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	NationMaster - Encyclopedia: Natural deduction
		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.
		A natural deduction is an instruction on how to use binary logic to move from one line to another, during a linear sequential proof.
	www.nationmaster.com /encyclopedia/Natural-deduction (349 words)

	logic@Everything2.com (Site not responding. Last check: 2007-10-19)
		Logic is not the same as Common Sense, and while what one person's common sense tells him another person may reject, if they stick to formal logic they can always reach a joint conclusion.
		Natural selection has these and many other logical inconsistencies: (a.) Although evolutionists say that organisms are suited for their environment because they evolved into it, being suited for the environment is much better explained by the fact that they were created for the environment rather than that they evolved into it.
		Mathematics is a obviously a branch of logic.
	everything2.com /index.pl?node=logic (2397 words)

	PlanetMath: natural deduction
		Natural deduction refers to related proof systems for several different kinds of logic, intended to be similar to the way people actually reason.
		Sequents in natural deduction have only one formula on the right side.
		This is version 2 of natural deduction, born on 2002-10-02, modified 2004-04-11.
	planetmath.org /encyclopedia/NaturalDeduction.html (113 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)

	philosophy
		Formal logic, in contrast, analyzes the forms of arguments by developing specialized languages in which the basic structural relation between premises and conclusion is precisely symbolized and evaluated.
		By providing resources for evaluating arguments, logic promises to be a tool for exposing views that can not be held "for good reasons." If students make the effort to examine their views by articulating their reasons for holding them, then logic may well enhance their critical reasoning abilities.
		Logic is not, then, an empirical study of how we do think but, instead, a normative study of how we should reason.
	www.kzoo.edu /phil/Logic2001.html (407 words)

	Natural deduction logic
		Every natural deduction, is one of the tautologies of the propositional calculus.
		As an example of a natural deduction, consider the hypothetical syllogism HS.
		Natural deduction was rigorously worked on by S. Jaskowski in 1934, and G. Gentzen in 1935.
	www.brainyencyclopedia.com /encyclopedia/n/na/natural_deduction_logic.html (439 words)

	Hybrid Logic (Stanford Encyclopedia of Philosophy)
		Thus, in hybrid logic a term is a specific sort of propositional symbol whereas in first-order logic it is an argument to a predicate.
		A model for hybrid logic is a triple (W, R, V) where W is a non-empty set, R is a binary relation on W, and V is a function that to each pair consisting of an element of W and an ordinary propositional symbol assigns an element of the set {0,1}.
		The semantics of hybrid tense logic is the semantics of hybrid logic, cf.
	plato.stanford.edu /entries/logic-hybrid (3942 words)

	Natural deduction - RecipeFacts (Site not responding. Last check: 2007-10-19)
		Natural deduction grew out of a context of dissatisfaction with sentential axiomatizations common to the systems of Hilbert, Frege, and Russell.
		His 1965 monograph Natural deduction: a proof-theoretical study was to become the definitive work on natural deduction, and included applications for modal and second-order logic.
		Popular modern logical frameworks such as the calculus of constructions and LF are based on higher-order dependent type theory, with various trade-offs in terms of decidability and expressive power.
	www.recipeland.com:8080 /facts/Natural_deduction (5157 words)

	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)

	logic - Definitions from Dictionary.com
		The rules of natural deduction describe how we may proceed from valid premises to valid conclusions, where the premises and conclusions are expressions in predicate logic.
		In symbolic logic, arguments and proofs are made in terms of symbols representing propositions and logical connectives.
		Deduction describes how we may proceed from valid premises to valid conclusions, where these are expressions in predicate logic.
	dictionary.reference.com /browse/logic (876 words)

	Visualization of Natural Deduction as a Game of Dominoes
		Natural deduction (in the limited form presented here) is a calculus for syntactically deriving tautologies in propositional logic.
		A natural deduction proof is usually presented in a tree-like notation where the derived formula is the root, usually written at the bottom.
		In natural deduction domino, all tiles corresponding to instances of the three derivation rules are available without limitations at all times.
	data.schneepoesie.de /winterdrache/domino/article.html (7236 words)

