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	Logic : Thomas Alspaugh : UCI
		Logic is the abstraction of thought to its simplest possible components: we consider whether something is true or false only, and we analyze it based on its structure and whether its components are true or false.
		In logic, we study structures whose meaning is determined by the meaning of their substructures and the fashion in which those substructures are combined.
		First-order logic is the strongest logic that is complete and compact and for which every countable, satisfiable set of statements has a model whose domain is the natural numbers.
	www.ics.uci.edu /~alspaugh/logic/index.html (712 words)

	Logic - Wikipedia, the free encyclopedia
		The ambiguity is that "formal logic" is very often used with the alternate meaning of symbolic logic as we have defined it, with informal logic meaning any logical investigation that does not involve symbolic abstraction; it is this sense of 'formal' that is parallel to the received usages coming from "formal languages" or "formal theory".
		Logic cut to the heart of computer science as it emerged as a discipline: Alan Turing's work on the Entscheidungsproblem followed from Kurt Gödel's work on the incompleteness theorems, and the notion of general purpose computers that came from this work was of fundamental importance to the designers of the computer machinery in the 1940s.
		Relevance logic and paraconsistent logic are the most important approaches here, though the concerns are different: a key consequence of classical logic and some of its rivals, such as intuitionistic logic, is that they respect the principle of explosion, which means that the logic collapses if it is capable of deriving a contradiction.
	en.wikipedia.org /wiki/Logic (4997 words)

	truth in logic (Site not responding. Last check: 2007-10-10)
		Not only is logic difficult, fascinating and (in its further reaches) contentious, but it seems ultimately to depend on some human sense of rightness: perhaps not so different from poetry in the end.
		Logics that aim to represent situations in simple, context-free sentences are called sentential (also propositional, or propositional calculus), after Gottlob Frege who founded modern mathematical logic.
		Such logics cannot deal with expressions like he believed her (which appeal to the common understanding of the human heart) but are very powerful in their own field.
	www.textetc.com /theory/truth-in-logic.html (2136 words)

	Fundamental logic circuits
		Logic polarity is the type of voltage used to represent the logic 1 state of a statement.
		In practice, many variations of logic polarity are used; for example, from a high-positive to a low-positive voltage, or from positive to ground; or from a high-negative to a low-negative voltage, or from negative to ground.
		As you study logic circuits, it is important that you remember the state (1 or 0) of the inputs and outputs.
	www.tpub.com /neets/book13/54.htm (1603 words)

	Logic
		The basic principles of logic center on the law of contradiction, which states that a statement cannot be both true and false, and the law of the excluded middle, which stresses that a statement must be either true or false.
		Even though the science of logic was derived from mathematics, logic eventually came to be considered as a study independent of mathematics yet applicable to all reasoning.
		Logic serves as a set of rules that govern the structure and presentation of mathematical proofs.
	www.math.wichita.edu /history/topics/logic.html (970 words)

	LEO: Logic
		A logical demonstration of a belief, however, must be conclusive and convincing to be effective; any doubtful premises leads the audience to believe that the conclusion is weak.
		False Cause: The writer points out as the cause of an event something that is not the actual cause, or the writer has insufficient evidence for making a causal link.
		False Alternative: The writer only presents some of the alternatives for solving a problem when more possibilities exist because the writer assumes that the list of alternatives created is exhaustive.
	leo.stcloudstate.edu /acadwrite/logic.html (1986 words)

	Uses and Misuses of Logic.
		Because of this, some non-scientists think that mathematics and logic are used to "prove" scientific propositions, to deduce new laws and theories, and to establish laws and theories with mathematical certainty.
		Logic and mathematics are the cement that holds the scientific structure together, ensures its self-consistency, and helps us prevent errors of false inference.
		When the use of mathematics and logic in science is explained to them they respond, "If mathematics and logic can't produce absolute truths, then they produce only untruths or partial truths, and are therefore worthless." This sentence is itself an example of nonsense clothed in the appearance of logic.
	www.lhup.edu /~dsimanek/logic.htm (5089 words)

	Letter: False Logic Is Lying
		Bly quotes, “People buy based on emotion, then rationalize the purchase decision with logic.” I would counter that people think they buy based on logic and then rationalize the purchase decision based on emotion; they have to, to reassure themselves that they didn’t blunder into a dumb purchase.
		Cheats and crooks may make a lot of money, but using their tools — including false logic — is incompetence, failure to discharge fiduciary duties or both.
		“False logic” is not lying; it is using the available facts to prove your case.
	www.dmnews.com /cms/dm-opinion/editorials/24840.html (326 words)

	multi-valued logic: an introduction
		Logic on this site is defined as implementing a single input/single output or a two input/single output n-valued truth table, wherein an input can have one of n states and an output can have one of n states; n being an integer of 2 or greater.
		the logic '1' is assumed to be identical to the arithmetical '1' and the logical '0' is assumed to be identical to the arithmetical '0'.
		In binary logic the opposite of '1' is '0'.
	www.multivaluelogic.com (4679 words)

