Wiktionarypar implicationImplication may refer to In logic Logicalimplication , entailment, or consequence, a relation between statements Material implication , or conditional implication, a binary truth function In linguistics , specifically in pragmatics Implicature Entailment pragmatics Other uses In medical diagnosis , the scientific method , and forensics , a hypothetical cause is implicated or indicated when a reason for the condition can be found, given that cause. disambig fr Implication pl Implikacja simple Implication ... more details
Material implication may refer to Material conditional , a logical connective Material implication rule of inference , a rule of replacement for some propositional logic See also Implication disambiguation Conditional statement disambiguation disambiguation ... more details
Converse implication is the conversion logic converse of Material implicationimplication . That is to say that for any two proposition s P and Q, if Q implies P, then P is the converse implication of Q. It may take the following forms p q , Bpq , or p q Definition Truth table The truth table of A B border 1 cellpadding 1 cellspacing 0 style text align center style width 35px background aaaaaa a style width 35px background aaaaaa b style width 35px T T T T F T F T F F F T Venn diagram The Venn diagram of If B then A the white area shows where the statement is false File Venn1101.svg 150px Properties truth preserving The interpretation under which all variables are assigned a truth value of true produces a truth value of true as a result of converse implication. Symbol Empty section date July 2010 Natural language Not q without p. p if q. Boolean Algebra A B Computer Science Empty section date July 2010 See also Logical connective Material implicationLogical connectives Category Propositional calculus Category Logical connectives logic stub fa ... more details
Unreferenced date December 2006 orphan date November 2009 An implication table is a tool used to facilitate the minimization of state computer science states in a state machine . The concept is to start assuming that every state may be able to combine with every other state, then eliminate combinations that are not possible. When all the impossible combinations have been eliminated, the remaining state combinations are valid, and thus can be combined. The procedure is as follows List state combination possibilities in an implication table, Eliminate combinations that are impossible because the states produce different outputs, Eliminate combinations that are impossible because the combination depends on the equivalence of a previously eliminated possibility, Repeat the above step until no more eliminations are possible. See also Moore reduction procedure DEFAULTSORT Implication Table Category Automata theory Formalmethods stub hr Minimizacija kona nog automata ... more details
Image Implication graph.svg thumb 360px An implication graph representing the 2 satisfiability instance math scriptscriptstyle x 0 lor x 2 land x 0 lor lnot x 3 land x 1 lor lnot x 3 land x 1 lor lnot x 4 land x 2 lor lnot x 4 land atop quad scriptscriptstyle x 0 lor lnot x 5 land x 1 lor lnot x 5 land x 2 lor lnot x 5 land x 3 lor x 6 land x 4 lor x 6 land x 5 lor x 6 . math In mathematical logic , an implication graph is a skew symmetric graph skew symmetric directed graph G V , E composed of vertex set V and directed edge set E . Each vertex in V represents the truth status of a Boolean literal , and each directed edge from vertex u to vertex v represents the material implication If the literal u is true then the literal v is also true . Implication graphs were originally used for analyzing complex Boolean expression s. Applications A 2 satisfiability instance in conjunctive normal form can be transformed into an implication graph by replacing each of its disjunction s by a pair of implications. An instance is satisfiable if and only if no literal and its negation belong to the same strongly connected component of its implication graph this characterization can be used to solve 2 satisfiability instances in linear time. ref cite journal author Aspvall, Bengt Michael Plass Plass, Michael F. Robert Tarjan Tarjan, Robert E. title A linear time algorithm for testing the truth of certain quantified boolean formulas journal Information Processing Letters volume 8 issue 3 pages 121 123 year 1979 doi 10.1016 0020 0190 79 90002 4 ref References references Category Boolean algebra Category Application specific graphs Category Directed graphs Category Graph families ... more details
The Implication Realization I R model of melodic expectation was developed by Eugene Narmour as an alternative to Schenkerian analysis centered less on music analysis and more on cognitive aspects of expectation. The model is one of the most significant modern theories of melodic expectation, going into great detail about how certain melodic structures arouse particular expectations. History Meyer 1956 applied Gestalt psychology Gestalt effect principles to musical expectation, resulting in his ideas about completion, closure, and his Law of Good Continuation. In 1977, Narmour s book laid out problems he had with Schenkerian analysis and sketched ideas for a new model of analysis based on musical expectation as informed by the work of Meyer. Narmour mentioned a forthcoming book, The Melodic Structure of Tonal Music , but it did not