Formalizing a mathematical theory is a necessary first step to proving the correctness of programs that refer to that theory in their specification. This paper demonstrates how the mathematical theory of elliptic curves and their application to cryptography can be formalized in higher order logic. This formal development is mechanized using the HOL4 theorem prover, resulting in a collection of ...

All of you must have proved lot of mathematical statements by now and have pretty good intuition about what proofs are. So we will take an informal approach of proofs. The ideas of rigorous and correct mathematical proofs will be shown through examples. A more formal approach can be taken through logic, a brief introduction to logic is given at the end of these course notes and is meant as an a...

The study of the elements mathematical logic and its sections, especially in process teaching high school general specialized courses mathematics or higher educational institutions, is a rather tricky task. paper demonstrates how one can design develop package interactive applications to help learn, understand, apply essential logic. research aims describe an application for studying order cons...

Fuzzy logic, according to Lotfi Zadeh, can be broadly considered as the union of fuzzified crisp logics. Its primary aim is to provide a formal, computationally oriented system of concepts and techniques for dealing with modes of reasoning that are approximate rather than exact. Charles Elkan’s claims are derived mainly from entangled interpretations of fuzzy logic stemming from his mathematica...

Constraint answer set programming is a promising research direction that integrates answer set programming with constraint processing. Recently, the formal link between this research area and satisfiability modulo theories (or SMT) was established. This link allows the cross-fertilization between traditionally different solving technologies. The paper presents the system ezsmt, one of the first...

Constraint answer set programming is a promising research direction that integrates answer setprogramming with constraint processing. Recently, the formal link between this research area andsatisfiability modulo theories (or SMT) was established. This link allows the cross-fertilizationbetween traditionally different solving technologies. The paper presents the system ezsmt, one...