Formal grammars

In this paper we will attempt to classify Lindenmayer systems based on properties of sets of rules and the kind of strings those rules generate. This classification will be referred to as a ‘parametrization’ of the L-space: the L-space is the phase space in which all possible L-developments are represented.

n this talk we review some foundational notions that underlie theories of natural language syntax and, more generally, structure in formal symbolic systems. We introduce and explain the main features of the models that are used to characterise structure in a linguistic signal; these models are what we call grammars: finite sets of rules that operate over pre-defined alphabets of symbols and generate sequences, or strings. All grammars used in linguistic research and computer science belong in an inclusive hierarchy known as the Chomsky Hierarchy where they are classified depending on the properties of the structures they can generate (e.g,, is there embedding? Do we need some kind of memory buffer to account for dependencies in a signal? Can we have dependencies between non-adjacent symbols?): this is the space of normal grammars and the one we are most familiar with. We also venture into what lies outside the Chomsky Hierarchy, and explore the properties of systems that does not abide to the rules of normal grammars and thus cannot be pinpointed within the Chomsky Hierarchy: these are Lindenmayer grammars (L-grammars). We define, characterise, and classify L-grammars based on properties of the sets of rules defined in these formalisms and the kind of strings those rules generate. Just as the space of normal grammars is classified into Regular, Context-Free, Context-Sensitive, and Unrestricted (with proper containment relations holding among them; see Chomsky, 1959: Theorem 1), we contend here that the space of L-grammars is a very rich landscape of grammars which cluster into kinds that are not mutually translatable: symmetric and asymmetric grammars.

Искусственная нотации BFT предназначена для улучшения коммуникации между носителями различных формальных систем. Нотация дополняет текст логическими конструкциями удобными для осмысленного чтения и одновременно пригодными для машинного анализа. В отличие от иерархической разметки знаний формата XML или JSON-LD, предложенный формат BFT имеет сетевую модель.

El objetivo de la obra que aquí se presenta es sencillo; pretende ofrecer una aproximación a la génesis, evolución y repercusión lingüística de una teoría gramatical conocida como la Gramática Léxico-Funcional, pretende asentar los fundamentos teóricos de dicha gramática así como describir sus principales aplicaciones a la lengua castellana. Para ello, partiremos muy especialmente de dos trabajos capitales en el desarrollo de esta teoría, a saber, el capítulo de Kaplan y Bresnan (1982) –trabajo en el que se asientan las bases teóricas de la gramática– y el libro de Bresnan (2001) –trabajo en el que su autora desarrolla las últimas propuestas teóricas de la gramática–.
Para llevar a cabo esta empresa, el presente libro consta de seis capítulos. En el primer capítulo, queremos dar respuesta al primer objetivo formulado, esto es, qué es la Gramática Léxico-Funcional, cuáles fueron sus orígenes y qué ha supuesto la introducción de esta gramática para el conjunto de teorías gramaticales ya existentes. En concreto, nos centraremos en la cuestión de las influencias que ha recibido de, posiblemente, la teoría gramatical más importante desde la segunda mitad del siglo XX, a saber, la Gramática Generativa Transformacional así como de la repercusión que ha tenido para esta teoría gramatical el desarrollo de la Gramática Léxico-Funcional.
En segundo lugar, en los capítulos 2, 3 y 4, la finalidad que se persigue es presentar los conceptos básicos de la Gramática Léxico-Funcional que permitan comprender su funcionamiento así como los fenómenos sintácticos en los que estos conceptos se fundamentan. En estos capítulos, se introducirán conceptos tales como estructura-c, estructura-f, función matemática, Integridad léxica, Condición de Unicidad, Condición de Completitud, Condición de Coherencia, lenguas configuracionales y lenguas no configuracionales, ecuación funcional... Como se tratará en los capítulos indicados, la unión de algunos de estos conceptos otorgan a la Gramática Léxico-Funcional una considerable robustez y explicitud teórica que la convierten en un buen formalismo gramatical en el que todo queda bien justificado, relacionado y especificado.
Por último, en los capítulos 5 y 6, se introducen algunas de las aplicaciones más importantes de la LFG en el estudio de las lenguas naturales. En concreto, en el capítulo 5, se tratan cuatro fenómenos sintácticos cuya elección no es casual sino que responde a la importancia que se les ha concedido a estos fenómenos en las últimas décadas. Respecto al capítulo 6, cabe señalar que este capítulo presenta tanto un aspecto teórico –i e. presentar la teoría argumental de la Gramática Léxico-Funcional– como de aplicación a la lengua castellana –i. e. se describe cómo se asignan los papeles semánticos en los argumentos de algunos verbos del castellano–.

