A Discovery Procedure For Certain Phonological Rules

Acquisi t ion of phonological sys t ems can be insightfully s tudied in t e rms of discovery procedures. This paper describes a discovery procedure, implemented in Lisp, capable of determining a set of ordered phonological rules, which may be in opaque contexts~ from a set of surface forms arranged in paradigms. 1. I N T R O D U C T I O N For generat ive g rammar i ans , such as Chomsky (1965), a pr imary problem of l inguistics is to explain how the language learner can acquire the g r a m m a r of his or her language on the basis of the limited evidence available to him or her. Chomsky introduced the idealization of instantaneous acquisition, which 1 adopt here, in order to model the language acquisition device as a funct ion from primary linguistic data to possible grammars , ra ther than as a process. Assuming tha t the set of possible h u m a n languages is small , ra ther than large, appears to make acquisition easier, since there are fewer possible g r a m m a r s to choose from, and less da t a should be required to choose between them. Accordingly, generat ive l inguists are interested in del imit ing the class of possible h u m a n languages. This is done by looking for properties common to all h u m a n languages, or universals. Together , these universals form universal grammar, a set of principles tha t all h u m a n languages obey. Assuming tha t universal g r a m m a r is innate , the language learner can use it to restrict the number of possible g r a m m a r s he or she mus t consider when learning a language. As par t of universal g r ammar , the language learner is supposed to innately possess an evaluation metric, which is used to "decide" between two g r a m m a r s when both are cons is tent with other principles of universal g r a m m a r and the available language data . 2. D I S C O V E R Y P R O C E D U R E S This approach deals with acquisit ion wi thout reference to a specific discovery procedure, and so in some sense the resul ts of such research are general~ in tha t in principle they apply to all discovery procedures. Still, I think tha t there is some utility in considering the problem of acquisit ion in terms of actual discovery procedures. Firstly, we can identify the par ts of a g r a m m a r tha t are underspeeified with respect to the available data . Pa r t s of a g r a m m a r or a rule are strongly data determined if they are fixed or uniquely de termined by the da ta , given the requiremen t t ha t overall g r a m m a r be empirically correct. By cont ras t , a part of a g r a m m a r or of a rule is weakly data determined if there is a large class of g r a m m a r or rule par ts tha t are all consis tent with the available data . For example, if there are two possible analyses tha t equally well account for the available data , then the choice of which of these analyses should be incorporated in the final g r a m m a r is weakly d a t a de termined . Strong or weak da t a de terminat ion is therefore a property of the g r a m m a r formalism and the da t a combined, and independent of the choice of discovery procedure. Secondly, a discovery procedure may part i t ion a phonological sys tem in an interest ing way. For instance, in the discovery procedure described here tile evaluat ion metric is not called apon to compare one g r a m m a r with another , but rather to make smaller , more local, comparisons . This leads to a factoring of the evaluat ion metric tha t may prove useful for its fur ther invest igat ion. Thirdly , focussing on discovery procedures forces us to identify what the surface indications of the various construct ions in the g r a m m a r are. Of course, this does not mean one should look for a one-to-one correspondence between individual g r a m m a r cons t ruc t ions and the surface data; bu t ra ther complexes of g r a m m a r cons t ruc t ions tha t interact to yield part icular pa t t e rns on the surface. One is then inves t iga t ing the logical impl icat ions of the existence of a par t icular cons t ruc t ions in the da ta . Following from the last point, 1 think a discovery procedure should have a deductive ra ther than enumerative structure. In par t icular , procedures tha t work essentially by enumera t i ng all possible ( sub )g rammars and seeing which ones work are not only in general very inefficient, but. also not. very insightful . These discovery by enumera t ion procedures simply give us a list of all rule sys tems t ha t are empirically adequa te as a result , but they give us no idea as to wha t propert ies of these sys t ems were crucial in their being empirically adequate . This is because the s t ruc tu re imposed on the problem by a simple recursive enumera t ion procedure is in general not related to the intr insic s t ruc ture of the rule discovery problem. 3. A P H O N O L O G I C A L R U L E D I S C O V E R Y P R O C E D U R E Below and in Appendix A I outl ine a discovery procedure: which I have fully implemented in Franz Lisp on a VAX 11/750 compute r , for a restricted class of phonological rules, namely rules of the type shown in (1).