Quantitative Comparison of Languages

From the perspective of the linguist, the theory of formal languages serves as an abstract model to address issues such as complexity, learnability, information content, etc. which are hard to investigate directly on natural languages. One question that has not been sufficiently addressed in the literature is to what an a result proved on an abstract model be presumed to hold for the concrete languages that are, after all, the real object of interest in linguistics. In this paper we attempt to remedy this defect by developing some figures of merit that measure how well a formal language approximates an actual language. We will review and refine some standard notions of mathematical density to arrive at a numerical figure that shows the degree to which one language approximates another, and show how such a figure can be computed between some formal languages and empirically measured between a real language and its formal model. In the concluding section of the paper we will argue th...

• Type: Journal
• Year: 1998
• Where: GRAMMARS
• Authors: András Kornai
• Keywords: Abstract Model, Formal Languages, GRAMMARS 1998, Natural Languages