	Graduate Logic Requirement Exam (Site not responding. Last check: 2007-10-19)
		The graduate logic exam is designed to test students understanding of the basic concepts and methods of formal logic.
		The emphasis in the course is upon mastery of the formal concepts and techniques of first order logic with identity.
		Finally, a letter testifying that a graduate student is competent to teach an introductory symbolic logic course, which is potentially useful when on the job market, cannot be written unless the student enrolls for the intermediate level logic course, PHL 432 (see sample syllabus).
	www.msu.edu /~phl/dept/gradlogicexam.htm (403 words)

	Wikinfo \| Natural deduction
		The section on symbolic logic mentions axiomatic treatments of the subject.
		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.
	www.wikinfo.org /wiki.php?title=Natural_deduction (513 words)

	Logic and Discrete Maths
		Laws of boolean logic should become "hardwired" into the heads of students so that they do not even have to think about their use.
		Natural deduction (the currently used proof method in math2090) is good for simple proofs in predicate logic, but it does not scale well to other discrete domains.
		The GS logic has the virtue of (a) introducing a suitable notation and calculus that can be used for logic and in other domains, and (b) allowing a succint way for doing calculations (which subsumes proof derivations, simplifying, and solving in diverse domains).
	www.cse.yorku.ca /~logicE/curriculum/logic_discrete_maths.html (1593 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 (1377 words)

	Logic Syllabus
		Logic is the formal analysis of valid patterns of argument and deductive inference.
		Since Boole (in the mid 1800's) mathematicians have formalized logic so that it can be studied as part of the subject matter of mathematics as well as providing a careful check on the kind of reasoning allowed in mathematics.
		Logic sits firmly on the boundary between the three disciplines of mathematics, philosophy, and computer science.
	www.iwu.edu /~lstout/Logic/S02sylLogic.html (719 words)

	logic from FOLDOC
		This involves the formalisation of logical arguments and proofs in terms of symbols representing propositions and logical connectives.
		The rules of natural deduction describe how we may proceed from valid premises to valid conclusions, where the premises and conclusions are expressions in predicate logic.
		In symbolic logic, arguments and proofs are made in terms of symbols representing propositions and logical connectives.
	foldoc.org /?logic (397 words)

	natural deduction for linear logic; corrections;bibliography (Site not responding. Last check: 2007-10-19)
		ABSTRACT Natural deduction for intuitionistic linear logic by A.S. Troelstra The paper deals with two versions of the fragment with unit, tensor, linear implication and storage operator (the exponential !) of intuitionistic linear logic.
		It is relatively easy to adapt Prawitz's treatment of natural deduction for intuitionistic logic to ILLP; in particular one can formulate a notion of strong validity (as in Prawitz's ``Ideas and Results in Proof Theory'') permitting a proof of strong normalization.
		The file nat.ps is the postscript file of the paper "Natural deduction for intuitionistic linear logic", report ML-93-09 of The Institute for Logic.
	www.cis.upenn.edu /~bcpierce/types/archives/1993/msg00086.html (315 words)

	Propositional Logic [Internet Encyclopedia of Philosophy]
		In propositional logic, the simplest statements are considered as indivisible units, and hence, propositional logic does not study those logical properties and relations that depend upon parts of statements that are not themselves statements on their own, such as the subject and predicate of a statement.
		However, there are other forms of propositional logic in which other truth-values are considered, or in which there is consideration of connectives that are used to produce statements whose truth-values depend not simply on the truth-values of the parts, but additional things such as their necessity, possibility or relatedness to one another.
		In natural deduction an attempt is made to reduce the reasoning behind a valid argument to a series of steps each of which is intuitively justified by the premises of the argument or previous steps in the series.
	www.iep.utm.edu /p/prop-log.htm (8796 words)

	AsteroidMeta: Natural deduction based metamath system
		However in a natural deduction system the turnstile is normally used to separate the context from the statement.
		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 (14791 words)

	Deduction
		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)

	NationMaster - Encyclopedia: Assumption
		Proposition is a term used in logic to describe the content of assertions.
		In logic, more specifically in the context of natural deduction systems, an assumption is made in the expectation that it will be discharged in due course via a separate argument.
		Assumption may also refer to: 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.
	www.nationmaster.com /encyclopedia/Assumption (871 words)

