Showing papers on "Tree-adjoining grammar published in 2017"

The Grail Theorem Prover: Type Theory for Syntax and Semantics

Abstract: Type-logical grammars use a foundation of logic and type theory to model natural language. These grammars have been particularly successful giving an account of several well-known phenomena on the syntax-semantics interface, such as quantifier scope and its interaction with other phenomena. This chapter gives a high-level description of a family of theorem provers designed for grammar development in a variety of modern type-logical grammars. We discuss automated theorem proving for type-logical grammars from the perspective of proof nets, a graph-theoretic way to represent (partial) proofs during proof search.

Generalized LR Parsing Algorithm for Grammars with One-Sided Contexts

Abstract: The Generalized LR parsing algorithm for context-free grammars is notable for having a decent worst-case running time (cubic in the length of the input string, if implemented efficiently), as well as much better performance on “good” grammars. This paper extends the Generalized LR algorithm to the case of “grammars with left contexts” (M. Barash, A. Okhotin, “An extension of context-free grammars with one-sided context specifications”, Inform. Comput., 2014), which augment the context-free grammars with special operators for referring to the left context of the current substring, along with a conjunction operator (as in conjunctive grammars) for combining syntactical conditions. All usual components of the LR algorithm, such as the parsing table, shift and reduce actions, etc., are extended to handle the context operators. The resulting algorithm is applicable to any grammar with left contexts and has the same worst-case cubic-time performance as in the case of context-free grammars.

Fusion Grammars: A Novel Approach to the Generation of Graph Languages

Abstract: In this paper, we introduce the notion of fusion grammars as a novel device for the generation of (hyper)graph languages. Fusion grammars are motivated by the observation that many large and complex structures can be seen as compositions of a large number of small basic pieces. A fusion grammar is a hypergraph grammar that provides the small pieces as connected components of the start hypergraph. To get arbitrary large numbers of them, they can be copied multiple times. To get large connected hypergraphs, they can be fused by the application of fusion rules. As the first main results, we show that fusion grammars can simulate hyperedge replacement grammars that generate connected hypergraphs, that the membership problem is decidable, and that fusion grammars are more powerful than hyperedge replacement grammars.

Hybrid grammars for parsing of discontinuous phrase structures and non-projective dependency structures

Abstract: We explore the concept of hybrid grammars, which formalize and generalize a range of existing frameworks for dealing with discontinuous syntactic structures. Covered are both discontinuous phrase structures and non-projective dependency structures. Technically, hybrid grammars are related to synchronous grammars, where one grammar component generates linear structures and another generates hierarchical structures. By coupling lexical elements of both components together, discontinuous structures result. Several types of hybrid grammars are characterized. We also discuss grammar induction from treebanks. The main advantage over existing frameworks is the ability of hybrid grammars to separate discontinuity of the desired structures from time complexity of parsing. This permits exploration of a large variety of parsing algorithms for discontinuous structures, with different properties. This is confirmed by the reported experimental results, which show a wide variety of running time, accuracy, and frequency ...

Computational Learning of Syntax

Abstract: Learnability has traditionally been considered to be a crucial constraint on theoretical syntax; however, the issues involved have been poorly understood, partly as a result of the lack of simple learning algorithms for various types of formal grammars. Here I discuss the computational issues involved in learning hierarchically structured grammars from strings of symbols alone. The methods involved are based on an abstract notion of the derivational context of a syntactic category, which in the most elementary case of context-free grammars leads to learning algorithms based on a form of traditional distributional analysis. Crucially, these techniques can be extended to work with mildly context-sensitive grammars (and beyond), thus leading to learning methods that can in principle learn classes of grammars that are powerful enough to represent all natural languages. These learning methods require that the syntactic categories of the grammars be visible in a certain technical sense: They must be well charac...

Algorithmic Compression of Finite Tree Languages by Rigid Acyclic Grammars

Abstract: We present an algorithm to optimally compress a finite set of terms using a vectorial totally rigid acyclic tree grammar. This class of grammars has a tight connection to proof theory, and the grammar compression problem considered in this article has applications in automated deduction. The algorithm is based on a polynomial-time reduction to the MaxSAT optimization problem. The crucial step necessary to justify this reduction consists of applying a term rewriting relation to vectorial totally rigid acyclic tree grammars. Our implementation of this algorithm performs well on a large real-world dataset.

Active Learning of Input Grammars

Abstract: Knowing the precise format of a program's input is a necessary prerequisite for systematic testing. Given a program and a small set of sample inputs, we (1) track the data flow of inputs to aggregate input fragments that share the same data flow through program execution into lexical and syntactic entities; (2) assign these entities names that are based on the associated variable and function identifiers; and (3) systematically generalize production rules by means of membership queries. As a result, we need only a minimal set of sample inputs to obtain human-readable context-free grammars that reflect valid input structure. In our evaluation on inputs like URLs, spreadsheets, or configuration files, our AUTOGRAM prototype obtains input grammars that are both accurate and very readable - and that can be directly fed into test generators for comprehensive automated testing.

