In this paper we extend the work by Michaelis (1999) which shows how to encode an arbitrary Minimalist Grammar in the sense of Stabler (1997) into a weakly equivalent multiple contextfree grammar (MCFG). By viewing MCFG-rules as terms in a free Lawvere theory we can translate a given MCFG into a regular tree grammar. The latter is characterizable by both a tree automaton and a corresponding formula in monadic second-order (MSO) logic. The trees of the resulting regular tree language are then unpacked into the intended \linguistic" trees both through an MSO transduction based upon tree-walking automata and through a macro tree transduction. This two-step approach gives an operational as well as a logical description of the tree sets involved. As an interlude we show that MCFGs can be regarded as a particularly simple attribute grammar. 1 Introduction Algebraic, logical and regular characterizations of (tree) languages provide a natural framework for the denotational and opera...

The main result of this paper is a description of linguistically motivated non-contextfree 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 secondorder (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.

Cross-serial depcndencics in Dutch and Swiss-Gcrman arc the only known extracontext fi'cc natural laaguage syntactic phenomena. Psycholinguistic evidence suggests cross-serial orderings tend to be easier to process than Ilestcd COI18l'11c- (ions. We argue that the cxprcssivity requirements of the corresponding formal languages do not actually entail that procossing reduplication languages require the worst-case time complexity for lm- guagcs of the same expressivc class, We distinguish between contcxt-fi'ec representability and context-fi'cc processing.

and by majority vote has been found to be satisfactory.

We discuss two standard formal tools used to study models of grammar. One of these is formal language theory, which provides a way to describe the complexity of languages in terms of a sequence of standard language classes known as the Chomsky hierarchy. The other tool is learnability theory, which can describe, for a given class of languages, whether or not there exists a single learner that can learn every language in the class; we use a particular model for learning developed by Gold. These two tools can be used to obtain formal properties of a grammar system, and to evaluate the validity of a theory of natural language. After presenting the tools, we show how they can be applied to the linguistic theory of categorial grammars, and we discuss the results. 1

It is remarkable if any relationship at all persists between computational linguists (CL) and that part of general linguistics comprising the mainstream of MIT transformational-generative (TG) theoretical syntax. If the lines are still open, it represents something of a tribute to CL practitioners’ tolerance — a triumph of hope and goodwill over the experience of abuse — because the TG community has shown considerable hostility toward CL and everything it stands for over the past fifty years. I offer some brief historical notes, and hint at prospects for a better basis for collaboration in the future. 1

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There has been recent interest in looking at what is required for a tree query language for linguistic corpora. One approach is to start from existing formal machinery, such as tree grammars and automata, to see what kind of machine is an appropriate underlying one for the query language. The goal of the paper is then to examine what is an appropriate machine for a linguistic tree query language, with a view to future work defining a query language based on it. In this paper we review work relating XPath to regular tree grammars, and as the paper’s first contribution show how regular tree grammars can also be a basis for extensions proposed for XPath for common linguistic corpus querying. As the paper’s second contribution we demonstrate that, on the other hand, regular tree grammars cannot describe a number of structures of interest; we then show that, instead, a slightly more powerful machine is appropriate, and indicate how linguistic tree query languages might be augmented to include this extra power. 1