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	Logical equivalence - Wikipedia, the free encyclopedia
		Logical equivalence is often confused with material equivalence.
		But the material equivalence of p and q (often written "p ↔ q") is itself another statement in the object language.
		There is a relationship, however; p and q are syntactically equivalent if and only if p ↔ q is a theorem, while p and q are semantically equivalent if and only if p ↔ q is a tautology.
	www.wikipedia.org /wiki/Logical_equivalence (180 words)

	If and only if - Wikipedia, the free encyclopedia
		It should not be confused with logical equivalence which is a description of a relation between two sentences.
		By contrast "A is logically equivalent to B" mentions the two sentences: it describes a relation between those two sentences, and not between whatever matters they describe.
		This separate meaning can be explained by noting that a definition (for instance: A group is "abelian" if it satisfies the commutative law; or: A grape is a "raisin" if it is well dried) is not an equivalence to be proved, but a rule for interpreting the term defined.
	www.wikipedia.org /wiki/Material_equivalence (943 words)

	PL 120 Symbolic Logic I
		Material Equivalence (Equiv.) In propositional logic, material equivalence is a statement of logical equivalence falling under the Rule of Replacement that allows you to introduce or replace a statement containing a double arrow or triple bar.
		Material Implication (Impl.) In propositional logic, material implication is a statement of logical equivalence falling under the Rule of Replacement that allows you to replace a conditional statement with a disjunction consisting of the denial of the antecedent of the conditional and the consequent or to replace such a disjunction with a conditional statement.
		Transposition (Trans.) In propositional logic, transposition is an equivalence falling under the rule of replacement that a conditional is logically equivalent to another statement in which the denial of the consequent of the first is the antecedent and the denial of the antecedent of the first is the consequent.
	cstl-cla.semo.edu /hill/pl120/glossary.htm (10152 words)

	Airbag inflation gas generation via a decomposing material with a linear ignition source - Patent 6170867
		Preferably, such that the ignition material burns for an elapse time comparable to the residence time of the gas source material within the decomposition chamber so that the gas source material is preferably continuously heated to its dissociation temperature as gas is released from the chamber into an associated inflatable airbag cushion.
		Hydrogen bearing sensitizer materials useable in the practice of the invention are typically gaseous, liquid, solid, or multi-phase combinations thereof including hydrogen, hydrocarbons, hydrocarbon derivatives and cellulosic materials.
		For this example, however, the supplemental ignition material surrounding the RDC linear ignition cord within the ignition tube was composed of a mixture of 2.71 grams of BKNO.sub.3 and 12.12 grams of an extruded pyrotechnic composed of transition metal amine nitrate with oxidizer and binder.
	www.freepatentsonline.com /6170867.html (6698 words)

	Injection Molding Magazine
		The material supplier may produce a polycarbonate of appropriate molecular weight, but processing the material with excess moisture will reduce that molecular weight to a point where the molded article may not function.
		If a material is stiffer, and stiffness is what fillers and increased crystallinity provide, it will take more energy to produce the initial deformation required for crack initiation.
		The material used to produce the parts had a nominal melt flow rate of 8 g/10 min and a density of.954 g/cu cm.
	www.immnet.com /articles?article=2326 (1576 words)

	Encyclopedia: Material equivalence (Site not responding. Last check: 2007-10-22)
		However, some texts of mathematical logic (particularly those on first-order logic, rather than propositional logic) make a distinction between these, in which the former is used as a symbol in logic formulas, while the latter -- in reasoning about those formulas (e.g., in metalogic).
		When proving the statement "P iff Q", it is equivalent to prove both of the statements "if P, then Q" and "if Q, then P".
		Alternatively, one can prove both "If P, then Q" and "If not P, then not Q", the latter being a contrapositive of (and thus equivalent to) "If Q, then P".
	www.nationmaster.com /encyclopedia/Material-equivalence (727 words)

