Jens Michaelis

Transforming Linear Context-Free Rewriting Systems into Minimalist Grammars

The type of a minimalist grammar (MG) as introduced by Stabler [11,12] provides an attempt of a rigorous algebraic formalization of the new perspectives adopted within the linguistic framework of transformational grammar due to the change from GB-theory to minimalism. Michaelis [6] has shown that MGs constitute a subclass of mildly context-sensitive grammars in the sense that for each MG there is a weakly equivalent linear context-free rewriting system (LCFRS). However, it has been left open in [6], whether the respective classes of string languages derivable by MGs and LCFRSs coincide. This paper completes the picture by showing that MGs in the sense of [11] and LCFRSs give in fact rise to the same class of derivable string languages.

Semilinearity as a Syntactic Invariant

Mildly context sensitive grammar formalisms such as multi-component TAGs and linear context free rewrite systems have been introduced to capture the full complexity of natural languages. We show that, in a formal sense, Old Georgian can be taken to provide an example of a non-semilinear language. This implies that none of the aforementioned grammar formalisms is strong enough to generate this language.

An operational and denotational approach to non-context-freeness

The main result of this paper is a description of linguistically motivated non-context-free phenomena equivalently in terms of regular tree languages (to express the recursive properties) and both a logical and an operational perspective (to establish the intended linguistic relations). The result is exemplified with a particular non-context-free phenomenon, namely cross-serial dependencies in natural languages such as Swiss German or Dutch. The logical description is specified in terms of binary monadic second-order (MSO) formulas and the operational description is achieved by means of a linear and non-deleting macro tree transducer. Besides giving a grammatical presentation for the regular tree language we shall also specify an implementation in the form of a finite-state (tree) automaton to emphasize the effectivity of our approach.

A note on the complexity of constraint interaction: locality conditions and minimalist grammars

Locality Conditions (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 intervention-based LCs (ILCs) often formulated as “minimality constraints” (“minimal link condition,” “minimize chain links”, “shortest move”, “attract closest,” etc.). On the other hand there are containment-based LCs (CLCs) 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 minimalist grammars (MGs) 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 shortest move condition (SMC) have been shown to belong to the mildly context-sensitive 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 specifier island condition (SPIC). 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 linear context-free rewriting systems (LCFRSs) 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.

Observations on Strict Derivational Minimalism

Abstract Deviating from the definition originally presented in [12], Stabler [13] introduced—inspired by some recent proposals in terms of a minimalist approach to transformational syntax–a (revised) type of a minimalist grammar (MG) as well as a certain type of a strict minimalist grammar (SMG). These two types can be shown to determine the same class of derivable string languages.

The Failure of the Strong Pumping Lemma for Multiple Context-Free Languages

Seki et al. (Theor. Comput. Sci. 88(2):191–229, 1991) showed that every m-multiple context-free language L is weakly 2m-iterative in the sense that either L is finite or L contains a subset of the form

Disentangling notions of specifier impenetrability: late adjunction, islands, and expressive power

\{ u_{0} w_{1}^{i} u_{1} \cdots w_{2m}^{i} u_{2m} \mid i \in \mathbb {N}\}

Adaptation of Ontological Knowledge from Structured Textual Data

, where w1⋯w2n≠ε. Whether every m-multiple context-free language L is 2m-iterative, that is to say, whether all but finitely many elements z of L can be written as z=u0w1u1⋯w2mu2m with w1⋯w2m≠ε and

On Formal Properties of Minimalist Grammars

\{ u_{0} w_{1}^{i} u_{1} \cdots w_{2m}^{i} u_{2m} \mid i \in \mathbb {N}\} \subseteq L

Two Type 0-Variants of Minimalist Grammars

, has been open. We show that there is a 3-multiple context-free language that is not k-iterative for any k.