	Logic 1
		The examination is open to all students who could not come to the first examination, as well as to students who want to improve their previous grade.
		The course is an introduction to logic for students in Computer Science and Mathematics.
		In fact, I would prefer that you register after you see the first lecture[s] and you take the final decision to participate for the rest of the semester (the deadline for registration is 3rd of November).
	www.risc.uni-linz.ac.at /education/courses/ws2004/logic-1 (705 words)

	Oxford University Press: Proof and Disproof in Formal Logic: Richard Bornat (Site not responding. Last check: 2007-10-19)
		The logic it uses-natural deduction-is very small and very simple; working with it helps you see how large mathematical universes can be built on small foundations.
		Aimed at undergraduates and graduates in computer science, logic, mathematics and philosophy, the text includes reference to and exercises based on the computer software package Jape, an interactive teaching and research tool designed and hosted by the author that is freely available on the web.
		Covering propositional logic, first-order logic, and second-order logic, as well as proof theory, computability theory, and model theory, the text also contains numerous carefully graded exercises and is ideal for a first or refresher course.
	www.oup.com /us/catalog/general/subject/Mathematics/Logic/~~/dmlldz11c2EmY2k9OTc4MDE5ODUzMDI2OA== (444 words)

	Intuitionistic Logic
		Intuitionistic logic encompasses the principles of logical reasoning which were used by L. Brouwer in developing his intuitionistic mathematics, beginning in [1907].
		Philosophically, intuitionism differs from logicism by treating logic as a part of mathematics rather than as the foundation of mathematics; from finitism by allowing (constructive) reasoning about infinite collections; and from platonism by viewing mathematical objects as mental constructs with no independent ideal existence.
		A derivation of a formula E from a collection F of assumptions is any sequence of formulas, each of which belongs to F or is an axiom or an immediate consequence, by a rule of inference, of preceding formulas of the sequence, such that E is the last formula of the sequence.
	www.seop.leeds.ac.uk /archives/sum2003/entries/logic-intuitionistic (2215 words)

	Math Forum - Ask Dr. Math Archives: High School Logic (Site not responding. Last check: 2007-10-19)
		Solve by deduction and then induction: Bob wants to figure out what his teacher wants for his birthday, but he cannot ask his teacher directly.
		An interesting logic puzzle about determining a birthday leads to a discussion about interpretation, logic, and seeming confusion when one of the logic statements is rewritten in a different but equivalent form.
		The Math Forum is a research and educational enterprise of the Drexel School of Education.
	mathforum.org /dr.math/tocs/logic.high.html (840 words)

	Mailgate: sci.logic: Re: Disjunction in propositional logic (Site not responding. Last check: 2007-10-19)
		On Thu, 9 Sep 2004 23:07:09 -0400, "Dan Christensen" wrote: > > > > Here is a basic question regarding propositional logic...
		You could start with > the premise: A or B. Then, applying the rules of logic, you can infer other > statements like: not (not A and not B).
		> Dan, the OP was asking for a reasonable logical analysis of the statement P. Your software can't provide that.
	mailgate.supereva.com /sci/sci.logic/msg19821.html (106 words)

	The home page of Jan von Plato
		In 1995-1996 I was Lecturer in Philosophy at the Department of Logic and Scientific Method of the London School of Economics.
		My present research is mainly in logic and foundations of mathematics, particularly, proof theory, constructive geometry, and elementary intuitionistic axiomatics and logical issues related to the latter.
		Sequent calculus in natural deduction style, written with Sara Negri, The Journal of Symbolic Logic 66 (2001): 4, pp..
	www.helsinki.fi /%7evonplato (654 words)

	CFP: International Workshop on Hybrid Logic 2006 (HyLo 2006)
		What is less obvious is that the route hybrid logic takes to overcome this problem (the basic mechanism being to add nominals --- atomic symbols true at a unique point --- together with extra modalities to exploit them) often actually improves the behavior of the underlying modal formalism.
		For example, it becomes far simpler to formulate modal tableau, resolution, and natural deduction in hybrid logic, and completeness and interpolation results can be proved of a generality that is not available in orthodox modal logic.
		Hybrid logic is now a mature field, therefore a theme of special interest at this HyLo workshop will be the combination of hybrid logic with other logics, the basic methodological question being "what is the best way of hybridizing a given logic?" However, submissions in all areas of hybrid logic are welcome.
	www.erlang.org /pipermail/erlang-questions/2006-January/018800.html (595 words)

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