A logical treatment of semi-free word order and bounded discontinuous constituency

A logical treatment of semi-free word order and bounded discontinuous constituency Mike Reape Centre for Cognitive Science, University of Edinburgh 2 Buccleuch Place, Edinburgh EH8 9LW Scotland, UK Abstract In this paper we present a logical treatment of semi- free word order and bounded discontinuous constituency. We extend standard feature value logics to treat word order in a single formalism with a rigorous semantics without phrase structure rules. The elimination of phrase structure rules allows a natural generalisation of the approach to nonconfigurational word order and bounded discontinuous continuency via sequence union. Sequence union formalises the notions of clause union and scrambling by providing a mechanism for describing word order domains larger than the local tree. The formalism incorporates the distinction between bounded and unbounded forms of discontinuous constituency. Grammars are organised as algebraic theories. This means that linguistic generalisations are stated as axioms about the structure of signs. This permits a natural interpretation of implicational universals in terms of theories, subtheories and implicational axioms. The accompanying linguistic analysis is eclectic, borrowing insights from many current linguistic theories. 1. Introduction In this paper we present a logical treatment of semi- free word order and bounded discontinuous constituency. By a logical treatment, we mean that the grammar is an axiomatic algebraic theory, i.e., a set of axioms formalised in a logic. By bounded discontinuous constituency, we refer to phenomena such as Dutch cross-serial dependencies, German Mittelfeld word order and clause-bounded extraposition in contrast to unbounded forms of discontinuous constituency such as cross-serial multiple extractions in Swedish relative clauses. There is no scope within this paper to provide the linguistic argumentation sufficient to justify the approach described below. We shall have to limit ourselves to describing the key linguistic insight that we wish to formalise. That is that semi-free word order and nonconfigurationality are local phenomenon (i.e., bounded) and that word order domains are larger than the local trees of context- free based accounts of syntax. (This includes nearly all well-known unification-based grammar formalisms such as GPSG, IF'G, I-IPSG and CUG.) This is simply a restatement of the notion of clause union or scrambling familiar from transformational analyses. Our proposal is to provide a feature-value logic with a rigorous semantics with sufficient expressive power to allow the encoding of even syntactic structure within the single formalism. This means that the work of encoding syntactic structure is carried by the feature-value logic and not by formal language theoretic devices (i.e., phrase structure rules). Sequences of linguistic categories, or signs (following Saussure, HI~G and UCG), do the work of PSRs in our logic. The phon attribute of signs is functionally dependent on the phon attributes of the signs in sequences encoding local order domains. This allows us to trivially introduce word order domains larger than the local tree by introducing a sequence union operation. GPSG-style linear precedence (LP) statements express partial ordering constraints on elements of sequences. The grammars we use consist of three types of elements: (1) descriptions of lexical signs, (2) descriptions …

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