A Mathematical Analysis of Panini's Sivasutras
نویسنده
چکیده
In Pān. ini’s grammar of Sanskrit one finds the Śivasūtras, a table which defines the natural classes of phonological segments in Sanskrit by intervals. We present a formal argument which shows that, using his representation method, Pān. ini’s way of ordering the phonological segments to represent the natural classes is optimal. The argument is based on a strictly set-theoretical point of view depending only on the set of natural classes and does not explicitly take into account the phonological features of the segments, which are, however, implicitly given in the way a language clusters its phonological inventory. The key idea is to link the graph of the Hasse-diagram of the set of natural classes closed under intersection to Śivasūtra-style representations of the classes. Moreover, the argument is so general that it allows one to decide for each set of sets whether it can be represented with Pān. ini’s method. Actually, Pān. ini had to modify the set of natural classes to define it by the Śivasūtras (the segment h plays a special role). We show that this modification was necessary and, in fact, the best possible modification. We discuss how every set of classes can be modified in such a way that it can be defined in a Śivasūtra-style representation.1
منابع مشابه
Fuzzy Modeling and Natural Language Processing for Panini's Sanskrit Grammar
Indian languages have long history in World Natural languages. Panini was the first to define Grammar for Sanskrit language with about 4000 rules in fifth century. These rules contain uncertainty information. It is not possible to Computer processing of Sanskrit language with uncertain information. In this paper, fuzzy logic and fuzzy reasoning are proposed to deal to eliminate uncertain inform...
متن کاملOn the Construction of Sivasutras-Alphabets
In the present paper, a formalization of the technique used by Pān. ini in his Śivasūtras for the denotation of sound classes is given. Furthermore, a general notion of Śivasūtra-alphabets and of Śivasūtrasortability is developed. The presented main theorem poses three sufficient conditions for the Śivasūtra-sortability of sets of classes. Finally, the problem of ordering sets of classes which ...
متن کاملA Critical Analysis of the Origin and Nature of Classical Mathematical Economics: Why Classical Economists Did Not Use Mathematics?
The role of mathematics in economic analysis is not yet a settled question. Smith, Ricardo, Mill and other eminent classical economists did not use mathematics in their economic theorizations. We have defined classical mathematical economics as the whole body of literature in mathematical treatment of economics originating mainly from the contributions of Cournot, Jevons and Walras. There are ...
متن کاملNumerical Analysis of a Simple Mathematical Model to Design Bioremediation System in Rhizosphere
متن کامل
A Mathematical Analysis of New L-curve to Estimate the Parameters of Regularization in TSVD Method
A new technique to find the optimization parameter in TSVD regularization method is based on a curve which is drawn against the residual norm [5]. Since the TSVD regularization is a method with discrete regularization parameter, then the above-mentioned curve is also discrete. In this paper we present a mathematical analysis of this curve, showing that the curve has L-shaped path very similar t...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
- Journal of Logic, Language and Information
دوره 13 شماره
صفحات -
تاریخ انتشار 2004