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Topic: Principle of distributivity

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Quantum logic

	Distributivity - Wikipedia, the free encyclopedia
		In mathematics, and in particular in abstract algebra, distributivity is a property of binary operations that generalises the distributive law from elementary algebra.
		Multiplication of numbers is distributive over addition of numbers, for a broad class of different kinds of numbers ranging from natural numbers to complex numbers and cardinal numbers.
		Distributivity is most commonly found in rings and distributive lattices.
	en.wikipedia.org /wiki/Distributive_property (789 words)

	Is logic empirical? - Wikipedia, the free encyclopedia
		The algebraic properties of their proposed logic are somewhat different from those of classical propositional logic in that the principle of distributivity fails.
		Quine argued that all beliefs are in principle subject to revision in the face of empirical data, including the so-called analytic propositions.
		Since the uncertainty principle says that either the one is determined or the other, but both cannot be determined at the same time, he faces a paradox.
	en.wikipedia.org /wiki/Is_logic_empirical%3F (1177 words)

	Encyclopedia: Principle of distributivity
		The principle of distributivity states that the algebraic distributive law is valid for classical logic, where both logical conjunction and logical disjunction are distributive over each other.
		The principle is valid in classical logic, but invalid in quantum logic.
		For some logical propositions A, B and C, the principle of distributivity means that
	www.nationmaster.com /encyclopedia/Principle-of-distributivity (452 words)

	Logic - Wikipedia, the free encyclopedia
		The analytical generality of the predicate logic allowed the formalisation of mathematics, and drove the investigation of set theory, allowed the development of Alfred Tarski's approach to model theory; it is no exaggeration to say that it is the foundation of modern mathematical logic.
		However, modal logic is normally formalised with the principle of the excluded middle, and its relational semantics is bivalent, so this inclusion is disputable.
		Again, relevance logic and dialetheism are the most important approaches here, though the concerns are different: the key issue that classical logic and some of its rivals, such as intuitionistic logic have is that they respect the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction.
	www.wikipedia.org /wiki/Formal_logic (3986 words)

	Distributivity - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-10-14)
		# Multiplication of numbers is distributive over addition of numbers, for a broad class of different kinds of numbers ranging from natural numbers to complex numbers and cardinal numbers.
		# Logical disjunction ("or") is distributive over logical conjunction ("and"), and conjunction is distributive over disjunction.
		Conditions for the distributivity of multiplication with respect to set addition and their effect on the design of array multipliers (UIUCDCS-R-82-1115)
	encyclopedia.worldsearch.com /distributive.htm (760 words)

	Distributed Systems Principles And Paradigms --> Info and Comparisons (Site not responding. Last check: 2007-10-14)
		The Spoke-hub distribution paradigm (also known as a hub and spoke model) derives its name from a bicycle wheel, which consists of a number of spokes jutting outward from a central hub.
		Because of the efficiency (and relative inflexibility) of the model, it requires that the items (or people) being distributed must be routed through a central hub before reaching their destination.
		Principle: ''underlying and long enduring fundamentals that are always (or almost always) valid.'' For each pricinple, a short description is provided, along with longer normative and descriptive explanations, and hopefully an example.
	www.crashdatabase.com /computers/32/distributed-systems-principles-and-paradigms.html (574 words)

	Convolution - Encyclopedia, History, Geography and Biography
		In statistics, the probability distribution of the sum of two independent random variables is the convolution of each of their distributions.
		If $X$ and $Y$ are two independent random variables with probability distributions f and g, respectively, then the probability distribution of the sum $X + Y$ is given by the convolution f $*$ g.
		A different generalization is the convolution of distributions.
	www.arikah.com /encyclopedia/Convolution (886 words)

	Proving Simple Set Equations (Site not responding. Last check: 2007-10-14)
		The proofs follow a well-known set theoretic proof principle: they are constructed first by application of simple natural deduction agents that reduce the set equations by applying set extensionality and definition expansion to a propositional logic statement.
		We prove distributivity of the intersection and union operators.
		We prove again the distributivity of the intersection and union operators.
	www.ags.uni-sb.de /~pollet/demo/set-equations.html (260 words)

	Logic (Site not responding. Last check: 2007-10-14)
		Today, Aristotle's system is mostly seen as of historical value (though there is some current interest in extending term logics), regarded as made obsolete by the advent of the predicate calculus.
		Logic as it is studied today is a very different subject to that studied before, and the principle difference is the innovation of predicate logic.
		Whereas Aristotelian syllogistic specified the forms that the relevant parts of the involved judgements took, predicate logic allows sentences to be analysed into subject and argument in several different ways, thus allowing predicate logic to solve the problem of multiple generality that had perplexed medieval logicians.
	www.worldhistory.com /wiki/L/Logic.htm (3500 words)

