Syntactic discontinuity is a grammatical phenomenon in which a constituent is split into more than one part because of the insertion of an element which is not part of the constituent. This is observed in many languages across the world such as Turkish, Russian, Japanese, Warlpiri, Navajo, Hopi, Dyirbal, Yidiny etc. Different formalisms/frameworks in current linguistic theory approach the problem of discontinuous structures in different ways. Each framework/formalism has widely been viewed as an independent and non-converging system of analysis. In this paper, we propose a unified system of representation for both continuity and discontinuity in structures of natural languages by taking into account three formalisms, in particular, Phrase Structure Grammar (PSG) for its widely used notion of constituency, Dependency Grammar (DG) for its head-dependent relations, and Categorial Grammar (CG) for its focus on functor-argument relations. We attempt to show that discontinuous expressions as well as continuous structures can be analysed through a unified mathematical derivation incorporating the representations of linguistic structure in these three grammar formalisms.

Unsupervised constituency parsers organize phrases within a sentence into a tree-shaped syntactic constituent structure that reflects the organization of sentence semantics. However, the traditional objective of maximizing sentence log-likelihood (LL) does not explicitly account for the close relationship between the constituent structure and the semantics, resulting in a weak correlation between LL values and parsing accuracy. In this paper, we introduce a novel objective for training unsupervised parsers: maximizing the information between constituent structures and sentence semantics (SemInfo). We introduce a bag-of-substrings model to represent the semantics and apply the probability-weighted information metric to estimate the SemInfo. Additionally, we develop a Tree Conditional Random Field (TreeCRF)-based model to apply the SemInfo maximization objective to Probabilistic Context-Free Grammar (PCFG) induction, the state-of-the-art method for unsupervised constituency parsing. Experiments demonstrate that SemInfo correlates more strongly with parsing accuracy than LL. Our algorithm significantly enhances parsing accuracy by an average of 7.85 points across five PCFG variants and in four languages, achieving new state-of-the-art results in three of the four languages.

A general method, the tensor product representation, is described for the distributed representation of value/variable bindings. The method allows the fully distributed representation of symbolic structures: the roles in the structures, as well as the fillers for those roles, can be arbitrarily non-local. Fully and partially localized special cases reduce to existing cases of connectionist representations of structured data; the tensor product representation generalizes these and the few existing examples of fuUy distributed representations of structures. The representation saturates gracefully as larger structures are represented; it penn its recursive construction of complex representations from simpler ones; it respects the independence of the capacities to generate and maintain multiple bindings in parallel; it extends naturally to continuous structures and continuous representational patterns; it pennits values to also serve as variables; it enables analysis of the interference of symbolic structures stored in associative memories; and it leads to characterization of optimal distributed representations of roles and a recirculation algorithm for learning them.