appear. Much time passed without the alternative theory, but finally in 1989 Narmour published his I R model, detailed in the 1990 and 1992 books. As of 2007, Narmour is working on a new book, which will extend the I R theory to the parameters of harmony and rhythm and explore potential applications to the analysis of performance. Theory Narmour s I R model was published in two separate books, dealing with basic melodic structures and melodic complexity ... General Claims The Analysis and Cognition of Basic Melodic Structures The Implication Realization ... monad one element which does not yield an implication Central to the discussion is the notion ... References Cross, I. 1995 Review of The analysis and cognition of melodic complexity the implication ... code of melody Cognitive structures generated by the implication realization model. In Music and the cognitive ... The Analysis and Cognition of Basic Melodic Structures The Implication Realization Model . Chicago ... Complexity The Implication Realization Model . Chicago University of Chicago Press. ISBN 0 226 56842 3. Schellenberg, E. 1997 . Simplifying the Implication Realization Model of Musical Expectancy ... more details
conjunction conjunction is logically false. One statement Logicalimplication logically implies another ...Logical truth is one of the most fundamental concept s in logic , and there are different theories on its nature. A logical truth is a Statement logic statement which is true and remains true under all interpretation logic reinterpretations of its components other than its logical constant s. It is a type of Analytic synthetic distinction analytic statement . Logical truths including Tautology logic ... to reject a logical truth. However, it is not universally agreed that there are any statements which are necessarily true. A logical truth was considered by Ludwig Wittgenstein to be a statement which ... married people are married are logical truths because they are true due to their inherent meanings and not because of any facts of the world. Later, with the rise of formal logic a logical truth was considered to be a statement which is true under all possible interpretations. The existence of logical ... for our knowledge of logical truths on empiricist grounds. Logical truths and analytic truths Main Analytic synthetic distinction Logical truths, being analytic statements, do not contain any information about any matters of fact . Other than logical truths, there is also a second class of analytic ... be turned into a logical truth by substituting synonyms for synonyms salva veritate . No bachelor ... in need of clarification. In his conclusion, Quine rejects that logical truths are necessary truths. Instead he posits that the truth value of any statement can be changed, including logical truths ... the context . This is synonymous to logical truth. However, the term tautology is also commonly used ... a tautology or logical truth is true solely because of the logical terms it contains in general e.g. ... is true because of the logical terms it contains which are logical connective s e.g. logical disjunction or , logical conjunction and , and joint denial nor . Not all logical truths are tautologies ... more details
A logical assertion is a statement that Speech act Classifying illocutionary speech acts asserts that a certain premise is true, and is useful for statements in proof. It is equivalent to a sequent with an empty antecedent logic antecedent . For example, if p x is even , the implication math vdash p rightarrow x pmod 2 equiv 0 math is thus true. We can also write this using the logical assertion symbol, as math vdash left vdash p rightarrow x pmod 2 equiv 0 right math Category Mathematical logic Mathlogic stub es Aserci n l gica pl Asercja logika zh ... more details
Material implication if...then math rightarrow math , math Rightarrow math , math supset math logical ... the symbol for converse implication is redundant. In some logical calculi notably, in classical logic ...about connectives in logical systems connectors in natural languages discourse connective other logical symbols table of logic symbols In logic , a logical connective also called a logical operator is a symbol .... The most common logical connectives are binary connectives also called dyadic connectives which join ... to be a unary connective . Logical connectives along with quantifier s are the two main types of logical constant s used in formal system s such as propositional logic and predicate logic . In language ... joining the sentences A and B to form the compound sentences C and D . The and in C is a logical ... A and B but deny C . However so in D is not a logical connective, since it would be quite reasonable ..., not because Jack had gone up the Hill at all. Various English words and word pairs express logical ... are and conjunction or disjunction either...or exclusive disjunction implies implication if...then implication if and only if equivalence only if implication just in case equivalence but conjunction ... that negation and it is not the case that negation also express a logical connective even though ... logical connectives , logical operators , propositional operators , or, in classical logic , truth function .... Logical connectives can be used to link more than two statements, so one can speak about arity var n ary logical connective . Common logical connectives align right style margin left 2em margin ... Q bgcolor FFFF66 0 bgcolor FFFF66 1 bgcolor FFFF66 0 bgcolor FFFF66 1 Logical conjunction Conjunction ... 1 1 0 Image Venn1110.svg 40px Logical disjunction Disjunction align right 0 1 1 1 Image Venn0111.svg 40px Logical NOR Joint denial align right 1 0 0 0 Image Venn1000.svg 40px Material conditional align ... 0 Image Venn0110.svg 40px logical biconditional Biconditional align right 1 0 0 1 Image Venn1001.svg ... more details
