Implicative structure and joint predictiveness

(Ackerman et al., 2009) go on to argue that speakers rely on knowledge of the IMPLICATIVE STRUCTURE of paradigms (Wurzel, 1984): paradigms are structured in such a way that there are reliable correlations between the form filling one paradigm cell A and the form filling another cell B. The reliability of these correlations depends on the particular pair of cells A and B under scrutiny; it can be assessed quantitatively by examining the statistical distribution of operations required to go from A to B in the lexicon. This presentation focuses on one particular aspect of implicative structure, which we call JOINT PREDICTIVENESS. In some situations, joint knowledge of two paradigm cells A and B provides more information on cell C than could be inferred from knowledge of eitherA orB. Table 1 below provides a simple example from French, using lexemes illustrating 7 patterns corresponding to of 95% of the verbs documented in the Flexique phoneticized lexicon (Bonami et al., 2014). In French conjugation, predicting the past participle from the infinitive is hard, because of the opacity between second conjugation infinitives, such as BÂTIR, and some third conjugation infinitives, such as TENIR, OUVRIR, MOURIR. Predicting the past participle from present SG forms is also hard, this time because some first conjugation verbs with a stem in -i (e.g. RELIER) are not distinguished from second conjugation verbs. A different subset of first conjugation verbs (e.g. RATISSER) raises similar problems for PL forms. Overall, no other cell in the paradigm is a very good predictor of the past participle. However, joint knowledge of some pairs of paradigm cells radically improves the quality of prediction. For instance, joint knowledge of the infinitive and some present plural form removes all uncertainty in the sample in Table 1: knowledge of the infinitive form partitions the set of lexemes in two classes within which the PRS.3PL is fully predictive of the past participle. Although the existence of joint predictiveness is acknowledged in the literature (Matthews, 1972; Thymé et al., 1994; Ackerman et al., 2009; Stump and Finkel, 2013; Blevins, forthcoming; Sims, forthcoming), little attention has been given to quantifying its importance. In this paper we first give further arguments that joint predictiveness is a crucial aspect of implicative structure, and that a careful empirical examination of joint predictiveness is essential to both linguistic and psycholinguistic assessment of the PCFP and related issues. We then propose and illustrate a method for the quantitative evaluation of joint predictiveness. We end with a discussion of principal part systems.