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Articles 1 - 6 of 6
Full-Text Articles in Logic and Foundations
Transparency In Formal Proof, Cap Petschulat
Transparency In Formal Proof, Cap Petschulat
Boise State University Theses and Dissertations
The oft-emphasized virtue of formal proof is correctness; a machine-checked proof adds greatly to our confidence in a result. But the rigors of formalization give rise to another possible virtue, namely clarity. Given the state of the art, clarity and formality are at odds: complexity of formalization obscures the content of proof. To address this, we develop a notion of proof strategies which extend the well-known notion of proof tactics. Beginning with the foundations of logic, we describe the methods and structures necessary to implement proof strategies, concluding with a proof-of-concept implementation in CheQED, a web-based proof assistant.
Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto
Neutrosophic Logic, Wave Mechanics, And Other Stories: Selected Works 2005-2008, Florentin Smarandache, Victor Christianto
Branch Mathematics and Statistics Faculty and Staff Publications
There is beginning for anything; we used to hear that phrase. The same wisdom word applies to us too. What began in 2005 as a short email on some ideas related to interpretation of the Wave Mechanics results in a number of papers and books up to now. Some of these papers can be found in Progress in Physics or elsewhere. It is often recognized that when a mathematician meets a physics-inclined mind then the result is either a series of endless debates or publication. In our story, we prefer to publish rather than perish. Therefore, our purpose with this …
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Equational Coalgebraic Logic, Alexander Kurz, Raul Leal
Engineering Faculty Articles and Research
Coalgebra develops a general theory of transition systems, parametric in a functor T; the functor T specifies the possible one-step behaviours of the system. A fundamental question in this area is how to obtain, for an arbitrary functor T, a logic for T-coalgebras. We compare two existing proposals, Moss’s coalgebraic logic and the logic of all predicate liftings, by providing one-step translations between them, extending the results in [21] by making systematic use of Stone duality. Our main contribution then is a novel coalgebraic logic, which can be seen as an equational axiomatization of Moss’s logic. The three logics are …
Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy
Superbimatrices And Their Generalizations, Florentin Smarandache, W.B Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
The systematic study of supermatrices and super linear algebra has been carried out in 2008. These new algebraic structures find their applications in fuzzy models, Leontief economic models and data-storage in computers. In this book the authors introduce the new notion of superbimatrices and generalize it to super trimatrices and super n-matrices. Study of these structures is not only interesting and innovative but is also best suited for the computerized world. The main difference between simple bimatrices and super bimatrices is that in case of simple bimatrices we have only one type of product defined on them, whereas in case …
Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Groups As Graphs, Florentin Smarandache, W.B. Vasantha Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
Through this book, for the first time we represent every finite group in the form of a graph. The authors choose to call these graphs as identity graph, since the main role in obtaining the graph is played by the identity element of the group. This study is innovative because through this description one can immediately look at the graph and say the number of elements in the group G which are self-inversed. Also study of different properties like the subgroups of a group, normal subgroups of a group, p-sylow subgroups of a group and conjugate elements of a group …
Reservation For Other Backward Classes In Indian Central Government Institutions Like Iits, Iims And Aiims – A Study Of The Role Of Media Using Fuzzy Super Frm Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy
Reservation For Other Backward Classes In Indian Central Government Institutions Like Iits, Iims And Aiims – A Study Of The Role Of Media Using Fuzzy Super Frm Models, Florentin Smarandache, W.B. Vasantha Kandasamy, K. Kandasamy
Branch Mathematics and Statistics Faculty and Staff Publications
The new notions of super column FRM model, super row FRM model and mixed super FRM model are introduced in this book. These three models are introduced specially to analyze the biased role of the print media on 27 percent reservation for the Other Backward Classes (OBCs) in educational institutions run by the Indian Central Government. This book has four chapters. In chapter one the authors introduce the three types of super FRM models. Chapter two uses these three new super fuzzy models to study the role of media which feverishly argued against 27 percent reservation for OBCs in Central …