Showing papers on "Context-sensitive grammar published in 2017"
TL;DR: 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, including a graph-theoretic way to represent (partial) proofs during proof search.
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.
21 citations
TL;DR: The Generalized LR parsing algorithm is extended to the case of “grammars with left contexts” and has the same worst-case cubic-time performance as in the cases of context-free grammars.
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.
14 citations
18 Jul 2017
TL;DR: The notion of fusion grammars as a novel device for the generation of (hyper)graph languages is introduced and it is shown that fusion Grammars can simulate hyperedge replacement grammARS that generate connected hypergraphs, that the membership problem is decidable, and that fusiongrammars are more powerful than hyperedGE replacement gramMars.
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.
10 citations
TL;DR: The main advantage over existing frameworks is the ability of hybrid grammars to separate discontinuity of the desired structures from time complexity of parsing, which permits exploration of a large variety of parsing algorithms for discontinuous structures, with different properties.
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 ...
10 citations
TL;DR: The computational issues involved in learning hierarchically structured grammars from strings of symbols alone are discussed and methods based on an abstract notion of the derivational context of a syntactic category lead to learning algorithms based on a form of traditional distributional analysis.
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...
9 citations
TL;DR: An algorithm to optimally compress a finite set of terms using a vectorial totally rigid acyclic tree grammar, based on a polynomial-time reduction to the MaxSAT optimization problem.
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.
8 citations
TL;DR: This work considers d-dimensional contextual array grammars and investigates their computational power when using various control mechanisms – matrices, regular control languages, and tissue P systems, which work like regular control Languages, but may end up with a final check for the non-applicability of some rules.
7 citations
TL;DR: There is strong evidence from the laboratory for the emergence of compositional grammars in the subjects' common codes that facilitate learning efficiency and when there is a scarcity of symbols in the repertoire.
5 citations
Posted Content•
TL;DR: In this paper, the authors investigated multiple context-free tree grammars, where "simple" means linear and nondeleting, and showed that 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.
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.
5 citations
TL;DR: This paper presents a distributional learning algorithm for conjunctive grammars with the k -finite context property ( k - fcp) for each natural number k and shows that every exact cbfg has the k- fcp, while not all of them are learnable by their algorithm.
4 citations
06 Mar 2017
TL;DR: Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of P EGs.
Abstract: PEGs were formalized by Ford in 2004, and have several pragmatic operators (such as ordered choice and unlimited lookahead) for better expressing modern programming language syntax. Since these operators are not explicitly defined in the classic formal language theory, it is significant and still challenging to argue PEGs’ expressiveness in the context of formal language theory. Since PEGs are relatively new, there are several unsolved problems. One of the problems is revealing a subclass of PEGs that is equivalent to DFAs. This allows application of some techniques from the theory of regular grammar to PEGs. In this paper, we define Linear PEGs (LPEGs), a subclass of PEGs that is equivalent to DFAs. Surprisingly, LPEGs are formalized by only excluding some patterns of recursive nonterminal in PEGs, and include the full set of ordered choice, unlimited lookahead, and greedy repetition, which are characteristic of PEGs. Although the conversion judgement of parsing expressions into DFAs is undecidable in general, the formalism of LPEGs allows for a syntactical judgement of parsing expressions.
TL;DR: It is proved in this paper that every language described by a grammar with contexts can be recognized in deterministic linear space.
Proceedings Article•
01 Jan 201701 Jan 2017
TL;DR: This paper demonstrates this with a minimal example, discusses various suggestions from literature, and proposes a novel approach that can be used to address this shortcoming in the future.
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.
Posted Content•
TL;DR: The problem of context-free grammars comparison can be reduced to numerical solution of systems of nonlinear matrix equations and forms a basis for probabilistic comparison algorithms oriented to automatic assessment of of student's answers in computer science.
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.
Posted Content•
31 Oct 2017
TL;DR: A generative model for a minimalist grammar formalism is defined and a generalized algorithm for the application of variational bayesian inference to lexicalized mildly context sensitive grammars is presented.
Abstract: We define a generative model for a minimalist grammar formalism. We present a generalized algorithm for the application of variational bayesian inference to lexicalized mildly context sensitive grammars. We apply this algorithm to the minimalist grammar model.
TL;DR: It is investigated in which cases the number of active symbols induces infinite strict hierarchies and when the hierarchies collapse and the induced language families are compared among one another.
23 Oct 2017
TL;DR: Saiga is presented, a core language and small-step operational semantics that precisely captures the fundamental concepts of the specification and execution of parameterised reference attribute grammars and demonstrates the utility by proving a meta-theoretic property about attribute caching.
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.
18 Oct 2017
TL;DR: The grammar net should be considered as a new graphical tool that helps in an analysis of whether a particular sentence belongs to a given context-sensitive grammar.
Abstract: A new type of graph is introduced, the grammar graph. The possibility of assigning labels to each node in such a graph extends it to the grammar net. The grammar net should be considered as a new graphical tool that helps in an analysis of whether a particular sentence belongs to a given context-sensitive grammar. Another concept, the derivation net, closely related to the grammar graph and of a similar structure, will be used to show an algorithm that is able to decide that some sentences do not belong to a language generated by a context sensitive grammar, while leaving others as a candidate members of it.
04 Sep 2017
TL;DR: The ACG formalism is presented and how to use it as a model of the syntax-semantics interface of Tree Adjoining Grammars.
Abstract: We present the ACG formalism and how to use it as a model of the syntax-semantics interface of Tree Adjoining Grammars.
Posted Content•
TL;DR: A single parsing framework is developed which is capable of parsing grammars which are at least up to GCFGs on the hierarchy, and which can parse any particular grammar formalism that can be reduced to an Abstract Grammar.
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.
TL;DR: Evidence is not found for the idea that semantics facilitates grammar acquisition, which seems to support the view of an independent syntactic processing component.
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.
01 Jan 2017
TL;DR: The present chapter introduces and investigates the context-free and E0L grammatical derivations over different algebraic structures in order to increase the generative power of these grammars.
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
TL;DR: It is proved that for each pPN-controlled grammar, one can construct an equivalent place-labelled ordinary net controlled grammar, which has the same generative power as matrix 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.