Logical Investigations German Logische Untersuchungen can refer to Logical Investigations , 1840 work by Friedrich Adolf Trendelenburg Logical Investigations Husserl Logical Investigations , 1900 work by Edmund Husserl Logical Investigations Frege Logical Investigations , 1918 ff. work by Gottlob Frege See also Investigations into Logical Deduction Untersuchungen ber das logische Schlie en 1934 5 works by Gerhard Gentzen disambig ... more details
In computing, Logical partition may refer to Logical partition virtual computing platform A partition found within an disk partitioning Extended partition extended partition disambig ... more details
Logical equivalent may refer to logical equivalence exclusive nor , a logic gate disambig Long comment to avoid being listed on short pages ... more details
angles . The antecedent is the premise or the cause and the consequent is the consequence . When an implication .... A simple theorem gives rise to an implication whose antecedent is the hypothesis and whose ... time both cause and consequence. Definition Logical equality also known as biconditional is an logical operation operation on two logical value s, typically the values of two proposition ... Venn0001.svg 40px for Logical disjunction and . border 0 style width 100 style vertical align ... also Portal Thinking If and only if Logical equivalence Logical equality XNOR gate Biconditional elimination ... & Row . 1961 Logical connectives PlanetMath attribution id 484 title Biconditional DEFAULTSORT Logical Biconditional Category Binary operations Category Logical connectives Category Propositional ... more details
For other uses of the term see Material implication . Disputed date February 2012 nobots Transformation rules In propositional logic , material implication ref cite book title A Concise Introduction to Logic 4th edition last Hurley first Patrick authorlink coauthors year 1991 publisher Wadsworth Publishing location isbn page pages 364 5 url accessdate ref verify source date February 2012 ref cite book ref harv last Copi first Irving M. last2 Cohen first2 Carl title Introduction to Logic publisher Prentice Hall year 2005 page 371 isbn ref is a Validity valid rule of replacement that allows for a material conditional conditional statement to be replaced by a logical disjunction disjunction if and only if the antecedent logic antecedent is Logical negation negated . The rule states that P implies Q is Logical equivalence logically equivalent to not P or Q and can replace each other in formal proof logical proofs . math P to Q Leftrightarrow neg P or Q math Where math Leftrightarrow math is a metalogic al symbol formal symbol representing can be replaced in a proof with. Formal notation The material implication rule may be written in sequent notation math P to Q vdash neg P or Q math where math vdash math is a metalogical symbol meaning that math neg P or Q math is a logical consequence syntactic consequence of math P to Q math in some logical system or in rule of inference rule form math frac P to Q neg P or Q math where the rule is that wherever an instance of math P to Q math appears on a line of a proof, it can be replaced with math neg P or Q math or as the statement of a truth functional Tautology logic tautology or theorem of propositional logic math P to Q to neg P or Q math where math P math and math Q math are propositions expressed in some formal system . Examples If it is December 25, it is Christmas. Thus, it is not December 25 or it is Christmas. Since it has to be the case that it is Christmas on December 25, the current day is either not December 25 Christmas ... more details
In logic , a logical constant of a formal language language math mathcal L math is a symbol formal symbol that has the same Formal semantics logic semantic value under every interpretation logic interpretation of math mathcal L math . Two important types of logical constants are logical connective s and quantifier s. The equality mathematics equality predicate usually written is also treated as a logical constant in many formal system systems of logic . Some symbols that are commonly treated as logical constants are table border 1 class wikitable tr th Symbol th th Meaning in English th tr tr td T td td true td tr tr td F td td false td tr tr td td td not td tr tr td td td and td tr tr td td td or td tr tr td td td implies , if...then td tr tr td td td for all td tr tr td td td there exists , for some td tr tr td td td equals td tr tr td math Box math td td necessary td tr tr td math Diamond math td td possible td tr table For many logical constants also other symbols are commonly used to denote them, such as the symbol & for logical and . One of the fundamental questions in the philosophy of logic is What is a logical constant? that is, what special feature of certain constants that makes them logical in nature? ref Carnap ref See also Non logical symbol Logical value Logical connective References reflist External links http plato.stanford.edu entries logical constants Stanford Encyclopedia of Philosophy entry on logical constants Category Philosophical logic Category Concepts in logic Category Syntax logic Category Logical truth Category Logic symbols logic stub philosophy stub ca Constant l gica de Konstante Logik es Constante l gica nl Logische constante ja pl Sta a logiczna ... more details