	Multi-valued logic - Wikipedia, the free encyclopedia
		Traditionally, logical calculi are bivalent—that is, there are only two possible truth values for any proposition, true and false (which generally correspond to our intuitive notions of truth and falsity).
		Fuzzy logics were introduced by Lotfi Zadeh as a formalization of vagueness; i.e., the phenomenon that a predicate may apply to an object not absolutely, but to a certain degree, and that there may be borderline cases.
		Kurt Gödel in 1932 showed that intuitionistic logic is not a finitely-many valued logic, and defined a system of Gödel logics intermediate between classical and intuitionistic logic; such logics are known as intermediate logics.
	en.wikipedia.org /wiki/Multi-valued_logic (723 words)

	Digital Logic Gates IC's: AND, OR, NOT, NAND, NOR, etc. - Page 1 of 2
		Thus, the logic state in which the output of a logic gate will be put in depends on the logic states of each of its individual inputs.
		This essentially is the function of logic gates in digital circuits - to determine which outputs will be true or false, given a set of inputs that can either be true (logic '1') or false (logic '0').
		is a logic gate that gives an output that is opposite the state of its input.
	www.siliconfareast.com /logicgates.htm (460 words)

	False Cause
		Abstract: The fallacy of false cause and its forms as non causa pro causa and post hoc ergo propter hoc is disussed with examples.
		False Cause: the fallacy committed when an argument mistakenly attempt to establish a causal connection.
		Post hoc ergo propter hoc: (literally "after this, therefore because of this") the fallacy of arguing that one event was caused by another event merely because it occurred after that event.
	philosophy.lander.edu /logic/cause.html (661 words)

	Propositional Logic [Internet Encyclopedia of Philosophy]
		Propositional logic, also known as sentential logic, is the branch of logic that studies ways of joining and/or modifying entire propositions, statements or sentences to form more complicated propositions, statements or sentences, as well as the logical relationships and properties that are derived from these methods of combining or altering statements.
		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.
	www.iep.utm.edu /p/prop-log.htm (8796 words)

	Logic principle
		Logic uses evidence and scientific laws with cause-and-effect arguments to incontrovertibly prove a point.
		The actual truth and real logic are often relatively unimportant as compared with the social benefits of appearing rational.
		Conversations and debates are filled with people who are desperately seeking to impose their logic over that of others and aggression often replaces rationale, particularly if they feel that the other person's logic is superior.
	www.changingminds.org /principles/logic.htm (229 words)

	CSISS Classics - Lotfi Zadeh: Fuzzy logic-Incoporating Real-World Vagueness
		Fuzzy logic was first invented as a representation scheme and calculus for uncertain or vague notions.
		In the early 1900s, Lukasiewicz extended on to the conventional bi-valued logic of Aristotle and proposed a tri-valued logic in his paper in 1920 titled On three-valued logic where a new truth value was added to the truth logic 0 and false logic 1.
		The idea that logic ought to countenance more than two truth-values arose naturally in ancient and medieval discussions of determinism and was re-examined by C. Peirce, Hugh MacColl, and Nikolai Vasiliev in the first decade of this century.
	www.csiss.org /classics/content/68 (1118 words)

	CHAPTER THREE - THE TRIVALENT LOGIC OF AYMARA (Site not responding. Last check: 2007-10-10)
		The research of the Polish thinker J. Lukasiewicz was a sharp departure from the Aristotelian interpretation of logic.
		Logic is only interested in the truth-value of statement regardless of any conceptual content they may also have.
		A "logical variable" is a symbol, for example "x", which represents the truth-value of a given statement, A "logical function", or "functor" for short, is a relationship p(x) which assigns a truth-value p according to the values of one or several variables.
	www.aymara.org /biblio/igr/igr3.html (2570 words)

	Al-Ahram Weekly \| Forced to accept false logic (Site not responding. Last check: 2007-10-10)
		A major irony is that Israel's desire to appear on the side of NATO has extended as far as offering about 120 Kosovar refugees asylum in Israel, on a kibbutz that stands on Palestinian land seized in l948; where the village once existed, nothing of its past owners, neither names, nor possessions, nor memory survives.
		Such is the logic of history and, it must be said, the logic of the conqueror.
		The only answer is not to refuse to look at the endless pictures of refugees, but to develop the resistance that comes from a real education in philosophy and the humanities, patient and repeated criticism, and intellectual courage.
	weekly.ahram.org.eg /1999/427/op1.htm (1378 words)

	Digital Logic principles and overview
		In logic statements like this we can talk about conditions and decisions as being TRUE or FALSE and the logic linking them as a combination of simple words such as AND, OR and NOT.
		Logic conditions that are being tested are the inputs to these devices and the decisions are the outputs.
		When logic statements are represented in this way they are normally shown as a circuit diagram using symbols to represent each of the common logic functions.
	www.pc-control.co.uk /digital_logic.htm (380 words)

