- implicational propositional calculus
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A minimalist version of propositional calculus which uses only the logical connectives ("implies") and ("false").
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implicational propositional calculus
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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
Propositional calculus — In mathematical logic, a propositional calculus or logic (also called sentential calculus or sentential logic) is a formal system in which formulas of a formal language may be interpreted as representing propositions. A system of inference rules… … 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
Material conditional — The material conditional, also known as material implication, is a binary truth function, such that the compound sentence p→q (typically read if p then q or p implies q ) is logically equivalent to the negative compound: not (p and not q). A… … Wikipedia
Peirce's law — noun The classically valid but intuitionistically non valid formula of propositional calculus, which can be used as an substitute for the law of excluded middle in implicational propositional calculus … Wiktionary
List of mathematics articles (I) — NOTOC Ia IA automorphism ICER Icosagon Icosahedral 120 cell Icosahedral prism Icosahedral symmetry Icosahedron Icosian Calculus Icosian game Icosidodecadodecahedron Icosidodecahedron Icositetrachoric honeycomb Icositruncated dodecadodecahedron… … 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
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
Necessary and sufficient condition — This article is about the formal terminology in logic. For causal meanings of the terms, see Causality. In logic, the words necessity and sufficiency refer to the implicational relationships between statements. The assertion that one statement is … 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