This paper examines Minimal Search, an operation that is at the core of current Minimalist inquiry. We argue that, given Minimalist assumptions about structure building consisting of unordered set formation, there are serious difficulties in defining Minimal Search as a search algorithm. Furthermore, some problematic configurations for Minimal Search (namely, {XP, YP} and {X, Y}) are argued to be an artefact of these set-theoretic commitments. However, if unordered sets are given up as the format of structural descriptions in favour of directed graphs such that Merge(X, Y) creates an arc from X to Y, Minimal Search can be straightforwardly characterised as a sequential deterministic search algorithm: the total order required to define MS as a sequential search algorithm is provided by structure building.

Gli algoritmi sono metodi per la soluzione di problemi. Possiamo caratterizzare un problema mediante i dati di cui si dispone all'inizio e dei risultati che si vogliono ottenere: risolvere un problema significa ottenere in uscita i risultati desiderati a partire da un certo insieme di dati presi in ingresso. I dati in ingresso vengono anche detti (valori in) input ei risultati in uscita (valori in) output. Possiamo assumere che ciascun problema consista di un insieme di casi particolari, o istanze.

Computational design has recently come to recast the conventional urban design strategies. The complexity of urban planning exceeds the potential owned by manual design techniques to produce an array of distinguishable solutions while competent to deal with varying demands during urban design process. This paper explores the means to create a flexible urban design tool that could afford to conceive complex solutions with cooperative computational design techniques. The computational process defined to accomplish a flexible tool is divided into two parts; shape grammars and evolutionary algorithms. The flexibility to satisfy constantly changing demands is constituted by parametric shape grammars that consist of variables. Genetic algorithms and genetic programming are compared and suggested to meet the optimisation problem of the flexibility controlled by parametric variables which are described by shape grammars. Since these techniques imitate evolutionary theories, primitive urban patterns and the philosophies in the background are discussed to elucidate the concept of urban. In so doing, it is aimed to adhere to a theoretically rich foundation on which a robust design tool could be built.
With regards to a pragmatic explanation, urban neoliberalism is addressed as it paves the way for large-scale developments. Urban projects such as urban renewals and neighbourhood extensions are prevalent implementations of Neoliberal urbanism in fast-growing countries where the accelerated urban design practices cause the distortion of existing urban texture. The parametric urban design tool proposed in this paper pays special attention to the coexistence of the new and old in harmony with each other. Therefore, the goal of this paper is to present a guidance for a computational solution within this complexity.

Proof-theoretic models of grammar are based on the view that an explicit characterization of a language comes in the form of the recursive enumeration of strings in that language. That recursive enumeration is carried out by a procedure which strongly generates a set of structural descriptions Σ and weakly generates a set of strings S; a grammar is thus a function that pairs an element of Σ with elements of S (Chomsky, 1965). Structural descriptions are obtained by means of Context-Free phrase structure rules (e.g., X-bar theory) or via recursive combinatorics (Merge) and structure is assumed to be uniform: binary branching trees all the way down. In this work we will analyse natural language constructions for which such a rigid conception of phrase structure results descriptively inadequate, and propose a solution for the problem of phrase structure grammars assigning too much or too little structure to natural language strings: we propose that the grammar can oscillate between levels of computational complexity in local domains, which correspond to elementary trees in a lexicalised Tree Adjoining Grammar.

The paper discusses the implementation of a multi-agent system as an integral component of a hybrid, digital-physical architectural environment. It contributes to the existing practice-based architectural research in two ways: 1) by describing an innovative integration of a multi-agent system for surface patterning; and 2) by discussing this integration in terms of emergent materiality. This case-study demonstrates suggestive creative approaches and observes in the field the operation of a concept that promises to be useful for future analysis, research and design."

