We first recall some basic notions on minimalist grammars and on categorial grammars. Next we shortly introduce partially commutative linear logic, and our representation of minimalist grammars within this categorial system, the so-called categorial minimalist grammars. Thereafter we briefly present λμ-DRT (Discourse Representation Theory) an extension of λ-DRT (compositional DRT) in the framework of λμcalculus: it avoids type raising and derives different readings from a single semantic representation, in a setting which follows discourse structure. We run a complete example which illustrates the various structures and rules that are needed to derive a semantic representation from the categorial view of a transformational syntactic analysis.
Stabler proposes an implementation of the Chomskyan Minimalist Program, Chomsky 95 with Minimalist Grammars - MG, Stabler 97. This framework inherits a long linguistic tradition. But the semantic calculus is more easily added if one uses the Curry-Howard isomorphism. Minimalist Categorial Grammars - MCG, based on an extension of the Lambek calculus, the mixed logic, were introduced to provide a theoretically-motivated syntax-semantics interface, Amblard 07. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a pro…
A well-known approach to treating syntactic island constraints in the setting of Lambek grammars consists in adding specific bracket modalities to the logic. We adapt this approach to abstract categorial grammars (ACG). Thus we define bracketed (implicational) linear logic, bracketed lambda-calculus, and, eventually, bracketed ACG based on bracketed $λ$-calculus. This allows us modeling at least simplest island constraints, typically, in the context of relativization. Next we identify specific safely bracketed ACG which, just like ordinary (bracket-free) second order ACG generate effectively d…
We present the LexGram system, an amalgam of (Lambek) categorial grammar and Head Driven Phrase Structure Grammar (HPSG), and show that the grammar formalism it implements is a well-structured and useful tool for actual grammar development.
The paper describes a parser for Categorial Grammar which provides fully word by word incremental interpretation. The parser does not require fragments of sentences to form constituents, and thereby avoids problems of spurious ambiguity. The paper includes a brief discussion of the relationship between basic Categorial Grammar and other formalisms such as HPSG, Dependency Grammar and the Lambek Calculus. It also includes a discussion of some of the issues which arise when parsing lexicalised grammars, and the possibilities for using statistical techniques for tuning to particular languages.
National Research University Higher School of Economics（俄罗斯国家研究型高等经济大学）
We consider tensor grammars, which are an example of \commutative" grammars, based on the classical (rather than intuitionistic) linear logic. They can be seen as a surface representation of abstract categorial grammars ACG in the sense that derivations of ACG translate to derivations of tensor grammars and this translation is isomorphic on the level of string languages. The basic ingredient are tensor terms, which can be seen as encoding and generalizing proof-nets. Using tensor terms makes the syntax extremely simple and a direct geometric meaning becomes transparent. Then we address the pro…
National Research University Higher School of Economics（国立研究大学高等经济学院）
We study relationship between first order multiplicative linear logic (MLL1), which has been known to provide representations to different categorial grammars, and the recently introduced extended tensor type calculus (ETTC). We identify a fragment of MLL1, which seems sufficient for many grammar representations, and establish a correspondence between ETTC and this fragment. The system ETTC, thus, can be seen as an alternative syntax and intrinsic deductive system together with a geometric representation for the latter. We also give a natural deduction formulation of ETTC, which might be conve…
We present a system for the investigation of computational properties of categorial grammar parsing based on a labelled analytic tableaux theorem prover. This proof method allows us to take a modular approach, in which the basic grammar can be kept constant, while a range of categorial calculi can be captured by assigning different properties to the labelling algebra. The theorem proving strategy is particularly well suited to the treatment of categorial grammar, because it allows us to distribute the computational cost between the algorithm which deals with the grammatical types and the algeb…
We propose a generalization of Categorial Grammar in which lexical categories are defined by means of recursive constraints. In particular, the introduction of relational constraints allows one to capture the effects of (recursive) lexical rules in a computationally attractive manner. We illustrate the linguistic merits of the new approach by showing how it accounts for the syntax of Dutch cross-serial dependencies and the position and scope of adjuncts in such constructions. Delayed evaluation is used to process grammars containing recursive constraints.