Parsing Minimalist Languages with Interpreted Regular Tree Grammars

Abstract: Minimalist Grammars (MGs) (Stabler, 1997) are a formalisation of Chomsky’s minimalist program (Chomsky, 1995), which currently dominates much of mainstream syntax. MGs are simple and intuitive to work with, and are mildly context sensitive (Michaelis, 1998), putting them in the right general class for human language (Joshi, 1985).1 Minimalist Grammars are known to be more succinct than their Multiple ContextFree equivalents (Stabler, 2013), to have regular derivation tree languages (Kobele et al., 2007), and to be recognisable in polynomial time (Harkema, 2001) with a bottom-up CKY-like parser. However, the polynomial is large, O(n4k+4) where k is a grammar constant. By approaching minimalist grammars from the perspective of Interpreted Regular Tree Grammars, we show that standard chart-based parsing is substantially computationally cheaper than previously thought at O(n2k+3 · 2k).

Multiple Context-Free Tree Grammars: Lexicalization and Characterization

Abstract: Multiple (simple) context-free tree grammars are investigated, where "simple" means "linear and nondeleting". Every multiple context-free tree grammar that is finitely ambiguous can be lexicalized; i.e., it can be transformed into an equivalent one (generating the same tree language) in which each rule of the grammar contains a lexical symbol. Due to this transformation, the rank of the nonterminals increases at most by 1, and the multiplicity (or fan-out) of the grammar increases at most by the maximal rank of the lexical symbols; in particular, the multiplicity does not increase when all lexical symbols have rank 0. Multiple context-free tree grammars have the same tree generating power as multi-component tree adjoining grammars (provided the latter can use a root-marker). Moreover, every multi-component tree adjoining grammar that is finitely ambiguous can be lexicalized. Multiple context-free tree grammars have the same string generating power as multiple context-free (string) grammars and polynomial time parsing algorithms. A tree language can be generated by a multiple context-free tree grammar if and only if it is the image of a regular tree language under a deterministic finite-copying macro tree transducer. Multiple context-free tree grammars can be used as a synchronous translation device.

Multiple Context-Free Tree Grammars and Multi-component Tree Adjoining Grammars

Abstract: Strong lexicalization is the process of turning a grammar generating trees into an equivalent one, in which all rules contain a terminal leaf. It is known that tree adjoining grammars cannot be strongly lexicalized, whereas the more powerful simple context-free tree grammars can. It is demonstrated that multiple simple context-free tree grammars are as expressive as multi-component tree adjoining grammars and that both allow strong lexicalization.

Multiword expressions and lexicalism: the view from LFG.

Abstract: Multiword expressions (MWEs) pose a problem for lexicalist theories like Lexical Functional Grammar (LFG), since they are prima facie counterexamples to a strong form of the lexical integrity principle, which entails that a lexical item can only be realised as a single, syntactically atomic word. In this paper, I demonstrate some of the problems facing any strongly lexicalist account of MWEs, and argue that the lexical integrity principle must be weakened. I conclude by sketching a formalism which integrates a Tree Adjoining Grammar into the LFG architecture, taking advantage of this relaxation.

Existing and New Ideas on Least Change Triple Graph Grammars.

Abstract: At least two actively developed model synchronization frameworks employ a conceptually similar algorithm based on Triple Graph Grammars as an underlying formalism. Although this algorithm exhibits acceptable behavior for many use cases, there are still scenarios in which it is sub-optimal, especially regarding the “least change” criterion, i.e., the extent to which models are changed to restore consistency. In this paper, we demonstrate this with a minimal example, discuss various suggestions from literature, and propose a novel approach that can be used to address this shortcoming in the future.

On the Comparison of Context-Free Grammars.

Abstract: In this paper we consider the problem of context-free grammars comparison from the analysis point of view. We show that the problem can be reduced to numerical solution of systems of nonlinear matrix equations. The approach presented here forms a basis for probabilistic comparison algorithms oriented to automatic assessment of of student's answers in computer science.

Heap Abstraction Beyond Context-Freeness

Abstract: The aim of shape analysis is to discover precise abstractions of the reachable data structures in a program's heap. This paper develops a shape analysis for reasoning about relational properties of data structures, such as balancedness of trees or lengths of lists. Both the concrete and the abstract domain are represented by hypergraphs. The analysis is based on user-defined indexed graph grammars to guide concretization and abstraction. This novel extension of context-free graph grammars is powerful enough to model complex data structures, such as balanced binary trees with parent pointers, while preserving most desirable properties of context-free graph grammars. One strength of our analysis is that no artifacts apart from grammars are required from the user; it thus offers a high degree of automation. In particular, indexed graph grammars naturally describe how a data structure evolves and require no deep knowledge about relational properties. We have implemented a prototype of our analysis and report on first experimental results.

