# formal implication

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formal implication
In a logical calculus, one proposition A formally implies another B if there is a proof starting from A as an assumption and ending with B.

Philosophy dictionary. . 2011.

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• implication — [im΄pli kā′shən] n. [ME implicacioun < L implicatio] 1. an implicating or being implicated 2. an implying or being implied 3. a) something implied, from which an inference may be drawn b) Logic a formal relationship between two propositions… …   English World dictionary

• 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

• 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

• Implication-Realization — The Implication Realization (I R) model of melodic expectation was developed by Eugene Narmour as an alternative to Schenkerian analysis centered less on music analysis and more on cognitive aspects of expectation. The model is one of the most… …   Wikipedia

• Formal proof — See also: mathematical proof, proof theory, and axiomatic system A formal proof or derivation is a finite sequence of sentences (called well formed formulas in the case of a formal language) each of which is an axiom or follows from the… …   Wikipedia

• implication — n. 1 what is involved in or implied by something else. 2 the act of implicating or implying. Phrases and idioms: by implication by what is implied or suggested rather than by formal expression. Etymology: ME f. L implicatio (as IMPLICATE) …   Useful english dictionary

• Logical implication — In logic and mathematics, logical implication is a logical relation that holds between a set T of formulae and a formula B when every model (or interpretation or valuation) of T is also a model of B . In symbols,# T models B, # T Rightarrow B # T …   Wikipedia

• by implication — by what is implied or suggested rather than by formal expression he criticized her and, by implication, her country …   Useful english dictionary

• Propositional formula — In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value. If the values of all variables in a propositional formula are given, it determines a unique truth value. A propositional… …   Wikipedia

• Principia Mathematica — For Isaac Newton s book containing basic laws of physics, see Philosophiæ Naturalis Principia Mathematica. The title page of the shortened version of the Principia Mathematica to *56. The Principia Mathematica is a three volume work on the… …   Wikipedia