Actual Models of the Chomsky Grammar

Abstract

We defend that there is a link between the mathematical analytical models (characteristic of the structural tradition) and the mathematical synthetic models (characteristic of the generative tradition) that is peculiar to Chomsky’s grammar exposed in The Logical Structure of Linguistic Theory, CHG. To identify this link helps to identify the objects and the task of the grammars in CHG and also to detect some inadequacies in the exposition and conception underlying in CHG (related to the connection between levels of representations, the conception of the objects and the conception of transformational representation). In order to clarify these inadequacies, we defend that a grammar can be conceived as a theory that assigns the values of its notions to the sentences of a language, and we propose the following basic relational notions for CHG: phrase structure, transformed structure, phonemic representation and phonetic representation. By means of the structural metatheory, we define the potential models (after formulating the typifications and the characterizations of these notions) and the actual models of CHG (after formulating its fundamental law).