The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as “mental organs.” These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated (...) structures along an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term.Various types of knowledge and modes of knowledge acquisition are discussed in these terms. Some of the properties of the language faculty are investigated. The basic cognitive relation is “knowing a grammar”; knowledge of language is derivative and, correspondingly, raises further problems. Language as commonly understood is not a unitary phenomenon but involves a number of interacting systems: the “computational” system of grammar, which provides the representations of sound and meaning that permit a rich range of expressive potential, is distinct from a conceptual system with its own properties; knowledge of language must be distinguished from knowledge of how to use a language; and the various systems that enter into the knowledge and use of language must be further analyzed into their specific subcomponents. (shrink)

Category Theory has developed rapidly. This book aims to present those ideas and methods which can now be effectively used by Mathe­ maticians working in a variety of other fields of Mathematical research. This occurs at several levels. On the first level, categories provide a convenient conceptual language, based on the notions of category, functor, natural transformation, contravariance, and functor category. These notions are presented, with appropriate examples, in Chapters I and II. Next comes the fundamental idea of an adjoint (...) pair of functors. This appears in many substantially equivalent forms: That of universal construction, that of direct and inverse limit, and that of pairs offunctors with a natural isomorphism between corresponding sets of arrows. All these forms, with their interrelations, are examined in Chapters III to V. The slogan is "Adjoint functors arise everywhere". Alternatively, the fundamental notion of category theory is that of a monoid -a set with a binary operation of multiplication which is associative and which has a unit; a category itself can be regarded as a sort of general­ ized monoid. Chapters VI and VII explore this notion and its generaliza­ tions. Its close connection to pairs of adjoint functors illuminates the ideas of universal algebra and culminates in Beck's theorem characterizing categories of algebras; on the other hand, categories with a monoidal structure lead inter alia to the study of more convenient categories of topological spaces. (shrink)

Noam Chomsky's book on syntactic structures is a serious attempts on the part of a linguist to construct within the tradition of scientific theory-construction ...

The book from which these sections are excerpted is concerned with the prospects for assimilating the study of human intelligence and its products to the natural sciences through the investigation of cognitive structures, understood as systems of rules and representations that can be regarded as These mental structui′es serve as the vehicles for the exercise of various capacities. They develop in the mind on the basis of an innate endowment that permits the growth of rich and highly articulated structures along (...) an intrinsically determined course under the triggering and partially shaping effect of experience, which fixes parameters in an intricate system of predetermined form. It is argued that the mind is modular in character, with a diversity of cognitive structures, each with its specific properties arid principles. Knowledge of language, of the behavior of objects, and much else crucially involves these mental structures, and is thus not characterizable in terms of capacities, dispositions, or practical abilities, nor is it necessarily grounded in experience in the standard sense of this term. (shrink)

One way of coping with agreement of features in French is to perform two parallel computations, one in the free pregroup of syntactic types, the other in that of feature types. Technically speaking, this amounts to working in the direct product of two free pregroups.

The paper presents a generalization of pregroup, by which a freely-generated pregroup is augmented with a finite set of commuting inequations, allowing limited commutativity and cancelability. It is shown that grammars based on the commutation-augmented pregroups generate mildly context-sensitive languages. A version of Lambek’s switching lemma is established for these pregroups. Polynomial parsability and semilinearity are shown for languages generated by these grammars.

In this paper we consider the relations existing between four deductive systems that have been called categorial grammars and have relevant connections with linguistic investigations: the syntactic calculus, bilinear logic, compact bilinear logic and Curry''s semantic calculus.