National Research University Higher School of Economics（国立研究大学高等经济学院）
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)} are not abstract $λ$-terms, but simply tuples of words with labeled endpoints and supplied with specific {\it plugging instructions}: the sets of endpoints are subdivided into the {\it incoming} and the {\it outgoing} parts. We call such objects {\it word cobordisms}. A key observation is that word cobordisms can be organized in a category, very similar to …
Under categorial grammars that have powerful rules like composition, a simple n-word sentence can have exponentially many parses. Generating all parses is inefficient and obscures whatever true semantic ambiguities are in the input. This paper addresses the problem for a fairly general form of Combinatory Categorial Grammar, by means of an efficient, correct, and easy to implement normal-form parsing technique. The parser is proved to find exactly one parse in each semantic equivalence class of allowable parses; that is, spurious ambiguity (as carefully defined) is shown to be both safely and …
We discuss an extension of the standard logical rules (functional application and abstraction) in Categorial Grammar (CG), in order to deal with some specific cases of polysemy. We borrow from Generative Lexicon theory which proposes the mechanism of {\em coercion}, next to a rich nominal lexical semantic structure called {\em qualia structure}. In a previous paper we introduced coercion into the framework of {\em sign-based} Categorial Grammar and investigated its impact on traditional Fregean compositionality. In this paper we will elaborate on this idea, mostly working towards the introduct…
National Research University Higher School of Economics（国立研究型大学高等经济学院）
We propose a concrete surface representation of abstract categorial grammars in the category of word cobordisms or cowordisms for short, which are certain bipartite graphs decorated with words in a given alphabet, generalizing linear logic proof-nets. We also introduce and study linear logic grammars, directly based on cobordisms and using classical multiplicative linear logic as a typing system.
National Research University Higher School of Economics（俄罗斯国立高等经济大学）
We propose a categorial grammar based on classical multiplicative linear logic. This can be seen as an extension of abstract categorial grammars (ACG) and is at least as expressive. However, constituents of {\it linear logic grammars (LLG)} are not abstract $λ$-terms, but simply tuples of words with labeled endpoints, we call them {\it multiwords}. At least, this gives a concrete and intuitive representation of ACG. A key observation is that the class of multiwords has a fundamental algebraic structure. Namely, multiwords can be organized in a category, very similar to the category of topologi…
Although unification can be used to implement a weak form of $β$-reduction, several linguistic phenomena are better handled by using some form of $λ$-calculus. In this paper we present a higher order feature description calculus based on a typed $λ$-calculus. We show how the techniques used in \CLG for resolving complex feature constraints can be efficiently extended. \CCLG is a simple formalism, based on categorial grammars, designed to test the practical feasibility of such a calculus.
This paper addresses the problem of mapping natural language sentences to lambda-calculus encodings of their meaning. We describe a learning algorithm that takes as input a training set of sentences labeled with expressions in the lambda calculus. The algorithm induces a grammar for the problem, along with a log-linear model that represents a distribution over syntactic and semantic analyses conditioned on the input sentence. We apply the method to the task of learning natural language interfaces to databases and show that the learned parsers outperform previous methods in two benchmark databa…
Stanford University（斯坦福大学）；McGill University（麦吉尔大学）；École Polytechnique Fédérale de Lausanne（洛桑联邦理工学院）；University of California, San Diego（加利福尼亚大学圣地亚哥分校）
The following technical report presents a formal approach to probabilistic minimalist grammar parameter estimation. We describe a formalization of a minimalist grammar. We then present an algorithm for the application of variational Bayesian inference to this formalization.
In this article we show that hybrid type-logical grammars are a fragment of first-order linear logic. This embedding result has several important consequences: it not only provides a simple new proof theory for the calculus, thereby clarifying the proof-theoretic foundations of hybrid type-logical grammars, but, since the translation is simple and direct, it also provides several new parsing strategies for hybrid type-logical grammars. Second, NP-completeness of hybrid type-logical grammars follows immediately. The main embedding result also sheds new light on problems with lambda grammars/abs…
University of Washington（华盛顿大学）；The Chinese University of Hong Kong (Shenzhen)（香港中文大学（深圳））；Shenzhen Research Institute of Big Data（深圳大数据研究院）
Supertagging is conventionally regarded as an important task for combinatory categorial grammar (CCG) parsing, where effective modeling of contextual information is highly important to this task. However, existing studies have made limited efforts to leverage contextual features except for applying powerful encoders (e.g., bi-LSTM). In this paper, we propose attentive graph convolutional networks to enhance neural CCG supertagging through a novel solution of leveraging contextual information. Specifically, we build the graph from chunks (n-grams) extracted from a lexicon and apply attention ov…
This paper describes a probabilistic top-down parser for minimalist grammars. Top-down parsers have the great advantage of having a certain predictive power during the parsing, which takes place in a left-to-right reading of the sentence. Such parsers have already been well-implemented and studied in the case of Context-Free Grammars, which are already top-down, but these are difficult to adapt to Minimalist Grammars, which generate sentences bottom-up. I propose here a way of rewriting Minimalist Grammars as Linear Context-Free Rewriting Systems, allowing to easily create a top-down parser. T…
We introduce (1) a novel parser for Minimalist Grammars (MG), encoded as a system of first-order logic formulae that may be evaluated using an SMT-solver, and (2) a novel procedure for inferring Minimalist Grammars using this parser. The input to this procedure is a sequence of sentences that have been annotated with syntactic relations such as semantic role labels (connecting arguments to predicates) and subject-verb agreement. The output of this procedure is a set of minimalist grammars, each of which is able to parse the sentences in the input sequence such that the parse for a sentence has…
University of Kentucky（肯塔基大学）；Technische Universität Wien（维也纳工业大学）
Combinatory categorial grammar (CCG) is a grammar formalism used for natural language parsing. CCG assigns structured lexical categories to words and uses a small set of combinatory rules to combine these categories to parse a sentence. In this work we propose and implement a new approach to CCG parsing that relies on a prominent knowledge representation formalism, answer set programming (ASP) - a declarative programming paradigm. We formulate the task of CCG parsing as a planning problem and use an ASP computational tool to compute solutions that correspond to valid parses. Compared to other …
Utrecht Institute of Linguistics OTS（乌得勒支语言学研究所OTS）
The Lambek-Grishin calculus is a symmetric extension of the Lambek calculus: in addition to the residuated family of product, left and right division operations of Lambek's original calculus, one also considers a family of coproduct, right and left difference operations, related to the former by an arrow-reversing duality. Communication between the two families is implemented in terms of linear distributivity principles. The aim of this paper is to complement the symmetry between (dual) residuated type-forming operations with an orthogonal opposition that contrasts residuated and Galois connec…
Humboldt-Universität zu Berlin（柏林洪堡大学）；Bernstein Center for Computational Neuroscience（伯恩斯坦计算神经科学中心）；University of Potsdam（波茨坦大学）
We reformulate minimalist grammars as partial functions on term algebras for strings and trees. Using filler/role bindings and tensor product representations, we construct homomorphisms for these data structures into geometric vector spaces. We prove that the structure-building functions as well as simple processors for minimalist languages can be realized by piecewise linear operators in representation space. We also propose harmony, i.e. the distance of an intermediate processing step from the final well-formed state in representation space, as a measure of processing complexity. Finally, we…
NeTS – IUSS lab for NEurolinguistics, Computational Linguistics, and Theoretical Syntax, Pavia（帕维亚 IUSS 神经语言学、计算语言学与理论句法实验室（NeTS））
Expectation-based Minimalist Grammars (e-MGs) are simplified versions of the (Conflated) Minimalist Grammars, (C)MGs, formalized by Stabler (Stabler, 2011, 2013, 1997) and Phase-based Minimalist Grammars, PMGs (Chesi, 2005, 2007; Stabler, 2011). The crucial simplification consists of driving structure building only by relying on lexically encoded categorial top-down expectations. The commitment on a top-down derivation (as in e-MGs and PMGs, as opposed to (C)MGs, Chomsky, 1995; Stabler, 2011) allows us to define a core derivation that should be the same in both parsing and generation (Momma & …
This paper describes a computational framework for a grammar architecture in which different linguistic domains such as morphology, syntax, and semantics are treated not as separate components but compositional domains. Word and phrase formation are modeled as uniform processes contributing to the derivation of the semantic form. The morpheme, as well as the lexeme, has lexical representation in the form of semantic content, tactical constraints, and phonological realization. The motivation for this work is to handle morphology-syntax interaction (e.g., valency change in causatives, subcategor…
Center for the Study of Language and Information（语言与信息研究中心）
We propose an extension of Stabler's version of clitics treatment for a wider coverage of the French language. For this, we present the lexical entries needed in the lexicon. Then, we show the recognition of complex syntactic phenomena as (left and right) dislo- cation, clitic climbing over modal and extraction from determiner phrase. The aim of this presentation is the syntax-semantic interface for clitics analyses in which we will stress on clitic climbing over verb and raising verb.
