Results 1 
4 of
4
The Categorial FineStructure of Natural Language
, 2003
"... Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, i ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves  amongst others  mixtures of interpretation and inference.
Categorial Grammar at a CrossRoads
, 2003
"... Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vect ..."
Abstract
 Add to MetaCart
Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebrasarrow models, and vector spaces. This is the crossroads of our title, where open directions abound.
unknown title
"... Abstract Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper con ..."
Abstract
 Add to MetaCart
Abstract Categorial grammar analyzes linguistic syntax and semantics in terms of type theory and lambda calculus. A major attraction of this approach is its unifying power, as its basic function/argument structures occur across the foundations of mathematics, language and computation. This paper considers, in a light examplebased manner, where this elegant logical paradigm stands when confronted with the wear and tear of reality. Starting from a brief history of the Lambek tradition since the 1980s, we discuss three main issues: (a) the fit of the lambda calculus engine to characteristic semantic structures in natural language, (b) the coexistence of the original typetheoretic and more recent modal interpretations of categorial logics, and (c) the place of categorial grammars in the complex total architecture of natural language, which involves amongst others mixtures of interpretation and inference. 1 From Montague Grammar to Categorial Grammar Logic and linguistics have had lively connections from Antiquity right until today (GAMUT 1991). A recurrent theme in this history is the categorial structure of language and ontology, from Aristotle's grammatical categories to Russell's theory of types in the foundations of mathematics. Further bridges were thrown as logic and
unknown title
, 2003
"... Abstract Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebras–arrow models, ..."
Abstract
 Add to MetaCart
Abstract Categorial grammars are driven by substructural logics. These are fragments of modal logics for the structures the grammar deals with. We will discuss modal language as a means of access to families of relevant structures: formal languages, type hierarchies, relation algebras–arrow models, and vector spaces. This is the crossroads of our title, where open directions abound. 1 From categorial proof theory to categorial model theory Categorial grammars are driven by resource logics in a proof format (van Benthem 1991, Buszkowski 1997, Moortgat 1997). Thus, they revolve around derivation and computation, with the CurryHoward Gestalt switch taking proofs to typetheoretic denotations for the expression analyzed. But over the past decades, categorial logics have also been analyzed modeltheoretically in modal logics with standard possible worldsstyle models (cf. Kurtonina 1995). Thus, e.g., a categorial product A•B is ‘true ’ of some object s iff s is a concatenation, or some suitable semantic merge of two objects t, u satisfying A, B, respectively. This is a standard binary modality, which needs a ternary accessibility relation R for its abstract truth condition: