grammars are proved. In the last two parts, we focus on learning Pregroup Grammars from a special kind of input called feature-tagged examples. A learning algorithm based on the parsing strategy presented in the first part is given. Its validity is proved and its properties are examplified.

Unification grammars are widely accepted as an expressive means for describing the structure of natural languages. In general, the recognition problem is undecidable for unification grammars. Even with restricted variants of the formalism, off-line parsable grammars, the problem is computationally hard. We present two natural constraints on unification grammars which limit their expressivity and allow for efficient processing. We first show that non-reentrant unification grammars generate exactly the class of context-free languages. We then relax the constraint and show that one-reentrant unification grammars generate exactly the class of mildly context-sensitive languages. We thus relate the commonly used and linguistically motivated formalism of unification grammars to more restricted, computationally tractable classes of languages.

In this paper, we propose an extension of free pregroups with lower bounds on sets of pregroup elements. Pregroup grammars based on such pregroups provide a kind of an algebraic counterpart to universal quantification over type-variables. In particular, we show how our pregroup extensions can be used for pregroup grammars expressing natural-language coordination and extraction.

We introduce and study a natural extension of Marcus external contextual grammars. This mathematically simple mechanism which generates a proper subclass of simple matrix languages, known to be mildly context-sensitive ones, is still mildly context-sensitive. Furthermore, we get an infinite hierarchy of mildly context-sensitive families of languages. Then we attempt to fill a gap regarding the linguistic relevance of these mechanisms which consists in defining a tree structure on the strings generated by many-dimensional external contextual grammars, and investigate some related issues. Several open problems are finally discussed.

Pregroups are partially ordered monoids in which each element has two “adjoints”. Pregroup grammars provide a computational approach to natural languages by assigning to each word in the mental dictionary a type, namely an element of the pregroup freely generated by a partially ordered set of basic types. In this expository article, the attempt is made to introduce linguists to a pregroup grammar of English by looking at Chomsky’s earliest examples.