	Richard Sylvan (born; Richard Routley) on Nonexistent Objects (Site not responding. Last check: 2007-10-14)
		Unless general principles are formulated and justified, it remains obscure which critical arguments are valid within and against a particular theory.
		As one example of the need to make explicit the principles which are assumed, and the need to evaluate them, consider Russell's assumption, which is nowhere justified, that the paradox argument evaporates and the conclusion no longer follows once it has been shown that the premisses are meaningless.
		The class of sentential logics that satisfy weak principles of relevance is however wide and includes many logics which are, in principle, rivals to the position(s) we shall be advancing.
	www.formalontology.it /sylvanr.htm (6671 words)

	CiteULike: The instantiation principle in natural categories (Site not responding. Last check: 2007-10-14)
		Nevertheless, the instantiation principle can be implemented in a wide class of models, including both exemplar and abstraction models.
		To assess the instantiation principle empirically, a parameter-free exemplar-based model of instantiation was applied to typicality judgments for 16 simple categories (e.g.
		In Study 3, predicting the skew of typicality distributions was successful as well (a fit of 0.87), and dropping atypical exemplars from the simulations degraded prediction.
	www.citeulike.org /user/shanelindsay/article/148038 (257 words)

	Technical Monograph PRG-98
		Roughly, the principle of optimality says that an optimal solution is composed of optimal solutions to subproblems.
		In a first attempt, we formalise the principle of optimality as a distributivity condition.
		This distributivity condition is elegant, but difficult to check in practice.
	web.comlab.ox.ac.uk /oucl/publications/monos/prg-98.html (364 words)

	TECH RE: The Distribution Problem: An Ambiguity? (Site not responding. Last check: 2007-10-14)
		You mentioned them, which meant they were in my mind while considering the distribution problem, and led to me drawing the analogy I did.
		The point of this analogy was simply to emphasise, by means of a specific example, the problems, not to say absurdities, which would be caused by arbitrarily mandating that tanru modification should be allowed to distribute over connectives.
		I agree that this example only works because of the specific nature of the tanru modification, but then I was choosing an extreme case to show that distributivity wouldn't work as a general principle.
	www.wiw.org /~jkominek/lojban/9301/msg00045.html (338 words)

	Principle Based Semantics for HPSG - Frank, Reyle (ResearchIndex) (Site not responding. Last check: 2007-10-14)
		The syntax-semantics interface directly implements syntactic conditions on quantifier scoping and distributivity.
		The con- struction of semantic representations is guided' by general principles governing the interaction between syntax and semantics.
		or UMRS (Egg, 1998) Branco Crysmann Negative Concord and the Distribution of Quantifiers 12 (27) # # # # # #...
	citeseer.ist.psu.edu /frank94principle.html (344 words)

	Principle of distributivity - Encyclopedia, History, Geography and Biography
		Principle of distributivity - Encyclopedia, History, Geography and Biography
		This page was last modified 04:53, 12 December 2005.
		This encyclopedia, history, geography and biography article about Principle of distributivity contains research on
	www.arikah.com /encyclopedia/Principle_of_distributivity (113 words)

	setops.nb (Site not responding. Last check: 2007-10-14)
		Proof: This is a direct consequence of the principle of associativity (see "The Proof is in the..."), I leave the details as an exercise.
		Proof: Apply (5) to the principle of associativity (see "The Proof is in the..."), I leave the details as an exercise.
		Proof: Apply (2) to (5) and use the principle of distributivity (see "The Proof is in the..."), I leave the details as an exercise.
	www.madscitech.org /mathematics/setops/setops.html (1083 words)

	Math Forum: Ask Dr. Math: A Mathematical Essay
		This condition is satisfied by something called the transfer principle, a very powerful result of mathematical logic that is in turn a consequence of another theorem by a Polish mathematician, Los's theorem.
		So powerful is this principle that sometimes nonstandard analysis is considered a branch of mathematical logic, because it is possible to bypass practically all of the ultrafilter construction of the hyperreals and instead jump in with transfer.
		The reason the transfer principle holds is largely due to the method we used to construct the hyperreal numbers, our "almost-all" criterion with ultrafilters.
	mathforum.org /dr.math/faq/analysis_hyperreals.html (9021 words)