In this paper we present two approaches to Lindenmayer systems (L-systems): the procedural (or ‘generative’) approach, which focuses on L-systems as string rewriting systems, and a declarative (or ‘model-theoretic’) approach, where the grammar is a set of local admissibility conditions: in this paper, these conditions will be defined over graphs. We contend that it is possible, for a subset of L-systems and the languages they generate, to map superficial regularities in the distribution of symbols at the string level to local tree admissibility conditions, effectively providing a way to link string languages and tree languages in a novel manner. We will work out how to construct structure assuming only superficial constraints on expressions, and define a set of constraints that well-formed expressions of specific L-languages must satisfy. A significant result is that L-systems which are distinguished by methods focused on derivational properties turn out to satisfy the same model: this has consequences for the use of L-systems as probes for human sensitivity to hierarchical structure in Artificial Grammar Learning (AGL) protocols.

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This short sketch is a version 7.1 description of Analytical Syntax of the Sanskrit language basing on both formal (syntactic and morphological) and logico-semantic criteria. The work is written in Russian. The source of the work is both bulk reading of Classical Sanskrit texts and elaborating the Paninian system, as well as some comparative work on Classical Tibetan, English, Russian, Spanish, Chinese, and Nahuatl. The work is aimed at building a system which would help to both automatically process (parse) Sanskrit texts and improve both reference and study-books on Classical Sanskrit.

Top-down (LL) context-sensitive parsers with integrated synthesis and use of attributes are easy to expressin functional programming languages, but the elegant functional programming model can also serve as an exact prototype for a more efficient implementation of the technology in ANSI C. The result is a compiler-compiler that takes unlimited lookahead and backtracking, the extended BNF notation, and parameterized grammars with (higher-order) meta-parameters to the world of C programming. This article reports on the utility in question three years after public release. Precc generates standard ANSI C and is ‘plug compatible’ with lex-generated lexical analyzers prepared for the UNIX yacc compiler-compiler. In contrast to yacc, however, the generated code is modular, which allows parts of scripts to be compiled separately and linked together incrementally. The constructed code is relatively efficient, as is demonstrated by the example Occam parser treated in depth here, but the main advantages we claim are ease of use, separation of specification and implementation concerns, and maintainability.

Keywords: compiler-compiler; parsers; yacc; infinite-lookahead; top-down parsing; grammars; Occam

In the present work we will present and analyze some basic processes at the local and global level in linguistic derivations that do not seem to conform to either Markovian or Turing-like computation, particularly as they are modeled within generative linguistics. We will first present briefly the working hypothesis and then focus on the empirical domain. At the same time, we will argue that a model of the mind that assumes that computational processes are uniform (i.e., that a single formal grammar can and should be used to model the generation of all cognitive structures) is necessarily insufficient as it either falls short or assigns too much structure to different stimuli, and thus computationally mixed formal models are to be invoked in order to pursue a fuller understanding of mental processes within a unified framework.

[Old and outdated, but fun all the same. At the time, it was a reaction to Collins and Stabler's paper 'A formalization of Minimalist Syntax' (published in 2016). The few things that are worth keeping from this piece have been incorporated into my thesis and recent papers on graph theoretic analyses]

In this paper we attempt a logic-mathematical formalization of the program for (linguistic) investigation that we have called Radical Minimalism, in order to make the model fully explicit and reveal its potential to be applied not only sub-personally and to the language domain exclusively, but to any physical system one considers. For those purposes, we have devised a logical model of syntax (understood as a general-purpose free and unbounded generative algorithm), with which we capture the properties of mental workspaces and the cognitive organization of the phenomenological reality. We will combine our Strong Radically Minimalist Thesis with Tegmark’s (2007) Mathematical Universe Hypothesis, and analyze how both strengthen in interaction gaining in empirical coverage and theoretical weight. The aim is to formalize a possibility for the study of language as a physical system from an interdisciplinary perspective: a joint work between Formal Linguistics, Logic, Physics and Mathematics.

