Case alternation in lexicalized grammar

In this paper, we propose to extend the Przepiórkowski's 2000 analysis of Long Distance Genitive of Negation to the same phenomenon in Lithuanian. We discuss the features that have their origin in Categorial Grammar. We then develop a novel analysis of the case alternation in Categorial Grammar incorporating features of the HPSG analysis. The two accounts show a surprising convergence in basic assumptions and predictions.

From Generative Linguistics to Categorial Grammars: Overt Subjects in Control Infinitives

The present thesis lies at the interface of logic and linguistics; its object of study are control sentences with overt pronouns in Romance languages (European and Brazilian Portuguese, Italian and Spanish). This is a topic that has received considerably more attention on the part of linguists, especially in recent years, than from logicians. Perhaps for this reason, much remains to be understood about these linguistic structures and their underlying logical properties. This thesis seeks to fill the lacunas in the literature or at least take steps in this direction by way of addressing a number of issues that have so far been under-explored. To this end, we put forward two key questions, one linguistic and the other logical. These are, respectively, (1) What is the syntactic status of the surface pronoun? and (2) What are the available mechanisms to reuse semantic resources in a contraction-free logical grammar? Accordingly, the thesis is divided into two parts: generative linguistics and categorial grammar. Part I starts by reviewing the recent discussion within the generative literature on infinitive clauses with overt subjects, paying detailed attention to the main accounts in the field. Part II does the same on the logical grammar front, addressing in particular the issues of control and of anaphoric pronouns. Ultimately, the leading accounts from both camps will be found wanting. The closing chapter of each of Part I and Part II will thus put forward alternative candidates, that we contend are more successful than their predecessors. More specifically, in Part I, we offer a linguistic account along the lines of Landau’s T/Agr theory of control. In Part II, we present two alternative categorial accounts: one based on Combinatory Categorial Grammar, the other on Type-Logical Grammar. Each of these accounts offers an improved, more fine-grained perspective on control infinitives featuring overt pronominal subjects. Finally, we include an Appendix in which our type-logical proposal is implemented in a categorial parser/theorem-prover.Abstract prepared by María Inés Corbalán.E-mail: [email protected]: http://repositorio.unicamp.br/jspui/handle/REPOSIP/331697

Strong Equivalence of TAG and CCG

Tree-adjoining grammar (TAG) and combinatory categorial grammar (CCG) are two well-established mildly context-sensitive grammar formalisms that are known to have the same expressive power on strings (i.e., generate the same class of string languages). It is demonstrated that their expressive power on trees also essentially coincides. In fact, CCG without lexicon entries for the empty string and only first-order rules of degree at most 2 are sufficient for its full expressive power.

Category theory

This chapter aims to introduce sufficient category theory to enable a formal understanding of the rest of the book. It first introduces the fundamental notion of a category. It then introduces functors, which are maps between categories. Next it introduces natural transformations, which are natural ways of mapping between functors. The stage is then set to at last introduces monads, which are defined in terms of functors and natural transformations. The last part of the chapter provides a compositional calculus with monads for natural language semantics (in other words, a logic for working with monads) and then relates the compositional calculus to Glue Semantics and to a very simple categorial grammar for parsing. The chapter ends with some exercises to aid understanding.

Categorial Grammar

The term “categorial grammar” refers to a variety of approaches to syntax and semantics in which expressions are categorized by recursively defined types and in which grammatical structure is the projection of the properties of the lexical types of words. In the earliest forms of categorical grammar types are functional/implicational and interact by the logical rule of Modus Ponens. In categorial grammar there are two traditions: the logical tradition that grew out of the work of Joachim Lambek, and the combinatory tradition associated with the work of Mark Steedman. The logical approach employs methods from mathematical logic and situates categorial grammars in the context of substructural logic. The combinatory approach emphasizes practical applicability to natural language processing and situates categorial grammars within extended rewriting systems. The logical tradition interprets the history of categorial grammar as comprising evolution and generalization of basic functional/implicational types into a rich categorial logic suited to the characterization of the syntax and semantics of natural language which is at once logical, formal, computational, and mathematical, reaching a level of formal explicitness not achieved in other grammar formalisms. This is the interpretation of the field that is being made in this article. This research has been partially supported by MINICO project TIN2017–89244-R. Thanks to Stepan Kuznetsov, Oriol Valentín and Sylvain Salvati for comments and suggestions. All errors and shortcomings are the author’s own.