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Topic: Biconditional introduction

	Propositional calculus (Site not responding. Last check: 2007-09-10)
		These rules are introduction and elimination rules for each logical operator, used for deriving argument forms.
		Introducing a hypothesis means adding a wff to a derivation not originally present as a premise; discharging the hypothesis means eliminating the wff justifiably--any wffs correctly derived from the hypothesis justify the introduction of the hypothesis after the fact.
		With wffs and rules of inference, it's possible to derive wffs; the derivation[?] is a valid argument form[?], while the derived wff is known as a lemma.
	www.ebroadcast.com.au /lookup/encyclopedia/lo/Logical_calculus.html (344 words)

	Maggie Johnson
		Biconditional Proof: Same as a conditional proof but it must be proven in two ways: A®B and B®A.
		Conditional Introduction: This is the formal counterpart of a conditional proof.
		Biconditional Elimination: You can conclude Q if you establish P and either P « Q or Q « P. Biconditional Introduction: To introduce P « Q, you must give two subproofs, one showing that Q follows from P, and one showing that P follows from Q. Prove: P ® Q « (~Q ® ~P) Notes
	cse.stanford.edu /class/cs103a/h14Conditionals.htm (934 words)

	Friday, February 4
		In combination with implication introduction, this justifies the rule G - PQ G,P - R G,Q - R --------- proof by cases with subproofs G - R which really captures the structure of a proof by cases.
		~B: it should be proved by disjunction introduction in a subproof with hypothesis ~~A and conclusion ~B (or hypothesis ~~B and conclusion ~A, but this is symmetrical).
		Continuing, we think that the natural way to prove ~B is by negation introduction, using a proof with premise B and conclusion a contradiction.
	math.boisestate.edu /~holmes/M387syllabus/node25.html (558 words)

	Logic terms and concepts : Thomas Alspaugh : UCI
		Logical equivalence is a meta-logical relationship, not to be confused with the logical operation material biconditional.
		The material biconditional is a logical formula, not to be confused with the meta-logical relation of logical equivalence.
		Perhaps because of this potential confusion, the material biconditional does not seem to be used as commonly now as in the past.
	www.isr.uci.edu /~alspaugh/logic/logicConcepts.html (4121 words)

	Socrates User's Guide
		A biconditional is in effect the conjunction of two material conditionals, one reading from left to right and the other reading in the reverse direction.
		A biconditional adds information that is simultaneously disjunctive and conjunctive, but the precise nature of this information depends on whether the biconditional occurs on the left or right side.
		If the biconditional '(AâB)' occurs on the premise side (and is assumed to be true), then either 'A' and 'B' are both true, or 'A' and B are both false.
	www.utdallas.edu /~pervin/sug.html (11351 words)

	Why game balance based on 4 encounters/day is not balanced - Page 31 - Wizards Community
		The biconditional "A iff B" uses the sentences A and B, describing a relation between the states of affairs A and B describe.
		Biconditional introduction requires separately proving if A then B and if B then A, that's why it's called a biconditional.
		In order for it to be a biconditional you also need to prove if this is a fruit then it's an apple (if B then A), which you can't do.
	boards1.wizards.com /showthread.php?p=10557231#post10557231 (5011 words)

	Review of The Propositional Logic (Introduction to Logic 1) course by IMACS.
		LM1: Introduction to Logic I is an online course meant for mathematically precocious middle and high school students.
		LM1: Introduction to Logic 1, first part of the Elements of Mathematics course by IMACS (Institute for Mathematics and Computer Science.
		Price: There is a tuition fee for a period of enrollment in which a student may cover as much material within the LM1-4 sequence as he or she is able.
	www.homeschoolmath.net /reviews/eimacs-logic.php (1377 words)