Abstract. As the current digitally-mediated architectural practice evolves, architectural models, regardless of their expressiveness or type, are a way to craft the interaction between the designer and the designed object. Models become artefacts that engage on a continuous interaction with the designer via different media, interpretation and knowledge retrieval schemes, organizational flows and tools. These interactions have recently been facilitated by the use of physical and digital production and analysis methods. In this report, we introduce a novel understanding of the relationships  between physical and digital modelling techniques. We propose an updated framework that allocates these relationships into four categories: directed production, non-directed production, dual modelling, and mixed modelling. A review of different modelling classifications and frameworks is presented and exemplary case studies from the design domain are introduced for each category.

Abstract. As the current digitally-mediated architectural practice evolves, architectural models, regardless of their expressiveness or type, are a way to craft the interaction between the designer and the designed object. Models become artefacts that engage on a continuous interaction with the designer via different media, interpretation and knowledge retrieval schemes, organizational flows and tools. These interactions have recently been facilitated by the use of physical and digital production and analysis methods. In this report, we introduce a novel understanding of the relationships between physical and digital modelling techniques. We propose an updated framework that allocates these relationships into four categories: directed production, non-directed production, dual modelling, and mixed modelling. A review of different modelling classifications and frameworks is presented and exemplary case studies from the design domain are introduced for each category.

In this work we will develop the thesis that the concept of dynamical frustration (Binder, 2008), involving the tension between conflicting tendencies in a physical system, is essential when analyzing the cognitive-computational bases of language. We will argue that there are two kinds of frustrations interplaying, in principle as independent theses: an architectural global frustration relating phrase structural and Markovian processes in general computations; and a local derivational frustration relating semantic and phonological cycles within language processing. After developing and analyzing each frustration, with particular focus on human language, we will briefly explore the consequences these frustrations have on the “design” of mental faculties, and the impact our theory has on the Minimalist notion of “perfection in language design”.

While a compiler produces low-level object code from high-level source code, a decompiler produces high-level code from low-level code and has applications in the testing and validation of safety-critical software. The decompilation of an object code provides an independent demonstration of correctness that is hard to better for industrial purposes (an alternative is to prove the compiler correct). But, although compiler compilers are in common use in the software industry, a decompiler compiler is much more unusual.It turns out that a data type specification for a programming-language grammar can be remolded into a functional program that enumerates all of the abstract syntax trees of the grammar. This observation is the springboard for a general method for compiling decompilers from the specifications of (non-optimizing) compilers.This paper deals with methods and theory, together with an application of the technique. The correctness of a decompiler generated from a simple occam-like compiler specification is demonstrated. The basic problem of enumerating the syntax trees of grammars, and then stopping, is shown to have no recursive solution, but methods of abstract interpretation can be used to guarantee the adequacy and completeness of our technique in practical instances, including the decompiler for the language presented here.

A primary issue facing architects of the Islamic world is the generation of contemporary designs based on architecture of the past. We discuss shape grammars as a framework for the design generation of plans of courtyard buildings of Islamic architecture and describe ongoing research for the transformation of grammars of historic Islamic building types to generate new, contemporary designs or design styles. We raise issues in the grammar transformation framework and discuss directions of exploration that could be relevant to the design methods of Islamic architecture.

This paper entitled 'Free word order and modelling of inversion' is published in the 2006 volume of the 'Dialogue' series (=Computational linguistics and intellectual technologies), issue 6 (13). I show the advantages of the movement analysis both in theoretical and in computational linguistics. Meanwhile, the constraint on unidirectional movement is dubious, since several movement patterns can be more effectively analyzed as instances of left-to-right movement than as instances of right-to-left movement, as they are usually explained in the minimalist Chomskyan framework

The paper focuses on the problems of design and development of the linguistically motivated mechanisms for parallel texts alignment and grammatical (functional semantic) matches extraction for design of statistical language portraits to be further incorporated into the hybrid models of machine translation. By hybrid models we mean those employing both statistical and rule-based mechanisms within one framework for natural language processing. Our approach consists in the use of the starting (“seed”) grammar to be further enriched by the matches discovered in parallel texts. The seed grammar is used featuring the cognitive and functional characteristics of phrase structures. The grammar formalism employed is the Cognitive Transfer Grammar based on the transfemes (bilingual phrase structures).

