Uwe Mönnich

Closure properties of linear context-free tree languages with an application to optimality theory

Context-free tree grammars, originally introduced by Rounds [Math. Systems Theory 4(3) (1970) 257-287], are powerful grammar devices for the definition of tree languages. The properties of the class of context-free tree languages have been studied for more than three decades now. Particularly important here is the work by Engelfriet and Schmidt [J. Comput. System Sci. 15(3) (1977) 328-353, 16(1) (1978) 67-99]. In the present paper, we consider a subclass of the class of context-free tree languages, namely the class of linear context-free tree languages. A context-free tree grammar is linear, if no rule permits the copying of subtrees. For this class of linear context-free tree languages we show that the grammar derivation mode, which is very important for the general class of context-free tree languages, is immaterial. The main result we present is the closure of the class of linear context-free tree languages under linear frontier-to-root tree transduction mappings. Two further results are the closure of this class under linear root-to-frontier tree transduction mappings and under intersection with regular tree languages.The results of the first part of the paper are applied to the formalisation of optimality theory. Optimality theory (OT), introduced by Prince and Smolensky [Tech. Report 1993], is a linguistic framework in which the mapping of one level of linguistic representation to another is based on rules and filters. The rules generate candidate expressions in the target representation, which are subsequently checked against the filters, so that only those candidates remain that survive this filtering process. A proposal to formalise the description of OT using formal language theory and in particular automata theory was presented by Karttunen [Proceedings of International Workshop on Finite-State Methods in Natural Language Processing, 1998, pp. 1-12] and Frank and Satta [Comput. Linguistics 24 (1998) 307-315]. The main result of these papers is that if the generator is defined as a finite-state string transducer and the filters are defined by finite-state string automata, then the whole OT-system can be defined by means of a finite-state string transducer. Considering the fact that most parts of linguistics have trees as their underlying data structures instead of strings, we show here that generators can be extended to linear frontier-to-root tree transducers on linear context-free tree languages--with constraints being regular tree languages--while the computation of optimal candidates can still be performed using finite-state techniques (over trees).

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.

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.

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.

Adaptation of Ontological Knowledge from Structured Textual Data

This paper provides a general framework for the extraction and adaptation of ontological knowledge from new structured information. The cycle of this process is described starting with the extraction of semantic knowledge from syntactically given information, the transformation of this information into an appropriate format of description logic, and the dynamic update of a given ontology with this new information where certain types of potentially occurring inconsistencies are automatically resolved. The framework uses crucially certain tools for this incremental update. In addition to WordNet, the usage of FrameNet plays an important role, in order to provide a consistent basis for reasoning applications. The cycle of rewriting textual definitions into description logic axioms is prototypically implemented as well as the resolution of certain types of inconsistencies in the dynamic update of ontologies.

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.