Appendix Iii Decision Procedures for Structure in Natural Languages*)

The rules of formation of a logistic system are by definition1) such that the notion of formula, well-formed formula or sentence, determined by these rules, is effectively decidable. However, I am not convinced that the arguments brought forth by Church2) to the effect that sentencehood has to be an effectively decidable notion for any system that may be used for communication purposes are conclusive. I therefore regard it to be a serious problem whether the syntactic structure of a natural language such as English can always be adequately described by a set of formation rules that guarantee the decidability of the notion of sentence or, for that matter, of any other syntactical structures such as phrases etc. Inasmuch as there exist good reasons for doubting whether the answer to this problem is affirmative, the prospects for fully-automatic, high-quality translation from one natural language into another natural language look dimmer than many workers in the field of machine translation would like to think. This is so since not even one necessary, though by no means sufficient, condition for this process, namely the mechanical determination of the syntactical structure of any given sentence in the source language, could possibly be completely fulfilled. Though applicability to machine translation is often in the back of my thinking on the description of the syntax of natural languages, I shall refer here no longer to this application, having dealt with it elsewhere at some length.3)