	Amazon.com: "biconditional elimination": Key Phrase page (Site not responding. Last check: 2007-09-10)
		Introduction to Mathematical Logic, Fourth Edition by Elliott Mendelson
		Biconditional Elimination (-E): From any wff of the form ~, we may infer either 4 - qj or q (~.
		The Languages of Logic: An Introduction to Formal Logic by Samuel Guttenplan
	www.amazon.com /phrase/biconditional-elimination (443 words)

	EPGY Theorem Proving Environment User Guide
		The biconditional proof strategy can only be used in the "backward" direction.
		That is, you must first enter the proof line you would like to justify and then select the strategy: highlight the proof line and select "Biconditional" from the Strategies menu (as in Figure 11).
		Like the biconditional proof strategy, it can only be used in the backward direction (that is, the proof goal must be entered before the strategy is selected).
	epgy.stanford.edu /tpe/Guide/index.html (6996 words)

	[No title]
		Transitivity of the biconditional: From A (B and B (C infer A (C 1.
		(P (Q) (((P (Q) (Intro 1-9, 10-18 This is a biconditional introduction so we will need two conditional introductions, one in which we prove that the right follows from the assumption of the left and another in which we prove that the left follows from the assumption of the right.
		Give the statement of conditional introduction and use it to prove (A (B) (C from A (C. First, the rule: Conditional Introduction ((Intro) P Q.
	www.courses.psu.edu /phil/phil012_pam208/hw10-solutions.doc (1425 words)

	Propositional calculus Summary
		Indeed, all of the logical connectives can be defined in terms of a sole sufficient operator.
		The biconditional (↔) can of course be defined in terms of conjunction and implication, with a ↔ b defined as (a → b) ∧ (b → a).
		Axioms OR-1 and OR-2 correspond to "disjunction introduction." The relation between OR-1 and OR-2 reflects the commutativity of the disjunction operator.
	www.bookrags.com /Propositional_calculus (4189 words)

	Startup guide for Bertie3 or Twootie (Site not responding. Last check: 2007-09-10)
		We cannot use "=" for the biconditional, since it is needed for identity.
		Premises in the proof are justified with a "P", and auxiliary assumptions in a conditional proof with "A".
		So "Biconditional Decomposition, "-]d" is Negated Existential Decomposition, and so on.
	www.ucc.uconn.edu /~wwwphil/startup.htm (532 words)

	Chapter 2: Parallelism and Conditinal Statements
		When a conditional statement is combined with its converse, then a biconditional statement is formed.
		A biconditional is written as p if and only if q or p
		The biconditional statement is true only if its conditional statement and converse statement are true.
	library.thinkquest.org /16284/g_parallel_2.htm (168 words)

	[No title]
		S(Q) The way this rule works is that if you have a biconditional expressing logical equivalence between P and Q, and you have a statement about P, by Gen Sub you may substitute Q wherever the P appears.
		Bottom Introduction ((Intro) We have already observed that whenever you encounter a contradiction, you are justified in asserting anything whatsoever.
		However, up to this point, we haven’t had a rule that expresses this principle.
	www.courses.psu.edu /phil/phil012_pam208/0404.doc (256 words)

	Propositional Logic
		These natural deduction systems present the logic by describing introduction and elimination rules for the connectives.
		However, since we are using the axiomatic method rather than a natural-deduction system, we first present the logic axiomatically and then prove that the introduction and elimination rules used in `natural deduction' systems are valid rules.
		Find rules for and Elimination, Disjunction Introduction and Elimination, Biconditional Introduction and Elimination, Contraposition and Disjunctive Syllogism.
	mally.stanford.edu /tutorial/sentential.html (1059 words)

