intuitionistic system
1Intuitionistic logic — Intuitionistic logic, or constructive logic, is a symbolic logic system differing from classical logic in its definition of the meaning of a statement being true. In classical logic, all well formed statements are assumed to be either true or… …
2Intuitionistic type theory — Intuitionistic type theory, or constructive type theory, or Martin Löf type theory or just Type Theory is a logical system and a set theory based on the principles of mathematical constructivism. Intuitionistic type theory was introduced by Per… …
3intuitionistic logic — The logical system developed initially by A. Heyting (b. 1898) to formalize the reasonings allowed by mathematical intuitionism . It is designed so that p ∨ ¬ p is not a theorem, and the rule of inference from ¬¬ p to p is disallowed (the logic… …
4Deductive system — A deductive system (also called a deductive apparatus of a formal system) consists of the axioms (or axiom schemata) and rules of inference that can be used to derive the theorems of the system.[1] Such a deductive system is intended to preserve… …
5Pure type system — In proof and type theory, a pure type system is a form of typed lambda calculus that obscures the distinction between types and terms and collapses the type hierarchy. It can be seen as a generalisation of Barendregt s lambda cube, and therefore… …
6Mathematical logic — (also known as symbolic logic) is a subfield of mathematics with close connections to foundations of mathematics, theoretical computer science and philosophical logic.[1] The field includes both the mathematical study of logic and the… …
7Curry–Howard correspondence — A proof written as a functional program: the proof of commutativity of addition on natural numbers in the proof assistant Coq. nat ind stands for mathematical induction, eq ind for substitution of equals and f equal for taking the same function… …
8Paraconsistent logic — A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way. Alternatively, paraconsistent logic is the subfield of logic that is concerned with studying and developing paraconsistent (or… …
9mathematics, foundations of — Scientific inquiry into the nature of mathematical theories and the scope of mathematical methods. It began with Euclid s Elements as an inquiry into the logical and philosophical basis of mathematics in essence, whether the axioms of any system… …
10Intuitionism — This article is about Intuitionism in mathematics and philosophical logic. For other uses, see Ethical intuitionism. In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach to mathematics as …