	Tapping Into the Magic of False Logic
		False logic, a term coined by my friend and master copywriter Michael Masterson, is copy that manipulates existing facts through skillful writing but does not lie about or misrepresent those facts.
		Perhaps they might reason that my advocating the use of false logic adds fuel to their argument.
		But false logic is not just the purview of direct marketers.
	www.dmnews.com /cms/dm-news/ad-agencies/24665.html (720 words)

	Propositional Logic Applet
		Categorical Logic: Three chapters in Copi address categorical logic, one on categorical propositions, one on syllogisms, and one on translation.
		The introduction of the ideas of predicate logic and quantification is good, but there is no discussion of relational predicates.
		This theorem is the basis of reasoning in propositional logic.
	www.wu.ece.ufl.edu /books/CS/TheoreticalCS/logic.html (1382 words)

	fUSION Anomaly. Fuzzy Logic
		With fuzzy logic, the outcome of an operation can be expressed as a probability rather than as a certainty.
		Because, almost by definition, commonsense knowledge is that knowledge which is not representable as a collection of well-formed formulae in predicate logic or other logical systems which have the same basic conceptual structure as predicate logic.
		In this logic, commonsense knowledge is defined to be a collection of dispositions, that is propositions with suppressed fuzzy quantifiers.
	fusionanomaly.net /fuzzylogic.html (442 words)

	Truth, Validity, and Soundness
		Abstract: The foundation-concepts of deductive logic are explained--truth, validity, and soundness.
		If it were possible to have true premisses and a false conclusion, logic would be useless to prove anything.
		If a deductive argument is valid and at least one of its premisses is false, then its conclusion is also false.
	philosophy.lander.edu /logic/tvs.html (433 words)

	Fuzzy Logic
		Fuzzy logic uses a set of Boolean conditions with values that are between the ranges of entirely false and entirely true.
		Fuzzy logic is a method of determining half-truths.
		Fuzzy logic is a range of values between zero (false) and one (true).
	www.public.iastate.edu /~baldusb/?M=A (491 words)

	PSIM - Instruction Set Reference
		If a true logic path is not established and the corresponding bit in memory was not previously set, the OTL instruction is not enabled.
		However, if a true logic path was previously established, the bit in memory is latched on and remains on, or enabled, even after the rung conditions go false.
		When the processor finds an input instruction whose logic is false, it scans the remainder of the rung as if it were false.
	www.thelearningpit.com /plc/psim/doc/instructions.html (2201 words)

	An Introduction To FUzzy Control Systems
		One main claim to fame for fuzzy logic is that it is useful in designing control systems - in spite of the fact that design techniques for control systems abound.
		Study of Fuzzy logic is a study of a kind of logic.
		Aristotle may not have been the first to assert the one statement at the foundations of traditional logic, but he certainly is the earliest on record to have done so.
	www.facstaff.bucknell.edu /mastascu/econtrolhtml/Fuzzy/Fuzzy1.html (3386 words)

	Contradiction Indicates False Fact
		For example: When I call the function that determines if this point is in that polygon, it returns False, in spite of the fact that the point really is in the polygon.
		In fuzzy logic "true AND false" is treated as the normal state not a contradiction.
		Fuzzy logic models a manifold with patches of the manifold and a basic heuristic to interpolate between those patches.
	c2.com /cgi/wiki?ContradictionIndicatesFalseFact (1220 words)

	Interesting Science : Math : Logic Questions - AskEarth
		That is they say with all certainty that this infinte series has a finite sum and that it is...
		Logically Simple solutions - Any body can try or Every one should try...
		Show, using mathematical induction, that every dollar amount of at least 18 dollars could be made from a combination of these bills.
	www.askearth.com /go/home?topic=4628 (574 words)

	Thinking Out Loud
		This may sound confusing, but it follows like this: Logic is always reasonable, whereas false logic is always unreasonable.
		It is not reasonable and is, therefore, false logic or illogical.
		I did not mean for this to turn into a lesson in logic or reason, but rather an explanation of how we can rationalize our own situations in direct conflict to what reason and logic tell us.
	mysite.verizon.net /edfinn3/loud.htm (525 words)

	PC AI - Fuzzy Logic
		Overview: Fuzzy logic is a superset of conventional (Boolean) logic that has been extended to handle the uncertainty in data.
		Fuzzy logic is useful to processes like manufacturing because of its ability to handle situations that the traditional true/false logic can't adequately deal with.
		What is fuzzy logic and how is it used, fuzzy expert systems, fuzzy numbers and arithmetic, and fuzzy state machines.
	www.pcai.com /web/ai_info/fuzzy_logic.html (942 words)

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