	Limb positioning and calibration apparatus for radiographic imaging - Patent 5005196
		The method of claim 2 wherein one of said calibration materials is a tissue equivalent material and another of said calibration materials is a bone equivalent material.
		By the use of two equivalence materials, the system can be calibrated to indicate possible changes in the energy spectrum of the radiation source or in the detector efficiency.
		By use of the two equivalence materials during radiographic imaging, the system can be calibrated to negate possible changes in the energy spectrum of the radiation source or in the detector efficiency.
	www.freepatentsonline.com /5005196.html (9152 words)

	Conditional Statements and Material Implication
		Abstract: The reasons for the conventions of material implication are outlined, and the resulting truth table for is vindicated.
		Material implication is the weakest common meaning for all types of "If … then …" statements.
		A Comparison of Techniques for Introducing Material Implication, a discussion of seven ways of introducing truth-functional definition of material implication by Matthew C. Clarke at the University of Natal.
	philosophy.lander.edu /logic/conditional.html (829 words)

	Chapter IV
		The "paradox of material implication" is dispelled by the clear understanding that the " if-then " (that is, the " É ") relation, as some logicians use it, is not intended to restrict what can be meant but solely to restrict truth-functional relations among whatever is meant by the data related.
		Logical implication in this sense is frequently distinguished from material implication, in that the former holds for a meaning relation dependent in part upon the factual status of the sentences related, whereas the latter holds for a truth-functional relation not dependent upon the factual status of the sentences related.
		Accordingly, we adopt (assume) the terminology of "logical implication" (and "logical equivalence") in the sense of material implication (and material equivalence).
	www.sjsu.edu /logic/symbolic.htm (5384 words)

	Sophia on the web: Logic Page ~ Truth Tables (Site not responding. Last check: 2007-10-22)
		MATERIAL EQUIVALENCE: P if and only if Q = "water if and only if H2O is present" (also called bi-conditional, in that they are both true or both false).
		Material implication is represented by the hook (a U on its side and open to the left) or an arrow (pointing from P to Q)
		Material equivalence is represented by the triple bar (or like an equal sign with an additional line)
	members.aol.com /moresophia/topic12.html (1001 words)

	Guidance for Industry BACPAC I: Intermediates in Drug Substance Synthesis Bulk Actives Postapproval Changes: Chemistry, ... (Site not responding. Last check: 2007-10-22)
		When equivalence cannot be demonstrated, applicants should submit a prior approval supplement and should consider appropriate tests for qualification of impurities, demonstration of bioequivalence, and assessment of stability.
		If equivalence cannot be demonstrated on the production batch, this would be considered evidence of an adverse effect on the identity, strength, quality, purity, and/or potency of the drug product, and the change should not be implemented (i.e., the drug product affected by the change should not be distributed).
		When equivalence is not established, applicants should consider conducting an assessment of the effect of the change on the safety and effectiveness of the drug product (e.g., qualification of impurities, bioequivalence studies).
	www.fda.gov /cder/guidance/3629fnl.htm (7082 words)

	A Note On Mr. De Morgan
		The De Morgan logical equivalence denying the dot, ^(p.q), is demonstrated by the identity of the truth tables in column 6 and column 9.
		Material equivalence means merely that, when the material equivalence is true, the propositions have the same truth values.
		The definition of a logical equivalence as a tautologous material equivalence is an alternative to defining two propositions to be logically equivalent when they have identical truth tables.
	www.apa.udel.edu /apa/archive/newsletters/v96n2/teaching/morgan.asp (1593 words)

	Lexicon of Linguistics
		(material equivalence) the combination of two formulas with the °connective <-> (if and only if, iff), which is only true if both formulas have the same °truth value.
		phi -> psi is logically equivalent with Neg [ phi & Neg psi ] in °propositional logic and ThereIs(x) [ P(x) ] is equivalent with Neg All(x) [ Neg P(x) ] in °predicate logic.
		When two expressions are logically equivalent, it is possible to substitute them for each other, without changing the truth values of the proposition they are contained in.
	www.u-grenoble3.fr /lebarbe/Linguistic_Lexicon/ll_e.html (2513 words)