	The Revision Theory of Truth (Stanford Encyclopedia of Philosophy)
		In a semantics for languages capable of expressing their own truth concepts, T will not, in general, have a classical signification; and the ‘iff’ in the T-biconditionals will not be read as the classical biconditional.
		Gupta and Belnap's related suggestion concerning the ‘iff’ in the T-biconditionals is that, rather than being the classical biconditional, this ‘iff’ is the distinctive biconditional used to define a previously undefined concept.
		Yaqu̅b 1993 agrees with Gupta and Belnap that the T-biconditionals are definitional rather than material biconditionals, and that the concept of truth is therefore circular.
	plato.stanford.edu /entries/truth-revision (7128 words)

	biconditional - OneLook Dictionary Search
		Tip: Click on the first link on a line below to go directly to a page where "biconditional" is defined.
		Biconditional : Eric Weisstein's World of Mathematics [home, info]
		Phrases that include biconditional: biconditional elimination, biconditional introduction, biconditional relation
	www.onelook.com /cgi-bin/cgiwrap/bware/dofind.cgi?word=biconditional (129 words)

	Wikinfo \| List of topics in logic (Site not responding. Last check: 2007-09-10)
		Biconditional elimination -- Biconditional introduction -- Bivalence and related laws -- Boolean algebra
		De Morgan's laws -- Deductive reasoning -- Denying the antecedent --Disjunction elimination -- Disjunction introduction -- Disjunctive normal form -- Disjunctive syllogism -- Double negative elimination
		Law of excluded middle -- Law of non-contradiction -- Laws of logic -- Logic -- Logic gate -- Logical assertion -- Logical biconditional -- Logical conditional --Logical conjunction -- Logical disjunction -- Logical equivalence -- Logical fallacy -- Logical nor -- Logical operator -- Logicism -- Logic programming
	www.wikinfo.org /wiki.php?title=List_of_topics_in_logic (457 words)

	Workflow automation: overview and research issues
		Biconditional Introduction ( EMBED Equation.DSMT4 ): From wffs of the form EMBED Equation.DSMT4 , EMBED Equation.DSMT4 infer EMBED Equation.DSMT4 .
		Biconditional Elimination ( EMBED Equation.DSMT4 ): From wffs of the form EMBED Equation.DSMT4 , infer either EMBED Equation.DSMT4 or EMBED Equation.DSMT4 .
		In this paper, we omit the introduction of basic Prolog program constructs, which are similar to the ones we discussed in logic programming.
	math.arizona.edu /~ksimic/ming.doc (6614 words)

	Logical Argument, Proof and Proof Theory Information Portal @ Proves.org (Site not responding. Last check: 2007-09-10)
		If you wish to use the open content of this page for your website or publication, please go to the original source page to ensure the most accurate and up-to-date information available.
		Contradiction • Logical argument • Category:Proofs • Biconditional elimination • J
		AltaVista - Brief introductions to combinatory logic, the incompleteness theorems and independence results, by Andrew D Burbanks.
	www.proves.org (1819 words)

	.::dvdcopymac.info Biconditional introduction::. (Site not responding. Last check: 2007-09-10)
		Biconditional introduction iѕ thе infеrеncе that, if B followѕ from A, and A followѕ from B, thеn A if and only if B. For еxamplе: if I'm brеathing, thеn I'm alivе; alѕo, if I'm alivе, thеn I'm brеathing.
		Biconditional еlimination allowѕ onе to infеr a conditional from a biconditional: if (A
		Thiѕ pagе iѕ baѕеd on thе copyrightеd Wikipеdia articlе 'Biconditional introduction' it iѕ uѕеd undеr thе GNU Frее Documеntation Licеnѕе.
	dvdcopymac.info /3240 (455 words)

	ocean-beach.info Biconditional introduction (Site not responding. Last check: 2007-09-10)
		Biconditional elimination allows one to infer a conditional from a biconditional: if (A
		B) is true; then one may infer one direction of the biconditional; either (A
		You may redistribute it; verbatim or modified; providing that you comply with the terms of the GFDL.
	ocean-beach.info /3240 (278 words)

