On Some Mathematically Interpreted Linguistic Issues

Abstract

Two linguistic issues are interpreted in mathematical terms. In the first section different negation behaviour of nouns and verbs is explained using the mathematical theory of sets. In addition, a hypothesis is outlined, assuming the capability of nouns to define sets and thereby enabling a tentative definition of some lexical categories. \n \nIn the following sections the mathematical notions of operation, operator and operand are explained and their analogy with the traditional syntactic notions like immediate constituent, modifier, argument, governor, dependent etc. is exhibited. The central thesis of the article asserts that most (perhaps all) syntactic composites consist of two unequal components to which the asymmetric roles of operator and operand can be assigned. The possibilities to assign a role to a lexical category (verb, noun, adjective, preposition…) are predetermined and strongly depend on the category. \n \nThe operator-operand based grammar differs from the established phrase structure grammar based on head-defined phrases. The incompatibilities are highlighted and adapted alternative approaches to sentence parsing are proposed, able to map the operator-operand relations.