implicational logic

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• Implicational propositional calculus — In mathematical logic, the implicational propositional calculus is a version of classical (two valued) propositional calculus which uses only one connective, called implication or conditional. In formulas, this binary operation is indicated by… …   Wikipedia

• logic, history of — Introduction       the history of the discipline from its origins among the ancient Greeks to the present time. Origins of logic in the West Precursors of ancient logic       There was a medieval tradition according to which the Greek philosopher …   Universalium

• Converse (logic) — In logic, the converse of a categorical or implicational statement is the result of reversing its two parts. For the implication P → Q, the converse is Q → P. For the categorical proposition All S is P, the converse is All P is S. In neither case …   Wikipedia

• Combinatory logic — Not to be confused with combinational logic, a topic in digital electronics. Combinatory logic is a notation introduced by Moses Schönfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. It has more recently been… …   Wikipedia

• formal logic — the branch of logic concerned exclusively with the principles of deductive reasoning and with the form rather than the content of propositions. [1855 60] * * * Introduction       the abstract study of propositions, statements, or assertively used …   Universalium

• Bunched logic — is a variety of substructural logic that, like linear logic, has classes of multiplicative and additive operators, but differs from usual proof calculi in having a tree like context of hypotheses instead of a flat list like structure; it is thus… …   Wikipedia

• Curry–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… …   Wikipedia

• Curry-Howard correspondence — The Curry Howard correspondence is the direct relationship between computer programs and mathematical proofs. Also known as Curry Howard isomorphism, proofs as programs correspondence and formulae as types correspondence, it refers to the… …   Wikipedia

• implication — implicational, adj. /im pli kay sheuhn/, n. 1. something implied or suggested as naturally to be inferred or understood: to resent an implication of dishonesty. 2. the act of implying: His implication of immediate changes surprised us. 3. the… …   Universalium

• SKI combinator calculus — is a computational system that is a reduced, untyped version of Lambda calculus. All operations in Lambda calculus are expressed in SKI as binary trees whose leaves are one of the three symbols S, K, and I (called combinators). In fact, the… …   Wikipedia

• Peirce's law — in logic is named after the philosopher and logician Charles Sanders Peirce. It was taken as an axiom in his first axiomatisation of propositional logic. In propositional calculus, Peirce s law says that (( P → Q )→ P )→ P . Written out, this… …   Wikipedia