natural deduction


Also found in: Encyclopedia, Wikipedia.

natural deduction

n
(Logic) a system of formal logic that has no axioms but permits the assumption of premises of an argument. Such a system uses sequents to record which assumptions are operative at any stage. Compare axiomatic3
Collins English Dictionary – Complete and Unabridged, 12th Edition 2014 © HarperCollins Publishers 1991, 1994, 1998, 2000, 2003, 2006, 2007, 2009, 2011, 2014
Mentioned in ?
References in periodicals archive ?
For example, a mathematical or philosophical argument may be made completely inferentially rigorous (atomized) by decomposing its inferential steps into the type of step found in a natural deduction system.
Topics include overlapping as a basic concept of subset spaces, representing public transport schedules as repeating trips, a heuristic approach to order events in narrative texts, and labeled natural deduction systems for a family of tense logics.
He works through informal logic, including meanings and definition of language and fallacies, formal logic, including categorical propositions and syllogisms, propositional logic, natural deduction in propositional logic and predicate logic, inductive logic, including analogies, legal and moral reasoning, causality and Mill's methods, probability, statistical reasoning, and hypothetical and scientific reasoning.
This system, called ETPS, consists primarily of the interactive facilities for natural deduction reasoning from TPS.
Gentzen's system of natural deduction is here a paradigm.
Although his methods, rules and structures have lead to verification programs essential to computer science, and his work on natural deduction, the sequent calculus and ordinal proof theory are still considered advanced, his life eventually ran contrary to the passions of his nation.
Topics include temporalizing tractable description logic, relational temporal machines, a proposal for a temporal-to-temporal query language, automated natural deduction for propositional linear-time temporal logic, conceptual modeling of temporal clinical workflows, the equivalence of automation-based representations of time granularities, and a comparison of statistic and rule-induction learners for automatic tagging of time expression in English.
Nevertheless, I would like to have seen natural deduction (or sequent calculi) included.
Topics of the 38 papers include research models for patient-centered healthcare services, natural deduction calculus for computation tree logic, intelligent traffic management through MPEG-7 vehicle flow surveillance, and performance modeling of the Blue Gene architecture.
According to Flannery, Alexander saw logic as the servant of scientific truth, viewing syllogistic as something like a set of inference schemes akin to a modern system of natural deduction.
Among the book's virtues must be mentioned its profuse illustration of so many different graphic methods in mathematical logic, including Venn diagrams, the square of opposition, Smullyan truth trees, Wallen's reduction technique, Beth's and Hintikka's semantic tableaux method, and several styles of axiomatic and natural deduction. The work is certain to be a valuable resource for French readers in need of a lucid, comprehensive guide to the history and practical techniques of logic in its elementary applications to the philsophy of mathematics and information sciences.