Tree-Adjoining Grammar: A Tree-Based Constructionist Grammar Framework for Natural Language Understanding

Abstract: In this paper, we propose to use Tree-Adjoining Grammar(TAG) as a means to formalize central tenets of ConstructionGrammar (CxG). We will show that TAG, beyond its lexicalized elementary trees, provides several levels of grammatical abstraction that correspond to constructions. In other words, within the specification of a TAG one can find specifications of non-lexicalized syntactic tree fragments with their attached meaning. This allows to capture many of the insights from CxG in an explicit way. Moreover, TAG is a well-established framework in mathematical and computational linguistics. These properties make TAG a highly relevant contender for hosting constructionist implementations of natural language understanding.

A new syntactic-semantic interface for ArabTAG an Arabic Tree Adjoining grammar

Abstract: For a reliable natural language processing (NLP), it is important to know how to link the meaning of a statement or a sentence to its syntactic structure. The link between semantic and syntax can be established using a syntax-semantic interface that allows the construction of sentence meaning. In this paper, we present a new approach, which built a tree adjoining grammar to represent the syntax and the semantic of modern standard Arabic. In the first part, we detail the process that automatically generates this grammar using Arab-XMG meta-grammar. Then we explain how we have established the link between syntax and semantic and how we have introduced the semantic frame -based dimension into the meta-grammar using Arabic Verbnet.

A formalisation of parameterised reference attribute grammars

Abstract: The similarities and differences between attribute grammar systems are obscured by their implementations. A formalism that captures the essence of such systems would allow for equivalence, correctness, and other analyses to be formally framed and proven. We present Saiga, a core language and small-step operational semantics that precisely captures the fundamental concepts of the specification and execution of parameterised reference attribute grammars. We demonstrate the utility of by a) proving a meta-theoretic property about attribute caching, and b) by specifying two attribute grammars for a realistic name analysis problem and proving that they are equivalent. The language, semantics and associated tests have been mechanised in Coq; we are currently mechanising the proofs.

Reflexives and Reciprocals in Synchronous Tree Adjoining Grammar

Abstract: Citation: Proceedings of the 13th International Workshop on Tree Adjoining Grammars and Related Formalisms (TAG+13), pages 31–42, Umea, Sweden, September 4–6, 2017.

The Role of Simple Semantics in the Process of Artificial Grammar Learning.

Abstract: This study investigated the effect of semantic information on artificial grammar learning (AGL). Recursive grammars of different complexity levels (regular language, mirror language, copy language) were investigated in a series of AGL experiments. In the with-semantics condition, participants acquired semantic information prior to the AGL experiment; in the without-semantics control condition, participants did not receive semantic information. It was hypothesized that semantics would generally facilitate grammar acquisition and that the learning benefit in the with-semantics conditions would increase with increasing grammar complexity. Experiment 1 showed learning effects for all grammars but no performance difference between conditions. Experiment 2 replicated the absence of a semantic benefit for all grammars even though semantic information was more prominent during grammar acquisition as compared to Experiment 1. Thus, we did not find evidence for the idea that semantics facilitates grammar acquisition, which seems to support the view of an independent syntactic processing component.

Abstract Categorial Grammars as a Model of the Syntax-Semantics Interface for TAG

Abstract: We present the ACG formalism and how to use it as a model of the syntax-semantics interface of Tree Adjoining Grammars.

A generalized parsing framework for Abstract Grammars

Abstract: This technical report presents a general framework for parsing a variety of grammar formalisms. We develop a grammar formalism, called an Abstract Grammar, which is general enough to represent grammars at many levels of the hierarchy, including Context Free Grammars, Minimalist Grammars, and Generalized Context-free Grammars. We then develop a single parsing framework which is capable of parsing grammars which are at least up to GCFGs on the hierarchy. Our parsing framework exposes a grammar interface, so that it can parse any particular grammar formalism that can be reduced to an Abstract Grammar.

Algebra, Grammars, and Computation

Abstract: In terms of algebra, the context-free and E0L grammatical derivations are traditionally defined over the free monoids generated by total alphabets of these grammars under the operation of concatenation The present chapter, however, introduces and investigates these derivations over different algebraic structures in order to increase the generative power of these grammars

Place-labelled Petri net controlled grammars

Abstract: A place-labelled Petri net (pPN) controlled grammar is a context-free grammar equipped with a Petri net and a function which maps places of the net to the productions of the grammar. The language consists of all terminal strings that can be obtained by simultaneously applying the rules of multisets which are the images of the sets of the input places of transitions in a successful occurrence sequence of the Petri net. In this paper, we study the generative power and structural properties of pPN-controlled grammars. We show that pPN-controlled grammars have the same generative power as matrix grammars. Moreover, we prove that for each pPN-controlled grammar, we can construct an equivalent place-labelled ordinary net controlled grammar.