Constructive logic is a family of logics where proofs must be constructive (i.e., proving something means one must build or exhibit it, not just argue...

logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by...

viewpoint on mathematics. Much constructive mathematics uses intuitionistic logic, which is essentially classical logic without the law of the excluded...

idea is explored in the Brouwer–Heyting–Kolmogorov interpretation of constructive logic, the Curry–Howard correspondence between proofs and programs, and...

Constructive dilemma is a valid rule of inference of propositional logic. It is the inference that, if P implies Q and R implies S and either P or R is...

call/cc to Peirce's law, which extends intuitionistic logic to non-constructive, classical logic: ((α → β) → α) → α. Here, ((α → β) → α) is the type of...

turned to relevance logic to supply a connection between the antecedent and consequent of provable conditionals. In a constructive setting, the symmetry...

valuation. Whereas in classical logic truth values form a Boolean algebra, in intuitionistic logic, and more generally, constructive mathematics, the truth values...

predicative versions. However, all versions keep the core design of constructive logic using dependent types. Martin-Löf designed the type theory on the...

constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality. That is, logic and...

logics and constructive mathematics. The study of constructive mathematics includes many different programs with various definitions of constructive....

introduction, disjunction elimination, constructive dilemma, destructive dilemma, absorption, and De Morgan's laws. First-order logic also employs the logical operators...

B} are any propositions. Most constructive logics only reject the former, the law of excluded middle. In classical logic, also the ex falso law ( A ∧ ¬...

constructive logic corresponds to a certain program in the lambda calculus. Converting a proof in this way is called program extraction. Hoare logic is...

framework of a type theory bears a resemblance to intuitionistic, or constructive, logic. Formally, type theory is often cited as an implementation of the...

of the constructive properties of the latter. Although the logic has also been studied for its own sake, more broadly, ideas from linear logic have been...

formula F of classical logic into a formula Fc' of intuitionistic (constructive) logic, such that Fc' is deducible in intuitionistic logic if and only if F...

logic', sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic...

In mathematical logic, a superintuitionistic logic is a propositional logic extending intuitionistic logic. Classical logic is the strongest consistent...

Logic is the study of correct reasoning. It includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical...

classical logic a special fragment of CoL. Thus CoL is a conservative extension of classical logic. Computability logic is more expressive, constructive and...

, a constructive counter-part of Z F {\displaystyle {\mathsf {ZF}}} . Of course, a direct axiomatization may be studied as well. The base logic of constructive...

middle Consequentia mirabilis – Pattern of reasoning in propositional logic Constructive set theory Diaconescu's theorem Dichotomy – Splitting of a whole into...

algebra/min-plus algebra). Constructive analysis, which is built upon a foundation of constructive, rather than classical, logic and set theory. Intuitionistic...

First-order logic, also called predicate logic, predicate calculus, or quantificational logic, is a collection of formal systems used in mathematics,...

In logic and formal semantics, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to...

P. J. Scott. What results is essentially an intuitionistic (i.e. constructive logic) theory, its content being clarified by the existence of a free topos...

mathematical logic, the disjunction and existence properties are the "hallmarks" of constructive theories such as Heyting arithmetic and constructive set theories...

Look up Appendix:Glossary of logic in Wiktionary, the free dictionary. This is a glossary of logic. Logic is the study of the principles of valid reasoning...

In mathematical logic, a tautology (from Ancient Greek: ταυτολογία) is a formula that is true regardless of the interpretation of its component terms...