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	Inductive reasoning: Definition and links by Encyclopedian.com Information about Inductive reasoning
		Inductive reasoning is the process of reasoning from the specific to the general.
		Inductive logic expresses the truth-value of its inferences in terms of probability rather than necessity.
		The nature of inductive reasoning, with examples, is discussed further at cogency.
	www.encyclopedian.com /in/Inductive-reasoning.html (334 words)

	Practice Questions on Recursive Definition (Site not responding. Last check: 2007-11-06)
		This part of the definition specifies the "seeds" of the set from which the elements of the set are generated using the methods given in the inductive clause.
		(or simply induction) of the definition establishes the ways in which elements of the set can be combined to produce new elements of the set.
		The inductive clause always asserts that if objects are elements of the set, then they can be combined in certain specified ways to create other objects.
	www.cs.odu.edu /~toida/nerzic/content/recursive_def/rec_def.html (1037 words)

	The Definition of Morality
		However, it is not useful to adopt a definition of “morality” as meaning the code of conduct accepted by the members of a society because in many large societies, not all members of the society accept the same code of conduct.
		Nor is it useful to adopt a somewhat more general definition of “morality” as the code of conduct accepted by the members of a group because it is not only always possible, it is often the case, that not all members of any group accept the same code.
		Although this definition allows as meaningful the question, “Why should I be moral?”, it guarantees that there is an answer that shows that it is not irrational to be moral, even though it may not show that it is irrational to be immoral.
	plato.stanford.edu /entries/morality-definition (5060 words)

	Reality - Wikipedia, the free encyclopedia
		It can be argued that statements of this nature are only trivially true, since the definitions of the concepts "set", "entity", "union", "one", "four", and "five" are all defined in terms of each other, and that these concepts have no inherent reality apart from this self-referencing structure.
		Mathematical formulations and propositions in mathematical logic are based on axioms, and hence these fields are often referred to as pure disciplines.
		If--what is rarely done--a philosopher wanted to proffer a positive definition of the concept "reality," it would be done under this heading.
	en.wikipedia.org /wiki/Reality (2868 words)

	Inductive - Definition of Inductive - Inductive in Encyclopedia - DictionaryWords.net (Site not responding. Last check: 2007-11-06)
		[1913 Webster] Inductive embarrassment (Physics), the retardation in signaling on an electric wire, produced by lateral induction.
		Inductive sciences, those sciences which admit of, and employ, the inductive method, as astronomy, botany, chemistry, etc. [1913 Webster]
		inductive adj 1: relating to logical induction; "inductive thinking" 2: arising from inductance; "inductive reactance" 3: of reasoning; proceeding from particular facts to a general conclusion; "inductive reasoning" [ant: deductive ] 4: inducing or influencing; leading on; "inductive to the sin of Eve"- John Milton [syn: inducive ]
	www.dictionarywords.net /find/word/Inductive (213 words)

	Propositional calculus - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-11-06)
		With this definition we can now formalize what it means for a formula φ to be implied by a certain set S of formulas.
		This leads to the following formal definition: We say that a set S of wffs semantically entails (or implies) a certain wff φ if all truth assignments that satisfy all the formulas in S also satisfy φ.
		By the definition of provability, there are no sentences provable other than by being a member of G, an axiom, or following by a rule; so if all of those are semantically implied, the deduction calculus is sound.
	encyclopedia.worldsearch.com /propositional_calculus.htm (2964 words)

	Calculus of Inductive Constructions
		An inductive definition is specified by a possibly huge set of declarations, clearly we want to share this specification among the various inductive objects and not to duplicate it.
		A (possibly mutual) inductive definition is specified by giving the names and the type of the inductive sets or families to be defined and the names and types of the constructors of the inductive predicates.
		In case the inductive definition is effectively a recursive one, we want to capture the extra property that we have built the smallest fixed point of this recursive equation.
	coq.inria.fr /doc/Reference-Manual006.html (6700 words)

	Inductive: Definition of Inductive in Webster's Dictionary 1913 Edition - Wunder Dictionary
		Leading to inferences; proceeding by, derived from, or using, induction; as, inductive reasoning.
		Operating by induction; as, an inductive electrical machine.
		Facilitating induction; susceptible of being acted upon by induction; as certain substances have a great inductive capacity.
	websters.wunderdictionary.com /dictionary/def/english/inductive.html (69 words)

	CST LECTURES: Lecture (Site not responding. Last check: 2007-11-06)
		For every inductive definition there is a smallest closed class, which may be called the class of theorems of the inductive definition.
		For every inductive definition that has a set bound and is weakly local the class of theorems forms a set.
		An inductive definition is weakly local if, for each set X the class of conclusions of all steps having exactly the set X of premisses, forms a set.
	www.cs.man.ac.uk /~petera/Padua_Lectures/lect12.html (490 words)