Brandenburgische Technische Universität Cottbus – Senftenberg（科特布斯-森夫滕堡勃兰登堡工业大学）
Speech-controlled user interfaces facilitate the operation of devices and household functions to laymen. State-of-the-art language technology scans the acoustically analyzed speech signal for relevant keywords that are subsequently inserted into semantic slots to interpret the user's intent. In order to develop proper cognitive information and communication technologies, simple slot-filling should be replaced by utterance meaning transducers (UMT) that are based on semantic parsers and a \emph{mental lexicon}, comprising syntactic, phonetic and semantic features of the language under considera…
Utrecht Institute of Language Sciences（乌得勒支语言科学研究所）
The syntactic categories of categorial grammar formalisms are structured units made of smaller, indivisible primitives, bound together by the underlying grammar's category formation rules. In the trending approach of constructive supertagging, neural models are increasingly made aware of the internal category structure, which in turn enables them to more reliably predict rare and out-of-vocabulary categories, with significant implications for grammars previously deemed too complex to find practical use. In this work, we revisit constructive supertagging from a graph-theoretic perspective, and …
Many theories of semantic interpretation use lambda-term manipulation to compositionally compute the meaning of a sentence. These theories are usually implemented in a language such as Prolog that can simulate lambda-term operations with first-order unification. However, for some interesting cases, such as a Combinatory Categorial Grammar account of coordination constructs, this can only be done by obscuring the underlying linguistic theory with the ``tricks'' needed for implementation. This paper shows how the use of abstract syntax permitted by higher-order logic programming allows an elegan…
While the DisCoCat model (Coecke et al., 2010) has been proved a valuable tool for studying compositional aspects of language at the level of semantics, its strong dependency on pregroup grammars poses important restrictions: first, it prevents large-scale experimentation due to the absence of a pregroup parser; and second, it limits the expressibility of the model to context-free grammars. In this paper we solve these problems by reformulating DisCoCat as a passage from Combinatory Categorial Grammar (CCG) to a category of semantics. We start by showing that standard categorial grammars can b…
University of Gothenburg（哥德堡大学）；University of Latvia（拉脱维亚大学）
Berkeley FrameNet is a lexico-semantic resource for English based on the theory of frame semantics. It has been exploited in a range of natural language processing applications and has inspired the development of framenets for many languages. We present a methodological approach to the extraction and generation of a computational multilingual FrameNet-based grammar and lexicon. The approach leverages FrameNet-annotated corpora to automatically extract a set of cross-lingual semantico-syntactic valence patterns. Based on data from Berkeley FrameNet and Swedish FrameNet, the proposed approach ha…
LORIA（洛林计算机科学及其应用实验室）；INRIA Nancy Grand Est（法国国家信息与自动化研究所南锡大东部分部）；Université Nancy 2（南锡第二大学）；INPL（洛林国立理工学院）
This article presents an extension of Minimalist Categorial Gram- mars (MCG) to encode Chomsky's phases. These grammars are based on Par- tially Commutative Logic (PCL) and encode properties of Minimalist Grammars (MG) of Stabler. The first implementation of MCG were using both non- commutative properties (to respect the linear word order in an utterance) and commutative ones (to model features of different constituents). Here, we pro- pose to adding Chomsky's phases with the non-commutative tensor product of the logic. Then we could give account of the PIC just by using logical prop- erties o…
The Lambek calculus provides a foundation for categorial grammar in the form of a logic of concatenation. But natural language is characterized by dependencies which may also be discontinuous. In this paper we introduce the displacement calculus, a generalization of Lambek calculus, which preserves its good proof-theoretic properties while embracing discontinuiity and subsuming it. We illustrate linguistic applications and prove Cut-elimination, the subformula property, and decidability
