Interlanguage and Set Theory

If one is to exploit the notion of interlanguage in error diagnosis systems, a precise definition of this concept is useful. We will define interlanguage set theoretically, on two different levels. A comparison of a first language and a target language on the X^-level makes it possible to compare structural similarity between languages, and a comparison on the Vx-level enables an explication of second language acquisition. We also comment on the limitations of set theory applied to interlanguage, and propose some augmentations which are needed in a theory of interlanguage that is to give a satisfactory account of interlanguage data. 0. Introduction The notion 'interlanguage' alludes to a language "between" two (or more) languages, i.e. a target language (Lt) norm which a student is trying to achieve, and his first language (LI). The interlanguage has characteristics of both of these languages. The nature of the blending, or how "between" is to be interpreted, however, has always been vague in second language acquisition (SLA) literature. In this paper, we will try to make the concept so clear that it can be exploited in a computational system for diagnosing second language errors. In our study, Lt is Norwegian, and LI is Spanish. The main features of interlanguages which will be used in the diagnosing system, are overgeneralisation of Lt rule statements and transfer from LI. In the diagnostic system, overgeneralisation will be implemented as constraint relaxation along the lines of Douglas and Dale (1992), and transfer will be implemented by means of an alternative LI based grammar. Transfer is understood in the sense it is used in SLA research (cf. Odlin (1989)), not in the sense of machine translation (although the planned system bears resemblances with transfer based MT systems). In the main section of this paper 'interlanguage' is defined set theoretically. In Section two some features which we want in a theory of interlanguage, but which fall outside the set theoretical study in section one, are discussed.