	Citations: Inductive definition in type theory - Mendler (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		....inductive types are considered as a primitive notion; induction and primitive recursion appear as two different aspects of the same typetheoretic concept.
		Inductive definition of recursive types requires considerable extra notation, so we will settle for a summary at the end of the paper of the steps necessary to inductively define CTTR.
		The development of the semantics of CTT now proceeds in three phases: untyped equality on terms is defined, the inductive definition of types is given, and the theory is proven sound with respect to this definition.
	citeseer.lcs.mit.edu /context/100004/0 (2264 words)

	INDUCTIVE - Definition
		A brutish vice, Inductive mainly to the sin of Eve.
		Leading to inferences ; proceeding by, derived from, or using, induction ; as, inductive reasoning.
		{ Inductive embarrassment } ( Physics), the retardation in signaling on an electric wire, produced by lateral induction.
	www.hyperdictionary.com /dictionary/inductive (221 words)

	Definition: inductive coupling (Site not responding. Last check: 2007-11-06)
		inductive coupling: The transfer of energy from one circuit to another by virtue of the mutual inductance between the circuits.
		( 188) Note 1: Inductive coupling may be deliberate and desired (as in an antenna coupler) or may be undesired (as in power line inductive coupling into telephone lines).
		Note 2: Capacitive coupling favors transfer of higher frequency components, whereas inductive coupling favors transfer of lower frequency components.
	www.its.bldrdoc.gov /fs-1037/dir-019/_2714.htm (83 words)

	Formal Foundations of Computer Science 1 -- 5.1 Inductive Definitions (Site not responding. Last check: 2007-11-06)
		A function introduced by an inductive definition is uniquely defined.
		The more complicated the recursive structure of a function definition is, the more important it becomes to show that a set of equations indeed defines a total function.
		A predicate introduced by an inductive definition is uniquely defined.
	www.risc.uni-linz.ac.at /education/courses/formal/report/index_39.html (469 words)

	[Coq-Club] mutually inductive definition (Site not responding. Last check: 2007-11-06)
		I thought > I'd define the type to be mutually inductive with a proposition type > indicating the uniqueness: > However, coq rejects the definition, complaining, > > Error: The reference uniq_list was not found in the current environment.
		What you are trying to do (as you said yourself) is defining a type and a predicate on this type mutually inductive; this is called induction-recursion, and is not supported by the CIC (calculus of inductive constructions), the type theory behind Coq.
		AFAIK, the canonical reference for the notion is: Peter Dybjer, A general formulation of simultaneous inductive-recursive definitions in type theory, Journal of Symbolic Logic, 65(2), June 2000.
	pauillac.inria.fr /pipermail/coq-club/2005/001737.html (254 words)

	Citations: Foundation of logic programming based on inductive definition - Hagiya, Sakurai (ResearchIndex) (Site not responding. Last check: 2007-11-06)
		Definition 3.14 (Calculus Nat(P) The provable objects of the calculus Nat(P) are closed Sigma formulas of the language L. Its inference rules are shown in Figure 3.2.
		The Well-founded Semantics Is the Principle of Inductive Definition - Denecker (1998)
		Inductive Definitions First we briefly review the kind of inductive definitions we use; the general theory can be....
	citeseer.lcs.mit.edu /context/135047/0 (1753 words)

	Inductive Definition in Type Theory, by Nax P. Mendler (Site not responding. Last check: 2007-11-06)
		First, we consider the the question of inductive types in the simpler setting of the second-order lambda calculus, where we prove a strong normalization property.
		We also consider typing terms in the presence of type constraints,and present a condition on the constraints (of polynomial complexity in the size of the constraints) for determining if the terms will be strongly normalizable or there will be a diverging typed term.
		Second, we develop a semantic account of the basic type theory, then relativize it to account for the impredicativity inherent in the definition of the new type constructors.
	www.nuprl.org /documents/Mendler/InductiveDefinition.html (348 words)

	[No title]
		Definition application':(A,B:(Form Atoms);E:gentzen_extension) (gentzenSequent E (OneForm (Dot B (Backslash B A))) A).
		Definition coApplication:(A,B:(Form Atoms); E:gentzen_extension) (gentzenSequent E (OneForm A) (Slash (Dot A B) B)).
		Definition coApplication':(A,B:(Form Atoms); E:gentzen_extension) (gentzenSequent E (OneForm A) (Backslash B (Dot B A))).
	dept-info.labri.u-bordeaux.fr /~anoun/CTL/Sequent.v (2712 words)

	Electronic Articles in Computer and Information Science
		To adequately model the constructive nature of the physical change propagation process, we base the semantics of the formalism on the principle of inductive definition, the main mathematical constructive principle.
		We use a generalised inductive definition principle, generalising Clark completion and circumscription, to define a unique intended semantics for causal theories.
		Our approach can deal in particular with cyclic dependencies between effects, in such a way that to some definitions, in spite of syntactic cycles, we can assign a unique intended semantics in a constructive way, while other "actually cyclic" definitions are explicitly detected by the semantics as bad definitions.
	www.ep.liu.se /ea/cis/1998/007 (299 words)

