PROLEGOMENON ON THE ONTOLOGY OF COMPLETE OR PARTIAL HOMOMORPHISMS IN THE SYNTAX-SEMANTICS INTERFACE IN GRAMMARS (original) (raw)
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Model theoretic semantics (MTS) has a special attitude to describe semantics, to characterize both artificial and natural languages by pure mathematical tools and some of the basic properties of this attitude are disscussed. The arsenal of MTS equipped here with such tools allowing the investigation at such a level of complexity that approximates the real situations. These tools are developed within the frame of category theory.
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2014
This essay describes and comments on some of the key developments in the history of formal semantics and its relation to syntax, focusing on the period from the beginnings of Chomskyan generative grammar in the 1950's up until the mature period of formal semantics in the 1980's, with only a few remarks about earlier background and later developments. One crucial theme is the challenge of developing a compositional semantic theory, and how that challenge has taken on different forms with respect to different syntactic and semantic theories. The ‚syntax-semantics interface‛ is a relatively young topic in the history of linguistics. In early Western linguistics, there was little syntax and essentially no semantics other than some non-formal lexical semantics. Formal syntax came first, with Zellig Harris's student Noam Chomsky revolutionizing the field of linguistics with his work on syntax. Chomsky shared the field's general skepticism about the possibility of semantics...
2011
Stabler proposes an implementation of the Chomskyan Minimalist Program, [1] with Minimalist Grammars-MG, [2]. 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 theoreticallymotivated syntax-semantics interface, [3]. In this article, we give full definitions of MG with algebraic tree descriptions and of MCG, and take the first steps towards giving a proof of inclusion of their generated languages. The Minimalist Program-MP, introduced by Chomsky, [1], unified more than fifty years of linguistic research in a theoretical way. MP postulates that a logical form and a sound could be derived from syntactic relations. Stabler, [2], proposes a framework for this program in a computational perspective with Minimalist Grammars-MG. These grammars inherit a long tradition of generative linguistics. The most interesting contribution of these grammars is certainly that the derivation system is defined with only two rules: merge and move. The word Minimalist is introduced in this perspective of simplicity of the definitions of the framework. If the merge rule seems to be classic for this kind of treatment, the second rule, move, accounts for the main concepts of this theory and makes it possible to modify relations between elements in the derived structure. Even if the phonological calculus is already defined, the logical one is more complex to express. Recently, solutions were explored that exploited Curry's distinction between tectogrammatical and phenogrammatical levels; for example, Lambda Grammars, [4], Abstract Categorial Grammars, [5], and Convergent Grammars [6]. First steps for a convergence between the Generative Theory and Categorial Grammars are due to S. Epstein, [7]. A full volume of Language and Computation proposes several articles in this perspective, [8], in particular [9], and Cornell's works on links between Lambek calculus and Transformational Grammars, [10]. Formulations of Minimalist Grammars in a Type-Theoretic way have also been proposed in [11], [12], [13]. These frameworks were evolved in [14], [3], [15] for the syntax-semantics interface. Defining a syntax-semantics interface is complex. In his works, Stabler proposes to include this treatment directly in MG. But interactions between syntax
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This project addresses the formal nature of grammars, from a mathematical and computational point of view, and asks which the requirements that natural languages impose the theoretician in developing a grammar are. We propose to revisit the so-called Chomsky Hierarchy, an inclusive hierarchy of formal grammars, under the light of recent developments in Biolinguistics and computational / mathematical linguistics; for the kind of transformational system advocated for in generative linguistics is often not appropriate to account for problematic data from natural languages, particularly adopting a comparative perspective.
DOI 10.3726/978-3-653-06463-6, 2020
About the book Peter Kosta The Syntax of Meaning and the Meaning of Syntax This book provides a summary of Radical Minimalism, putting forth a neurocognitively implementable theory of grammar as I-language. Radical Minimalism tries to give a ‘fully explicit’ description of syntactic structures mapped into cognitive frames of thought. It focuses on the division of labor between Narrow Syntax and Meaningful Units of the sentence and also on the role of Mental Lexicon (understood as a selection of Roots and Labels), the Labeling Mechanism, and the participation of the Senso-Motoric and Conceptual-Intentional Interfaces within a Crash-proof Grammar of Human Language. The data are taken from the languages of different genetic origins and types. The book is based on the idea that language and thought are closely connected and must be studied within the physical laws of the Anti-Entropy and Dynamical Frustration theory. Peter Kosta’s new book touches on an exceptional range of subjects in theoretical syntax and the philosophy of grammar, bearing ample proof of his lifelong engagement with these vital disciplines within the humanities of the 20th/21st centuries. His acute awareness of important insights and discussions in current day minimalism is evident from every page, informing his treatment of a wide diversity of problems in the morphosyntax of Slavic languages and beyond. (Jan-Wouter Zwart, University of Groningen) This book provides a breath of fresh air in linguistic theorising by combining empirically based syntactic innovations with original discussions of long-standing semantic puzzles and a revised architecture of the Faculty of Language. Foundational notions in generative theory are thoroughly revised in the light of detailed comparative analyses. This remarkable work represents the culmination of years of research on what meaning is, how it is structured, and to what extent syntax encodes meaning. (Diego Gabriel Krivochen, University of Verona)
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TheBench is a tool to study monadic structures in natural language. It is for writing monadic grammars to explore analyses, compare diverse languages through their categories, and to train models of grammar from form-meaning pairs where syntax is latent variable. Monadic structures are binary combinations of elements that employ semantics of composition only. TheBench is essentially old-school categorial grammar to syntacticize the idea, with the implication that although syntax is autonomous (recall \emph{colorless green ideas sleep furiously}), the treasure is in the baggage it carries at every step, viz. semantics, more narrowly, predicate-argument structures indicating choice of categorial reference and its consequent placeholders for decision in such structures. There is some new thought in old school. Unlike traditional categorial grammars, application is turned into composition in monadic analysis. Moreover, every correspondence requires specifying two command relations, one on syntactic command and the other on semantic command. A monadic grammar of TheBench contains only synthetic elements (called `objects' in category theory of mathematics) that are shaped by this analytic invariant, viz. composition. Both ingredients (command relations) of any analytic step must therefore be functions (`arrows' in category theory). TheBench is one implementation of the idea for iterative development of such functions along with grammar of synthetic elements.