As PART of a long-range goal to develop a language-instruction program for Arabic, a project to achieve a computerized VERPS, Verb Exercise and Reference Program with Speech, has been developed. The goal of the project was to develop a system for utilizing high-quality computersynthesized speech for teaching Arabic verbs, and to use this speech system as part of a drill and reference program for these verbs. Work was done on the three aspects of the project: verb selection and recording of basic forms, construction of the drill and practice program, and development of computerized audio synthesis of verb forms given prefix, stem, and suffix information.VERPS can be used to generate the sounds and printed tokens (using a standard transcription, adapted for a computer terminal; see Appendix A) for a large number of common verbs in Modern Standard Arabic (MSA) from a relatively small data base. It can also be used to present interactive drill exercises for students, with exercises presented on video-display terminals, accompanied by high-quality computer-synthesized speech. In addition, VERPS is usable as a reference source for information on Arabic verbs, including pronunciation, for both students and researchers.Potential uses of the VERPS system are many; we list here the most obvious:1. VERPS can be used by students to drill Arabic verb forms.2. Using VERPS, an instructor easily will be able to assign virtually limitless kinds of Arabic verb drills for his students.tNowat Four-Phase Systems, Cupertino, Calif.

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Since the time, about a century ago, when DeMorgan (8), Boole (1) and Jevons (12), inaugurated the study of the logic of numerically definite reasoning, no one has been concerned to establish the validity rules for a very general type of numerically definite inference which is a strong analogue of the classical syllogism. The reader will readily agree that the traditional rules of syllogistic inference cannot even begin to decide whether the following proportionally quantified syllogism is a valid argument: at most 4/7 p are at most 2/3 not-m and at least 3/5 s are precisely 7/8 m, hence, at most 1/3 s are p. Likely reasons, of broad methodological interest, why this readily definable type of formal inference has been neglected will presently be proposed. Among the masters of twentieth century logic, Hilbert and Bernays (11) have, to be sure, meticulously shown how such numerically definite propositions as “at least 7 individuals have the property p” can be expressed in the predicate calculus with the use of the identity relation. They do not, since their concern with such propositions is indirect, proceed to establish a systematic calculus of classes whose “size” or extent is numerically definite. As we shall always notice, traditional logic and even ordinary Boolean algebra prefer to generalize about the laws governing the interrelationship of classes in inference systems without making any hypotheses concerning class “size” or extent except by the classical quantifier “some”, which quantifier admits the measure or extent of a class only in terms of the proposition that a given class contains or does not contain at least one member. Such a restricted admission of the relevance for inference of class size is among the fundamental reasons for the neglect of proportional quantifiers, i.e., quantifiers where numerical value is any rational number r such that 0/100 ≤ r ≤ 100/100. It can, of course, also be pointed out that the traditional syllogism and ordinary Boolean algebra do not i.e. measure, numerically define, the degree of inclusion of one class in another. Inclusion is taken either as total or partial, with no discrimination of the degree of partial inclusion.