	Syllabus - Programming Languages and Methodologies
		1,2,3 (5) q ^ ~q 2,3 (^I) (6) ~p 3,5(~I) Since the introduction of the premise 3 leads to a contradiction we conclude that it is not true.
		In general, the rule of ~I says that if from some formula A as a premise we can derive B ^ ~B then we can infer ~A. example 5 (Conditional/ implication introduction):
		1,2 (6) p -> r 3, 5 (II) (->I) In general, whenever we can derive B having assumed A as a premise we summarize this by A -> B. Similar rules for <-> or biconditional introduction/elimination.
	www.ececs.uc.edu /~aralescu/AI_I/LECTURES/Lecture2_printable.html (719 words)

	Alan Fedoruk - Reference (Site not responding. Last check: 2007-09-10)
		A good introduction can be found in [WIW04] an introductory text on argument.
		Using redundancy by replication of individual agents within a multi-agent system is one possible approach for improving fault-tolerance, and hence improving reliability and availability---two key components of dependability.
		Unfortunately, the introduction of replication leads to increased complexity and system load, and it introduces new challenges to system construction.
	pages.cpsc.ucalgary.ca /~fedoruk/reference.html (12425 words)

	[No title]
		(Even if the subderivation is only two lines long, you need the dash to signal that you are citing a subderivation rather than two separate lines.) Negation Introduction and Negation Elimination (~I and ~E): Cite line numbers for 1 subderivation.
		(The subderivation where you assume the opposite of what you're trying to show and you derive a contradiction.) Example: (14.A Assumption(17.C(20.~C21.~A14-20 ~I Disjunction Introduction ((I): Cite 1 line number.
		(First, the number of the line where the "(" statement appears and second the number of the line where one side appears.) Example: (13.A (B(17.B(20.A13, 17 (E Biconditional Introduction ((I): Cite the line numbers for 2 subderivations.
	www.unc.edu /~theis/logic/usingrules.doc (466 words)

	Philosophical Dictionary: Beauty-Blanshard
		An Introduction to the Principles of Morals and Legislation
		The conjunction of two conditionals, the antecedent of each of which is the consequent of the other; that is, any statement of the form: "P if and only if Q." Although they may have other uses, all biconditionals involve at least the logical structure of material equivalence.
		Supposition that every proposition must be either true or false.
	www.philosophypages.com /dy/b2.htm (1130 words)

	Definitions and Theorems (Site not responding. Last check: 2007-09-10)
		Next: Disproving Statements Up: NOTES ON METHODS OF Previous: Introduction
		It happens to be true no matter which element x we consider.
		The second common form of a theorem statement is the biconditional.
	www.math.csusb.edu /notes/proofs/pfnot/node2.html (515 words)

	What is a "Formal Language"?
		If at the end of this subproof, you can derive the consequent, then conditional proof allows you to infer P
		Since the biconditional is logically equivalent to the conjunction of two conditionals.
		P, then if you can establish P, you can infer Q. ´
	www.philosophy.ilstu.edu /horvath/PHI112/Notes/FrmlCondProof.html (124 words)

	Symbolic Logic: Theorem In SD Text - Physics Forums Library
		Here is the text that we are using in my philosophy class of symbolic logic just in case you are interested.
		Given PvQ first assume P then arrive at R. Then assume Q and arrive at R. Then R by elimination of the disjunction.
		I think I follow: It seems like you are doing two negation elimination claims with a negation introduction claim as well.
	www.physicsforums.com /archive/index.php/t-16067.html (527 words)

	Iff - AoPSWiki
		Check out Art of Problem Solving's Introduction to Geometry by Richard Rusczyk.
		If a statement is an "iff" statement, then it is a biconditional statement.
		Add a glimpse of the Art of Problem Solving Forum to your own site!
	www.artofproblemsolving.com /Wiki/index.php/Iff (97 words)

	SD Theorems Logic HW due Please help Text - Physics Forums Library
		Class is at 1:30 U.S. Eastern standard time please help!
		In your proof, you assume ~A (hypothetically) and try to derive (B and A) -> C, so you can infer ~A -> (B and A) -> C. 1) ~A [conditional introduction]
		Maybe you can think of a way to do this using your rules.
	www.physicsforums.com /archive/index.php/t-78069.html (645 words)

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