	2.1.4 Inductive Definition and Proofs (Site not responding. Last check: 2007-11-06)
		Most ``recursive'' procedures are really just inductive definitions.
		Induction Principle II is needed for inductive definitions like the one for the fibonacci numbers:
		Permission is granted for personal (electronic and printed) copies of this document provided that each such copy (or portion thereof) is accompanied by this copyright notice.
	www.cs.pitt.edu /~daley/cs3120/cs3120w_node8.html (320 words)

	Learn more about Truth in the online encyclopedia. (Site not responding. Last check: 2007-11-06)
		That is, in Tarski's view, any adequate definition or theory of truth must imply all of the T-sentences (this constraint is known as Convention T).
		Tarski developed a rather complicated theory, involving what is known as an inductive definition of truth and introduced further ideas, such as the distinction between object language and meta-language (which is important in avoiding the semantic paradoxes such as the Liar Paradox).
		More worryingly, in the Soviet Union under Stalin, certain beliefs concerning biology were adopted because they were "useful to believe" and this led to what is called Lysenkoism.
	www.onlineencyclopedia.org /t/tr/truth.html (4838 words)

	Philosophical Dictionary: Decision-Deontology
		In a deductive argument, the truth of the premises is supposed to guarantee the truth of the conclusion; in an inductive argument, the truth of the premises merely makes it probable that the conclusion is true.
		Russell showed nearly a century ago that the proper analysis of such expressions, as the joint assertion of several distinct propositions, resolves a number of otherwise troubling difficulties.
		The five major kinds of definition (distinguished by the functions they may be used to perform) include:
	www.philosophypages.com /dy/d2.htm (1139 words)

	Operational semantics Article, Operationalsemantics Information (Site not responding. Last check: 2007-11-06)
		A common way to rigorously define the operational semantics is to provide a state transition system for the language of interest.
		Such a definition allows a formal analysis ofa language, permitting the study of relations betweenprograms.
		Defining operational semantics through a state transition system is usually done by giving an inductive definition ofthe set of possible transitions.
	www.anoca.org /program/language/operational_semantics.html (285 words)

	"Inductive reasoning" Definition (Site not responding. Last check: 2007-11-06)
		The attempt to use information about a specific situation to draw a conclusion.
		Inductive reasoning - The attempt to use information about a specific situation to draw a conclusion.
		Inductive reasoning : the attempt to use information about a specific situation to draw a conclusion.
	www.level2.ru /dictionary/i/inductive_reasoning.html (45 words)

	[Coq-Club] Strange error message during inductive definition (Site not responding. Last check: 2007-11-06)
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		Inductive Term : Set :=3D var : nat -> Term
	pauillac.inria.fr /pipermail/coq-club/2003/001095.html (380 words)

	Extensions of Gallina
		During the definition of the one-constructor inductive definition, all the errors of inductive definitions, as described in Section 1.3.3, may also occur.
		For inductive types with exactly two constructors and for pattern-matchings expressions which do not depend on the arguments of the constructors, it is possible to use a
		In case one wants that some arguments of a given object (constant, inductive types, constructors, assumptions, local or not) are always inferred by Coq, one may declare once for all which are the expected implicit arguments of this object.
	coq.inria.fr /doc/Reference-Manual004.html (3708 words)

	Inductive - Definition of Inductive by Webster Dictionary
		Inductive - Definition of Inductive by Webster Dictionary
		(Physics) Operating by induction ; as, an inductive electrical machine.
		those sciences which admit of, and employ, the inductive method, as astronomy, botany, chemistry, etc.
	www.webster-dictionary.net /definition/Inductive (129 words)

	[No title] (Site not responding. Last check: 2007-11-06)
		An Inductive Definition of Fully Abstract Models for PCF and PCF+OR A construction of fully abstract models for PCF and PCF^+ = PCF + parallel conditional function OR is presented on the base of quite general notions of sequential computational strategies and wittingly consistent non-deterministic strategies, respectively, introduced by the author in the seventies.
		This definition is given level-by-level of the finite type hierarchy and is an alternative and, in a sense, an analog to a later game semantics approaches of S. Abramsky, R.
		Thus, by analogy, continuity of such fully abstract model (with universal functionals) for pure PCF can be hardly expected.
	www.cs.tau.ac.il /%7Enachumd/Semester/Sazonov2.txt (231 words)

	"Archives: Strange message in inductive type definition (Site not responding. Last check: 2007-11-06)
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	pauillac.inria.fr /cdrom/www/coq/mailing-lists/coqclub/0099.html (169 words)

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