In the following, we discuss whether binding theory in generative grammar provided good and falsifiable hypotheses for the facts it aimed to explain. The main underlying issue is the confusion between natural language statements being true and being well formed. In our analyses, we consider the theories of Universal Grammar as metalanguages for natural languages.

Challenges for the study of Islamic architecture include its abundance and diversity in expression and its classification based on distinct functional or stylistic types. We address these issues by presenting shape grammars as a methodology for the analysis and design generation of Islamic architecture, with a specific example in the form of a parametric shape grammar for central Asian caravanserais. The grammar is developed by identifying distinct design types. Shape rules are created based on a study of the spatial elements and their organisation in the designs. We illustrate the utility of the grammar by deriving an extant design and as well as, previously unknown designs. We conclude by discussing possible extensions to the current grammar and future work involving the development of a grammar based framework for the comparative analysis of medieval Islamic courtyard buildings.

Currently available computer-aided design tools provide strong support for the later stages of product development processes where the structure and shape of the design have been fixed. Support for earlier stages of product development, when both the structure and shape of the design are still fluid, demands conceptual design tools that support designers' ways of thinking and working, and enhance creativity, for example, by offering design alternatives, difficult or not, possible without the use of such tools. The potential of spatial grammars as a technology to support such design tools has been demonstrated through experimental research prototypes since the 1970s. In this paper, we provide a review of recent spatial grammar implementations, which were presented in the Design Computing and Cognition 2010 workshop on which this paper is based, in the light of requirements for conceptual design tools and identify future research directions in both research and design education.

An important contrast between most current syntactic frameworks and Head-Driven Phrase Structure Grammar or Lexical Functional Grammar (hereafter HPSG and LFG respectively) is the common insistence of the latter two on the need to distinguish between the mathematical structures which model utterance types and the logical formulas which describe these structures (see Kaplan and Bresnan (1982), Pollard and Sag (1994), Kaplan (1995) inter alia). Grammars are viewed as sets of constraints expressed in a description language whose denotata serve as models of linguistic utterances. In such frameworks, it is possible to change the description language -- and the possible grammars which can be written within it -- without altering the modeling domain (the linguistic ontology). In this paper, I present a particular class of examples for which this distinction between the modeling domain and the formulas which describe it proves crucial. My goals are two-fold. Empirically, I wish to argue for the need to include a kind of constraints in our models of natural language only sparsely mentioned in previous literature. Methodologically, I want to illustrate the usefulness to linguistic theorizing of the aforementioned distinction by showing how modeling this new kind of constraints does not require an enrichment of our linguistic ontology, but a change in our descriptive metalanguage.

The paper focuses оп the problems of desigп апd developmeпt of the linguistically motivated mесhапisms for parallel texts аligпmепt апd grammatical fuпсtiопаl-sеmапtiс matches ехtrасtiоп for design of statistical language portraits to bе further iпcorporated iпtо the hybrid models of mасhiпе trапslаtiоп and multilingual knowledge extraction. Ву hybrid models we mеап those еmрlоуiпg both statistical апd rule-based mесhапisms withiп опе framework for паturаl lапguаgе processiпg. Our approach coпsists iп the use of the startiпg ("seed") gгammаг ro be further епriсhеd bу the matches discovered iп parallel texts. The seed grаmmаr is used featuriпg the cogпitive апd fuпсtiопаl characteristics of phrase structures. The grаmmаr formalism еmрlоуеd is the Cogпitive Тrаnsfer Grаmmаr based оп the transfemеs (biliпguаl and multilingual рhrasе structurеs).

One of several attempts to show that the relation between the formal models such as regular languages, context-free languages used as models of natural language and so on on the one hand and natural languages themselves was so poorly defined that one could depending on arbitrary choices decide that natural languages are or are not regular, are or are not context-free and so on.

Hybrid designs are those that develop from multiple sources. This paper presents the methodology of composite grammars, developed by merging multiple grammars, for the analysis of hybrid designs. The methodology is discussed with an example from Islamic architecture, which is known to have developed by borrowing from various sources. The methodology is seen to be useful for the analysis of the evolution of historic architecture, as well as for the development of new languages of designs.