	Difference between equality and equivalence: Philosophy Forums (Site not responding. Last check: 2007-10-22)
		Maybe a better way to put it is that two things that are equivalent have some of the same properties, and two things that are identical have all of the same properties (and in fact are not two things, but the same thing being looked at twice).
		So, saying that equivalent things can sometimes be substituted to get equivalent sentences, and identical things can always be substituted (which I suppose is what you were hinting at when you mentioned substitution) is just like saying equivalent things share some properties and identical things share all properties.
		Cr) is materially equivalent to the same formula Cs with s substituted for r (and vice versa); (ii) if r=s then Cs is provable from Cr (i.e.
	forums.philosophyforums.com /thread/13843/1 (3564 words)

	EQUIVALENCE RULES
		Equivalence can be defined as truth under the same conditions (and, since truth is bivalent, falsity under the same conditions).
		In order to make use of our equivalence rules, we need to map the formula we wish to modify onto one side of of the equivalence rule and then using that mapping create a substitution instance of the other side of the rule.
		So, now we use the WFF's in the original WFF that correspond to the sentential variables in the side of the rule pattern that is matched to generate a substitution instance of the other side of the rule.
	cstl-cla.semo.edu /hill/pl120/notes/equivalence.htm (362 words)

	EDCS Reference Manual
		The ratio of mass of dissolved in seawater to the mass of seawater; salinity.
		National security information or material which requires a substantial degree of protection and the unauthorized disclosure of which could reasonably be expected to cause serious damage to the national security.
		National security information or material which requires the highest degree of protection and the unauthorized disclosure of which could reasonably be expected to cause exceptionally grave damage to the national security.
	www.sedris.org /sdk_3.1.1/src/lib/edcs/docs/dictionary/EAC_S.htm (5562 words)

	Introduction to Logic: With eLogic - An Online Tutorial, Eleventh Edition
		We have therefore compressed the material of what was Part One into a single opening chapter in which the same topics are addressed, but more crisply, and in ways likely to provide a better base for the more advanced material in the later chapters of the book.
		Two illustrations: We have responded to the frequently expressed concern of colleagues by expanding the discussion of logical equivalence in Chapter 8, now more sharply emphasizing the differences between material equivalence as a truth-functional connective, and logical equivalence as a logical relation that justifies the rules of replacement.
		In earlier editions we allowed the equivalencies expressed by the rules of replacement–the last 10 of the 19 rules of inference–to be symbolized by the same three-bar symbol (?) with which material equivalence (_if and only if_) is symbolized throughout.
	www.prenhall.com /divisions/hss/marketing/copi/copi_preface.htm (1457 words)

	EDCS Reference Manual
		A material created by grinding calcined limestone and clay to a fine powder, which can be mixed with water and poured to set as a solid mass or used as an ingredient in making mortar or concrete.
		A brittle, noncrystalline, usually transparent or translucent material that is generally formed by the fusion of dissolved silica and silicates with soda and lime.
		Any of various synthetic or organic materials that can be moulded or shaped, generally when heated, and then hardened into a desired form; for example, polymers, resins, and cellulose derivatives.
	www.sedris.org /sdk_3.1.1/src/lib/edcs/docs/dictionary/EAC_R.htm (4600 words)

	[No title]
		The reasons for the conventions of material implication are outlined, and the resulting truth table for is vindicated.
		Material and logical equivalence are defined and discussed
		Some of the intuitive difficulties with material implication are outlined and illustrated.
	philosophy.lander.edu /logic/symbolic_topics.html (209 words)

	MTO 8.3: Capuzzo, Review of Morris
		SG iv determines sc equivalence on the basis of identical ic vectors; this erases some of the Z relations in SG2.
		Lewin’s protocol pairs (equivalent to the Cartesian product of a set S) and partially-ordered sets (1976, 1987) are instances of pc binary relations, which form the third section of the chapter.
		Material contained herein may be copied and/or distributed for research purposes only.
	www.societymusictheory.org /mto/issues/mto.02.8.3/mto.02.8.3.capuzzo.html (2716 words)

