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Topic: Natural deduction

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  Natural deduction - Wikipedia, the free encyclopedia
In mathematical logic, natural deduction is an approach to proof theory that attempts to provide a formal model of logical reasoning as it "naturally" occurs.
Natural deduction in its modern form was independently proposed by the German mathematician Gentzen in 1935, in a dissertation delivered to the faculty of mathematical sciences of the university of Göttingen.
The sequent calculus is the chief alternative to natural deduction as a foundation of mathematical logic.
en.wikipedia.org /wiki/Natural_deduction   (4782 words)

 Natural deduction logic - Wikipedia, the free encyclopedia
A natural deduction is an instruction on how to use binary logic to move from one line to another, during a linear sequential proof.
Thus, in order for a reasoning agent to learn that hypothetical syllogism is a valid natural deduction from this deduction(alternatively reasoning event), the reasoning agent had to already know that modus ponens is a natural deduction.
A reasoning agent who already knows enough natural deductions, so that in principle (memory limitations aside), he can determine whether or not some statement is a natural deduction, is said to be logically omnisicent.
en.wikipedia.org /wiki/Natural_deduction_logic   (386 words)

 Inference Rules of Natural Deduction
A Natural Deduction proof in PC is a sequence of wffs beginning with one or more wffs as premises; fresh premises may be added at any point in the course of a proof.
This means a Natural Deduction system has two aspects: A set of rules and a method for applying the rules.
Natural Deduction uses two kinds of rules: Rules of inference and rules of replacement.
www.mathpath.org /proof/proof.inference.htm   (1383 words)

 AsteroidMeta: Natural deduction based metamath system
Natural deduction was invented by Gentzen in the 30's (cf.
In the context of natural deduction it is an axiom.
However in natural deduction it is traditional to use axioms and not definitions to introduce the propositional calculus connectors.
planetx.cc.vt.edu /AsteroidMeta/Natural_deduction_based_metamath_system   (14030 words)

 Wikinfo | Natural deduction
One of the popular ways of cashing out natural deduction is that it is an application of the laws (rules, whatever) of logic to our "natural modes" of inference.
The advantage of a natural deduction system is that it has an apparatus for dealing with the sort of assumptions we just made.
Rather, the mathematician assumes something (which may be tentative, or an established fact- usually a fact) and then uses a bit of logic to show what must also be the case given the assumption (granted, s/he will almost always use certain "obvious" arithemtical properties in the proof-or other properties).
www.wikinfo.org /wiki.php?title=Natural_deduction   (513 words)

 Definition of natural - Merriam-Webster Online Dictionary
man> b : living in or as if in a state of nature untouched by the influences of civilization and society
implies lacking artificiality and self-consciousness and having a spontaneousness suggesting the natural rather than the man-made world natural manner>.
suggests a naturalness resulting from unawareness of the effect one is producing on others .
www.webster.com /dictionary/natural   (534 words)

Deduction presents classical first-order logic as efficiently and elegantly as possible.
It presents a truth tree system based on the work of Jeffrey, as well as a natural deduction system inspired by that of Kalish and Montague.
The definition of a formula excludes free variables, and the deduction system uses Show lines; the combination allows rules to be stated very simply.
www.utexas.edu /cola/depts/philosophy/faculty/bonevac/deduction   (167 words)

 Natural Deduction
Natural deduction was invented independently by S. Jaskowski in 1934 and G. Gentzen in 1935.
The nature of many proofs in natural deduction consists of picking apart a logical expression using the elimination rules to get at the constituent parts and then building up new expressions from the constituent parts using the introduction rules.
Natural deduction inference rules may be used in
cs.wwc.edu /~aabyan/Logic/natural.html   (201 words)

 A Brief History of Natural Deduction (ResearchIndex)
My view is that the current connotation of the term functions rather like a prototype: there is some exemplar that the term most clearly applies to and which manifests a number of characteristics.
1 Natural Deduction (context) - Anderson, Johnstone - 1962
1 On Natural Deduction (context) - Quine DBLP
citeseer.ist.psu.edu /390180.html   (653 words)

 CiteULike: A Natural Deduction System for Keisler's Quantification   (Site not responding. Last check: 2007-10-21)
Labelled deduction systems have been used to present a large class of logics.
The purpose of this paper is to show N DQ, a (labelled) natural deduction system for Keisler's logic, and discuss some of its properties.
This system is the result of the application of a general framework for dealing with quantifiers in natural deduction.
www.citeulike.org /user/greg_restall/article/686559   (177 words)

 CiteULike: Tag deduction   (Site not responding. Last check: 2007-10-21)
posted to ae argumentation calculus deduction dependence didactic ea historical inquiry logic mathematical natural practice predicate reasoning rule semantics statements syntax by yish as
posted to deduction fitch gentzen history jaskowski lc2005 lemmon logic natural pnc prawitz quine by greg_restall as
posted to belief deduction disposition epistemology externalism internalism kant knowledge logic motivation psychologism reason by greg_restall as
www.citeulike.org /tag/deduction   (203 words)

 Natural Deduction via Context   (Site not responding. Last check: 2007-10-21)
introduction in formal systems of natural deduction, we will have to restrict the rule of universal generalization to ensure that the variable being generalized does not occur free in any of the
We gave two treatments of the key argument: one in natural deduction (§4) and one Hilbert-style (above).
This kind of proof transformation is logical routine, and any textbook on proof theory (say, the recent [57]), tells all about it.
www-formal.stanford.edu /jmc/mccarthy-buvac-98/context/node5.html   (370 words)

 Natural Deduction (ResearchIndex)
Abstract: This paper presents a theoretical analysis of natural deduction.
First, a brief description will be given of a natural deduction system for sentential logic (i.e., no quantifiers or variables).
3.5: Skolemization and Unification in Natural Deduction - Pollock
citeseer.ist.psu.edu /522301.html   (157 words)

 Foundations of Mathematics
Platonism, Intuition and The Nature of Mathematics - by Karlis Podnieks
Natural Deduction for First-Order Logic - by Hans de Nivelle
From Natural Deduction to Sequent Calculus - Slides by Christoph Benzmüller
sakharov.net /foundation_rt.html   (2708 words)

 Domino On Acid - Natural Deduction Visualised   (Site not responding. Last check: 2007-10-21)
Superficially this is a colorful variant of dominoes with weird tiles, a simple matching game to play during lunch breaks.
But hidden behind this façade are the inference rules of natural deduction, so that every solved level represents a proof of a tautology.
This program demonstrates that logical reasoning can be done without any language or symbols, relying purely on the brain's visual capabilities.
www.winterdrache.de /freeware/domino   (271 words)

 Find in a Library: Natural deduction; a proof-theoretical study.
Find in a Library: Natural deduction; a proof-theoretical study.
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WorldCat is provided by OCLC Online Computer Library Center, Inc. on behalf of its member libraries.
www.worldcatlibraries.org /wcpa/ow/171b7ebf5bb27ff1.html   (44 words)

 University Library Nijmegen: Item 2066/17262
Please use this identifier to cite or link to this item:
Lambda terms for natural deduction, sequent calculus and cut elimination
There are no files associated with this item.
hdl.handle.net /2066/17262   (51 words)

 Natural Deduction by Dag Prawitz at Smarter.com
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www.smarter.com /natural_deduction---pd--ch-1--pi-2006838.html   (134 words)

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