We present a generative model for the unsupervised learning of dependency structures. We also describe the multiplicative combination of this dependency model with a model of linear constituency. The product model outperforms both components on their respective evaluation metrics, giving the best published figures for unsupervised dependency parsing and unsupervised constituency parsing. We also demonstrate that the combined model works and is robust cross-linguistically, being able to exploit either attachment or distributional regularities that are salient in the data. 1

algebra . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.1.1 Homomorphisms and free generators . . . . . . . . . . . . 34 3.1.2 Quotient algebras . . . . . . . . . . . . . . . . . . . . . . . 36 3.1.3 Reducts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37 3.2 Algebras of languages . . . . . . . . . . . . . . . . . . . . . . . . . 38 3.2.1 The algebra of formulae . . . . . . . . . . . . . . . . . . . 38 3.2.2 Substitutions . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.2.3 Associated algebras . . . . . . . . . . . . . . . . . . . . . . 40 3.2.4 Valuations . . . . . . . . . . . . . . . . . . . . . . . . . . . 41 3.2.5 Lindenbaum-Tarski quotient algebras . . . . . . . . . . . . 42 3.3 Algebras of deductive systems . . . . . . . . . . . . . . . . . . . . 44 3.3.1 Determining a class of algebras . . . . . . . . . . . . . . . 45 3.3.2 Algebra of a sequent calculus . . . . . . . . . . . . . . . . . 46 3.3.3 Completeness . . . . . . . . . . . . . . . . . . . . . . . . . 48 3.4 Subsuming special cases: an example . . . . . . . . . . . . . . . . 49 3.4.1 The sequent system GL . . . . . . . . . . . . . . . . . . . . 49 3.4.2 The equivalent system t(GL) . . . . . . . . . . . . . . . . . 51 3.4.3 Algebraic models for GL . . . . . . . . . . . . . . . . . . . 52 3.5 Kripke semantics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56 4 Categorial type logics 61 4.1 The typed lambda calculus . . . . . . . . . . . . . . . . . . . . . . 62 4.2 Categorial grammar . . . . . . . . . . . . . . . . . . . . . . . . . . 66 4.3 Forms of Lambek's calculus . . . . . . . . . . . . . . . . . . . . . . 69 4.3.1 Classical CG revisited . . . . . . . . . . . . . . . . . . . . . 70 4.3.2 The nonassociative product-free system . . . . . . . . . . . 70 4.3.3 Addin...

This paper presents a sketch of a formal proof of strong equivalence, where both grammars generate equivalent parse results, between any LTAG (Lexicalized Tree Adjoining Grammar: Schabes, Abeille and Joshi (1988)) G and an HPSG (Head-Driven Phrase Structure Grammar: Pollard and Sag (1994))-style grammar converted from G by a grammar conversion (Yoshinaga and Miyao, 2001). Our proof theoretically justifies some applications of the grammar conversion that exploit the nature of strong equivalence (Yoshinaga et al., 2001b; Yoshinaga et al., 2001a), applications which contribute much to the developments of the two formalisms

We investigate Global Index Grammars (GIGs), a grammar formalism that uses a stack of indices associated with productions and has restricted context-sensitive power. We discuss some of the structural descriptions that GIGs can generate compared with those generated by LIGs. We show also how GIGs can represent structural descriptions corresponding to HPSGs (Pollard and Sag, 1994) schemas.

We investigate Global Index Grammars (GIGs), a grammar formalism that uses a stack of indices associated with productions and has restricted context-sensitive power. We discuss some of the structural descriptions that GIGs can generate compared with those generated by LIGs. We show also how GIGs can represent structural descriptions corresponding to HPSGs (Pollard and Sag, 1994) schemas. 1