Semi-bracketed contextual grammars

Bracketed and fully bracketed contextual grammars were introduced to bring the concept of a tree structure to the strings by associating a pair of parentheses to the adjoined contexts in the derivation. In this paper, we show that these grammars fail to generate all the basic non-context-free languages, thus cannot be a syntactical model for natural languages. To overcome this failure, we introduce a new class of fully bracketed contextual grammars, called the semi-bracketed contextual grammars, where the selectors can also be non-minimally Dyck covered language. We see that the tree structure to the derived strings is still preserved in this variant. when this new grammar is combined with the maximality feature, the generative power of these grammars is increased to the extend of covering the family of context-free languages and some basic non-context-free languages, thus possessing many properties of the so called `MCS formalism'

On Dependency Analysis via Contractions and Weighted FSTs

Arc contractions in syntactic dependency graphs can be used to decide which graphs are trees. The paper observes that these contractions can be expressed with weighted finite-state transducers (weighted FST) that operate on string-encoded trees. The observation gives rise to a finite-state parsing algorithm that computes the parse forest and extracts the best parses from it. The algorithm is customizable to functional and bilexical dependency parsing, and it can be extended to non-projective parsing via a multi-planar encoding with prior results on high recall. Our experiments support an analysis of projective parsing according to which the worst-case time complexity of the algorithm is quadratic to the sentence length, and linear to the overlapping arcs and the number of functional categories of the arcs. The results suggest several interesting directions towards efficient and highprecision dependency parsing that takes advantage of the flexibility and the demonstrated ambiguity-packing capacity of such a parser.Peer reviewe

Algebraic optimization of recursive queries

Over the past few years, much attention has been paid to deductive databases. They offer a logic-based interface, and allow formulation of complex recursive queries. However, they do not offer appropriate update facilities, and do not support existing applications. To overcome these problems an SQL-like interface is required besides a logic-based interface.\ud \ud In the PRISMA project we have developed a tightly-coupled distributed database, on a multiprocessor machine, with two user interfaces: SQL and PRISMAlog. Query optimization is localized in one component: the relational query optimizer. Therefore, we have defined an eXtended Relational Algebra that allows recursive query formulation and can also be used for expressing executable schedules, and we have developed algebraic optimization strategies for recursive queries. In this paper we describe an optimization strategy that rewrites regular (in the context of formal grammars) mutually recursive queries into standard Relational Algebra and transitive closure operations. We also describe how to push selections into the resulting transitive closure operations.\ud \ud The reason we focus on algebraic optimization is that, in our opinion, the new generation of advanced database systems will be built starting from existing state-of-the-art relational technology, instead of building a completely new class of systems

Frequency Value Grammar and Information Theory

I previously laid the groundwork for Frequency Value Grammar (FVG) in papers I submitted in the proceedings of the 4th International Conference on Cognitive Science (2003), Sydney Australia, and Corpus Linguistics Conference (2003), Lancaster, UK. FVG is a formal syntax theoretically based in large part on Information Theory principles. FVG relies on dynamic physical principles external to the corpus which shape and mould the corpus whereas generative grammar and other formal syntactic theories are based exclusively on patterns (fractals) found occurring within the well-formed portion of the corpus. However, FVG should not be confused with Probability Syntax, (PS), as described by Manning (2003). PS is a corpus based approach that will yield the probability distribution of possible syntax constructions over a fixed corpus. PS makes no distinction between well and ill formed sentence constructions and assumes everything found in the corpus is well formed. In contrast, FVG’s primary objective is to distinguish between well and ill formed sentence constructions and, in so doing, relies on corpus based parameters which determine sentence competency. In PS, a syntax of high probability will not necessarily yield a well formed sentence. However, in FVG, a syntax or sentence construction of high ‘frequency value’ will yield a well-formed sentence, at least, 95% of the time satisfying most empirical standards. Moreover, in FVG, a sentence construction of ‘high frequency value’ could very well be represented by an underlying syntactic construction of low probability as determined by PS. The characteristic ‘frequency values’ calculated in FVG are not measures of probability but rather are fundamentally determined values derived from exogenous principles which impact and determine corpus based parameters serving as an index of sentence competency. The theoretical framework of FVG has broad applications beyond that of formal syntax and NLP. In this paper, I will demonstrate how FVG can be used as a model for improving the upper bound calculation of entropy of written English. Generally speaking, when a function word precedes an open class word, the backward n-gram analysis will be homomorphic with the information source and will result in frequency values more representative of co-occurrences in the information source