This paper presents a theory and a computational implementation for generating prosodically appropriate synthetic speech in response to database queries. Proper distinctions of contrast and emphasis are expressed in an intonation contour that is synthesized by rule under the control of a grammar, a discourse model, and a knowledge base. The theory is based on Combinatory Categorial Grammar, a formalism which easily integrates the notions of syntactic constituency, semantics, prosodic phrasing and information structure. Results from our current implementation demonstrate the system's ability to…
We present an analysis of the semantic interpretation of intensional verbs such as seek that allows them to take direct objects of either individual or quantifier type, producing both de dicto and de re readings in the quantifier case, all without needing to stipulate type-raising or quantifying-in rules. This simple account follows directly from our use of logical deduction in linear logic to express the relationship between syntactic structures and meanings. While our analysis resembles current categorial approaches in important ways, it differs from them in allowing the greater type flexibi…
Rutgers, The State University of New Jersey（罗格斯大学，新泽西州立大学）
In this thesis we present a semantic representation formalism based on directed graphs and explore its linguistic adequacy and explanatory benefits in the semantics of plurality and quantification. Our graph language covers the essentials of natural language semantics using only monadic second-order variables. We define its model-theoretical interpretation in terms of graph traversal, where the relative scope of variables arises from their order of valuation. We present a unification-based mechanism for constructing semantic graphs at a simple syntax-semantics interface, where syntax as a part…
We investigate the possibility of modelling the syntax and semantics of natural language by constraints, or rules, imposed by the multi-dimensional type theory Nabla. The only multiplicity we explicitly consider is two, namely one dimension for the syntax and one dimension for the semantics, but the general perspective is important. For example, issues of pragmatics could be handled as additional dimensions. One of the main problems addressed is the rather complicated repertoire of operations that exists besides the notion of categories in traditional Montague grammar. For the syntax we use a …
Comparative constructions play an important role in natural language inference. However, attempts to study semantic representations and logical inferences for comparatives from the computational perspective are not well developed, due to the complexity of their syntactic structures and inference patterns. In this study, using a framework based on Combinatory Categorial Grammar (CCG), we present a compositional semantics that maps various comparative constructions in English to semantic representations and introduces an inference system that effectively handles logical inference with comparativ…
The University of Tokyo（东京大学）；Ochanomizu University（御茶水女子大学）；Artificial Intelligence Research Center, AIST（产业技术综合研究所人工智能研究中心）
Determining semantic textual similarity is a core research subject in natural language processing. Since vector-based models for sentence representation often use shallow information, capturing accurate semantics is difficult. By contrast, logical semantic representations capture deeper levels of sentence semantics, but their symbolic nature does not offer graded notions of textual similarity. We propose a method for determining semantic textual similarity by combining shallow features with features extracted from natural deduction proofs of bidirectional entailment relations between sentence …
University of Groningen（格罗宁根大学）；École Normale Supérieure de Cachan（卡尚高等师范学院）；University of Trento（特伦托大学）
The Parallel Meaning Bank is a corpus of translations annotated with shared, formal meaning representations comprising over 11 million words divided over four languages (English, German, Italian, and Dutch). Our approach is based on cross-lingual projection: automatically produced (and manually corrected) semantic annotations for English sentences are mapped onto their word-aligned translations, assuming that the translations are meaning-preserving. The semantic annotation consists of five main steps: (i) segmentation of the text in sentences and lexical items; (ii) syntactic parsing with Comb…
