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Articles 1 - 5 of 5
Full-Text Articles in Logic and Foundations
Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan
Functorial Coalgebraic Logic: The Case Of Many-Sorted Varieties, Alexander Kurz, Daniela Petrişan
Engineering Faculty Articles and Research
Following earlier work, a modal logic for T-coalgebras is a functor L on a suitable variety. Syntax and proof system of the logic are given by presentations of the functor. This paper makes two contributions. First, a previous result characterizing those functors that have presentations is generalized from endofunctors on one-sorted varieties to functors between many-sorted varieties. This yields an equational logic for the presheaf semantics of higher-order abstract syntax. As another application, we show how the move to functors between many-sorted varieties allows to modularly combine syntax and proof systems of different logics. Second, we show how to associate …
Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie
Chinese Neutrosophy And Taoist Natural Philosophy, Florentin Smarandache, Jiang Zhengjie
Branch Mathematics and Statistics Faculty and Staff Publications
No abstract provided.
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
N- Linear Algebra Of Type I And Its Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
With the advent of computers one needs algebraic structures that can simultaneously work with bulk data. One such algebraic structure namely n-linear algebras of type I are introduced in this book and its applications to n-Markov chains and n-Leontief models are given. These structures can be thought of as the generalization of bilinear algebras and bivector spaces. Several interesting n-linear algebra properties are proved. This book has four chapters. The first chapter just introduces n-group which is essential for the definition of nvector spaces and n-linear algebras of type I. Chapter two gives the notion of n-vector spaces and several …
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Special Classes Of Set Codes And Their Applications, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
In this book the authors introduce the notion of set codes, set bicodes and set n-codes. These are the most generalized notions of semigroup n-codes and group n-codes. Several types of set ncodes are defined. Several examples are given to enable the reader to understand the concept. These new classes of codes will find applications in cryptography, computer networking (where fragmenting of codes is to be carried out) and data storage (where confidentiality is to be maintained). We also describe the error detection and error correction of these codes. The authors feel that these codes would be appropriate to the …
The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza
The Role Of Algebraic Inferences In Naîm Ibn Mûsa’S Collection Of Geometrical Propositions, Marco Panza
MPP Published Research
Na‘im ibn Musa's lived in Baghdad in the second half of the 9th century. He was probably not a major mathematician. Still his Collection of geometrical propositions---recently edited and translated in French by Roshdi Rashed and Christian Houzel---reflects quite well the mathematical practice that was common in Thabit ibn Qurra's school. A relevant characteristic of Na‘im's treatise is its large use of a form of inferences that can be said ‘algebric' in a sense that will be explained. They occur both in proofs of theorems and in solutions of problems. In the latter case, they enter different sorts of problematic …