Mathematic

In the mathematical definition of Higher Category Theory an mathematical machinery is set up that allows to concretely handle the explicit choices of composites of…

Group theory is a powerful formal method for analyzing abstract and physical systems in which (a • x = b) always has a unique solution.…

Enriched Category Theory thus encompasses within the same framework a wide variety of structures including ordinary categories where the hom-set carries additional structure beyond being a…

Domain theory is a mathematical theory of programming languages, and for nearly a quarter of a century developed almost exclusively in connection with denotational semantics…

Category theory has come to involve a focal position in contemporary arithmetic and hypothetical computer engineering, and is additionally connected to scientific material science. Generally,…

Metamathematics is a field of study that deals with the structure and formal properties of mathematics and similar formal systems. It also concerned with the formal…

Philosophy of Mathematics occupies a special place in the philosophy of science. Philosophers have accorded special attention to ontological and epistemological questions concerning in mathematics. Whereas the…

One can understand abductive reasoning as “inference to the best explanation”. Abductive reasoning (also called abduction, abductive inference or retroduction) is a kind of logical…

Defeasible reasoning is a particular kind of non-demonstrative reasoning, the location where the reasoning does not build a full, complete, or final demonstration of an…

Structural induction is used to prove which some proposition P(x) holds for those x of some form of recursively defined structure for instance lists or…

Mathematical induction is a mathematical proof approach, commonly helpful to establish a given statement for everyone natural numbers, although it enables to prove statements with…

Two forms of logical reasoning could be distinguished along with formal deduction: induction in addition to abduction. Given the precondition or assumption, a conclusion as…