Frank Morawietz

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.

Chart parsing and constraint programming

In this paper, parsing-as-deduction and constraint programming are brought together to outline a procedure for the specification of constraint-based chart parsers. Following the proposal in Shieber et al. (1995), we show how to directly realize the inference rules for deductive parsers as Constraint Handling Rules (Fruhwirth, 1998) by viewing the items of a chart parser as constraints and the constraint base as a chart. This allows the direct use of constraint resolution to parse sentences.

Descriptions of Cross-Serial Dependencies

The main result of this paper is a description of cross-serial dependencies equivalently in terms of (a) regular tree languages (to express the recursive properties) and regular string languages (to establish the intended linguistic relations) and (b) transductions definable in monadic second-order (MSO) logic which are defined on a domain of finite trees that is characterized as the model set of a closed MSO formula. In fact, we shall not deal directly with the two types of regular language families and MSO definable structures, but shall instead consider implementation in the form of finite-state (tree) automata to emphasize the effective nature of our approach.

Representing Constraints with Automata

In this paper we describe an approach to constraint based syntactic theories in terms of finite tree automata. The solutions to constraints expressed in weak monadic second order (MSO) logic are represented by tree automata recognizing the assignments which make the formulas true. We show that this allows an efficient representation of knowledge about the content of constraints which can be used as a practical tool for grammatical theory verification. We achieve this by using the intertranslatability of formulae of MSO logic and tree automata and the embedding of MSO logic into a constraint logic programming scheme. The usefulness of the approach is discussed with examples from the realm of Principles-and-Parameters based parsing.

A Model-Theoretic Description of Tree Adjoining Grammars

Abstract In this paper we show that non-context-free phenomena can be captured using only limited logical means. In particular, we show how to encode a Tree Adjoining Grammar [16] into a weakly equivalent monadic context-free tree grammar (MCFTG). By viewing MCFTG-rules as terms in a free Lawvere theory, we can translate a given MCFTG 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 through a model-theoretic interpretation in the form of an MSO transduction based upon tree-walking automata. This two-step approach gives a logical as well as an operational description of the tree sets involved.

The MSO Logic-Automaton Connection in Linguistics

In this paper we discuss possible applications of a system which uses automata-based theorem-proving techniques drawing on the decidability proof forweak monadic second-order (MSO) logic on trees to implement linguistic processing and theory verification. Despite a staggering complexcity bound, the success of and the continuing work on these techniques in computer science promises a usable tool to test formalizations of grammars. The advantages are readily apparent. The direct use of a succinct and flexible description language together with an environment to test the formaliz ations with the resulting finite, deterministic tree automata offers a way of combining the needs of both formalization and processing. The aim of this paper is threefold. Firstly we show how to use this technique for the verification of separate modules of a Principles-and-Parameters (P&P) grammar and secondly for the approximation of an entire P&P theory. And thirdly, we extend the language of the MSO tree logic to overcome remaining engineering problems.

Regular Query Techniques for XML-Documents

In this contribution we propose a query method for XML documents that provides a well chosen balance between expressive power of the query language and query complexity using methods derived from logic. Since XML documents are basically regular tree languages, it is appealing to use monadic second-order logic as a query language. But MSO is incapable of querying secondary relations in XML documents introduced via the ID-IDREF mechanism. We therefore show how a well-defined subclass of these ID-IDREF pairs can be queried using MSO, signature translations, and MSO-definable transductions. The ID-IDREF pairs will be coded by linear context-free tree grammars. And any query result is intersected with the coding of the ID-IDREF pairs to ensure only those matches are retained that respect the ID-IDREF informations contained in the document. The advantage of this method is that it uses regular techniques only. In consequence every query is computable.