We introduce and study a natural extension of Marcus external contextual grammars. This mathematically simple mechanism which generates a proper subclass of simple matrix languages, known to be mildly context-sensitive ones, is still mildly context-sensitive. Furthermore, we get an infinite hierarchy of mildly context-sensitive families of languages. Then we attempt to fill a gap regarding the linguistic relevance of these mechanisms which consists in defining a tree structure on the strings generated by many-dimensional external contextual grammars, and investigate some related (...) issues. Several open problems are finally discussed. (shrink)

Taking as its starting point significant similarities between a formal language model—Grammar Systems—and a grammatical theory—Autolexical Syntax—in this paper we suggest the application of the former to the topic of the latter. To show the applicability of Grammar Systems Theory to grammatical description, we introduce a formal-language-theoretic framework for the architecture of natural language grammar: Linguistic Grammar Systems. We prove the adequacy of this model by highlighting its features (modularity, parallelism, interaction) and by showing the similarity between this framework and (...) accepted and well-known grammatical models (e.g. Autolexical Syntax). (shrink)

Prototypes and fuzziness are regarded in this paper as fundamental phenomena in the inherent logic of concepts whose relationship, however, has not been sufficiently clarified. Therefore, modifications are proposed in the definition of both. Prototypes are defined as the elements possessing maximal degree of membership in the given category such thatthis membership has maximal cognitive efficiency in representing theelement. A modified fuzzy set (m-fuzzy set) is defined on aclass (possibly self-contradictory collection) such that its core (the collection of elements with (...) full membership) is aset (self-consistent collection) comprising the finite set of the prototypes. In this scheme of recursive representation the possibility of contradictions, which has been proven to be inevitable in the logic of concepts, islocalized. Finally a related model of the brain''s pattern recognition mechanism is briefly summarized. (shrink)

Theories of natural language syntax often characterize grammatical knowledge as a form of abstract computation. This paper argues that such a characterization is correct, and that fundamental properties of grammar can and should be understood in terms of restrictions on the complexity of possible grammatical computation, when defined in terms of generative capacity. More specifically, the paper demonstrates that the computational restrictiveness imposed by Tree Adjoining Grammar provides important insights into the nature of human grammatical knowledge.

We present a deductive theory of space-time which is realistic, objective, and relational. It is realistic because it assumes the existence of physical things endowed with concrete properties. It is objective because it can be formulated without any reference to cognoscent subjects or sensorial fields. Finally, it is relational because it assumes that space-time is not a thing but a complex of relations among things. In this way, the original program of Leibniz is consummated, in the sense that space is (...) ultimately an order of coexistents, and time is an order of succesives. In this context, we show that the metric and topological properties of Minkowskian space-time are reduced to relational properties of concrete things. We also sketch how our theory can be extended to encompass a Riemannian space-time. (shrink)