	M
		Material properties of characterization techniques of microstructure materials: microscopy atomic, electronic and optics force.
		Methodologies for the selection of materials with base in the requirements of the engineering design and considering the performance, the manufacturing, the economic aspects, and the cycle of life of the product.
		Properties of the materials and basic concepts of mechanics of materials.
	www.sistema.itesm.mx /va/Planes2000/Sinteticos/insin-m.html (1657 words)

	Material consideration (Site not responding. Last check: 2007-10-22)
		A material consideration in UK planning is an issue which planners are obliged to consult certain affected parties on, and take their views into account in any planning decision.
		being an essential component material terms of the contract> 4 : being relevant to a subject under consideration; specifically : being such as would affect or be taken into consideration by a...
		material for consideration may be sent to: Anil Prasad Innerviews P.O. Box 8548 Emeryville, CA 94662 USA Please note that submissions will not be returned.
	en.powerwissen.com /71Ey6HaeYiS0Rb7bCQRs7A%3D%3D_Material_consideration.html (113 words)

	[No title]
		Only E and I propositions are logically equivalent to their converses.
		Material Equivalence In propositional logic, material equivalence is represented by the double-arrow (
		Transposition In propositional logic, transposition is an equivalence falling under the rule of replacement that a conditional is logically equivalent to another statement in which the denial of the consequent of the first is the antecedent and the denial of the antecedent of the first is the consequent.
	www2.semo.edu /philosophy/courses/pl120/glossary.htm (7787 words)

	Introduction to Logic (11th Edition): Current Amazon U.S.A. One-Edition Data (Site not responding. Last check: 2007-10-22)
		But such sidebar material, we hope, will make it easier for instructors to guide their own students to a mastery of the elements of theory most critical for them--and perhaps to avoid some complexities not essential for their solid grasp of elementary logic.
		For example, we have responded to the frequently expressed concern of colleagues by expanding the discussion of logical equivalence in Chapter 8, now more sharply emphasizing the differences between material equivalence as a truth-functional connective, and logical equivalence as a logical relation that justifies the rules of replacement.
		In earlier editions we allowed the equivalences expressed by the rules of replacement--the last 10 of the 19 Rules of Inference--to be symbolized by the same three-bar symbol with which material equivalence ("if and only if") is symbolized throughout.
	php-web-hosting.us /stuff-0130337358.html (3341 words)

	FiberCote - News (Site not responding. Last check: 2007-10-22)
		In addition, material and process specifications developed by FiberCote for the original material qualification were deemed sufficient and were incorporated into Flight Structure's existing quality procedures without change.
		The material equivalence test plan was similar to the plan outlined in Table 4, but included the addition of the laminate allowables testing mentioned above.
		While only one batch of material was required to demonstrate of site equivalence, three batches were required for the creation of the new laminate property allowables.
	www.fibercote.com /pne2a211.html (418 words)

	Equiv (Site not responding. Last check: 2007-10-22)
		The first form shows that the statement that two expressions are equivalent is itself equivalent to the conjunction of the two statements implying each other.
		The first conjunct, (p => q) is equivalent in English to "If p, then q." or "q, if p." or "p is sufficient for q."(remeber "if" always introduces the antecedent).
		The second form of "equiv" shows that saying that two statements are equivalent is itself equivalent to say the disjunction: "Either both p and q are true or both p and q are false." This is, of course, the truth table defintion for the material equivalence symbol.
	www.loyno.edu /~folse/Equiv.html (152 words)

	Chapter 5: The Absolutely Strict Systems -- S1° and S1 (Site not responding. Last check: 2007-10-22)
		Lewis in SL defines material implication, equivalence, and alternation in terms of Κ and Ν just as we did at the end of the second chapter.
		Lewis shows some confusion in his references to the sign of strict equivalence; at one point he refers to it as if it were a primitive sign of his systems -- and then he goes on to define it.
		Now, if a modality Υ is equivalent to a shorter (in number of N's, M's, and L's) modality Χ, then Υ is said to reduce to Χ; if there is no shorter (than Χ) modality Ζ to which Χ is reducible, then we say that Χ is irreducible.
	www.clas.ufl.edu /users/jzeman/modallogic/chapter05.htm (4849 words)

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