	More on Logic
		There is interest in the idea of finding a logical calculus that naturally captures computability; the computability logic of Japaridze is an example of a recently embarked research programme in this direction.
		It is by no means the case that logicians agree on what the principles of logic are.
		Such sentences violate the Gricean maxim of relevance, and can be modelled by logics that reject the principle of monotonicity, such as relevance logic.
	www.artilifes.com /logic.htm (2632 words)

	No Title
		In its most familiar and accessible form, the Heisenberg uncertainty principle asserts that we cannot simultaneously know precisely the position and velocity of a particle.
		Logic cannot `go over to distributivity' in the limit of large quantum numbers.
		The failure of the distributive law in quantum logic does not depend on size, it depends only on Planck's constant being nonzero, and between zero and nonzero there is an absolute discontinuity.
	astarte.csustan.edu /~tom/MISC/particle/particle.html (1436 words)

	Coloration in renaissance music
		Before going on, be sure to be aware of the principles of mensuration - specially the ternary one, of course - that I won't recall here, to make the story shorter.
		Coloration is then distributed from the original note to the smaller ones replacing it.
		Restating what I said for distributivity: coloured notes created by associativity at upper level are of a different nature from those first created at the level of application - thus, one should always be aware of the function of these different levels!
	www.medieval.org /emfaq/anaigeon/e_coloration.html (1981 words)

	[No title]
		This could provide a new unifying principle in biology (a field sorely in need of such) and a new connection between math/CS and biology.
		Biologist Jonathan Miller (Baylor College of Medicine) and I plan to investigate to what extent these new principles are valid in nature; we are submitting a grant proposal.
		If certain weakened continuity and distributivity properties are permitted, there are a new kind of numbers forming a nonlinear 16-dimensional algebra, and containing all the previous kinds of numbers as subalgebras.
	www.math.temple.edu /~wds/homepage/resstmt.html (862 words)

	Abstract of "Plural Predication and the Strongest Meaning Hypothesis" (Site not responding. Last check: 2007-10-14)
		The Strongest Meaning Hypothesis of Dalrymple et al (1994,1998), which was originally proposed as a principle for the interpretation of reciprocals, is extended in this paper into a general principle of plural predication.
		This principle applies to complex predicates that are composed of lexical predicates that hold of atomic entities, and determines the pluralities in the extension of the predicate.
		the books are old and new) and 'atomic' distributivity in general are derived by a unified mechanism, which 'weakens' the basic universal meanings of strong reciprocals, boolean conjunction and quantification over atomic entities.
	www.cs.technion.ac.il /~winter/papers/smh.abs.html (156 words)

	A Chain of Fuzzy Strengthenings of Entailment Logic
		Moreover, the core motivation of entailmental logic was the Entailment Principle ([AndandBel], pp.
		Furthermore, system E postulates a principle of distributivity which also causes serious trouble for the natural-deduction and Gentzen implementations of the system (see [Dunn]), and which anyway is sufficiently convoluted to deserve being a proved theorem rather than postulated as an axiom.
		E bestows a privileged status to implicational formulae and countenances such principles as Suppression («p→p→q→q») and exported transitivity («p→q→.q→r→.p→r»), the only natural way of justifying which is to allow Exportation for implicational formulae, due to their special status -- something E falls short of accepting.
	www.ifs.csic.es /sorites/lp/articles/logica/santiago.htm (3024 words)

	Distributivity
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		Distributivity is most commonly found in ringss and distributive lattices.
		Rings and distributive lattices are both special kinds of rigss, certain generalisations of rings.
	www.sciencedaily.com /encyclopedia/distributivity (795 words)

	IngentaConnect Does the cue help? Childrens understanding of multiplicative conc... (Site not responding. Last check: 2007-10-14)
		Aims: This study investigated (a) children's ability to use commutative and distributive cues to solve multiplication problems, (b) whether their ability to use these cues depends on the problem context, and (c) whether separate mechanisms might underlie children's understanding of commutativity and distributivity.
		A common mistake in the distributive problems was to select the number that was one more, or one less, than the answer in the cue.
		When children do begin to understand the principle of distributivity, they most easily apply it in the context of Isomorphism of measures multiplication problems.
	dx.doi.org /10.1348/0007099042376364 (335 words)

	Principle of distributivity - Information
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		See the original editable 'Principle of distributivity' article.
	www.logicjungle.com /wiki/Principle_of_distributivity (185 words)

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