Logical topology also referred to as signal topology is a network computing term used to describe the arrangement of devices on a network and how they communicate with one another. How devices are connected to the network through the actual cables that transmit data, or the physical structure of the network, is called the Network topology physical topology . Logical topologies are bound to network protocols and describe how data is moved across the network. There are attempts to study the logical topology of the Internet by network scientists such as Albert L szl Barab si . Category Network topology ar ... more details
Logical model can refer to A model in logic, see model theory In computer science a logical data model disambig Short pages monitor This long comment was added to the page to prevent it being listed on Special Shortpages. It and the accompanying monitoring template were generated via Template Longcomment. Please do not remove the monitor template without removing the comment as well. ... more details
Unreferenced date December 2009 A logical disk is a device that provides an area of usable storage capacity on one or more physical disk drive components in a computer system. Other terms that are used to mean the same thing are disk partition partition , logical volume , and in some cases a virtual disk vdisk . The disk is described as logical because it does not actually exist as a single physical entity in its own right. There are many ways to define a logical disk or volume. Most modern operating systems provide some form of logical volume management which allows the creation and management of logical volumes. Logical disks are also defined at various levels in the storage infrastructure stack . From top to bottom Operating System Defines partitions on the disks to which it has visibility these disks may be logical themselves SAN If the SAN is virtualized, a device in the same presents logical disks vdisk to the host operating systems Storage Subsystem Usually providing some form of RAID where logical disks partitions are presented to the SAN from the RAID arrays themselves. The RAID arrays actually contain the physical disks. Why do we need them? When IBM first released the magnetic disk drive in the 1956 IBM 305 a single drive would be directly attached to the using system, with each disk managed as a single entity. As the development of drives continued, it became apparent ... one physical disks are RAID ed together to produce a single logical disk . In a modern home Personal ... into multiple logical drives Citation needed date November 2007 . In most modern business Information ... provide some capacity to one server, and some capacity to another. Therefore logical disks are used ... pool of logical disks. See also Logical volume management LVM RAID Storage Virtualization DEFAULTSORT Logical Disk Category Computer storage Category Storage virtualization pl Partycja logiczna simple Logical disk ... more details
nofootnotes date February 2012 The paradox es of material implication are a group of formula s which are truths of classical logic , but which are intuitively problematic. One of these paradoxes is the paradox of entailment . The root of the paradoxes lies in a mismatch between the interpretation of the validity of logicalimplication in natural language, and its formal Interpretation logic interpretation in classical logic, dating back to George Boole s algebraic logic. In classical logic, implication describes conditional if then statements using a truth functional interpretation, ie p implies q is defined to be it is not the case that p is true and q false . Also, p implies q is equivalent to p is false or q is true . For example, if it is raining, then I will bring an umbrella , is equivalent to it is not raining, or I will bring an umbrella, or both . This truth functional interpretation of implication is called material implication or material conditional. The paradoxes are logical statements which are true but whose truth is intuitively surprising to people who are not familiar ... implication arise because of the truth functional definition of material implication, which ... follows in ordinary usage, material implication does not capture the meaning of if... then . Paradox ... make an argument valid that is, inconsistent premises imply any logical consequence conclusion at all ... of entailment Validity is defined in classical logic as follows An Logical argument argument consisting ... never be sound. A suggested improvement to the notion of logical validity to eliminate this paradox ... with trying to use material implication as representing the English if ... then ... . For example ... but the conclusion is false. Thus, using classical logic and taking material implication to mean if then is an unsafe .... John Etchemendy Etchemendy, J. The Concept of Logical Consequence . Cambridge Harvard University ... University Press. 2001. Category Paradoxes Category Logical consequence es Paradojas de la implicaci n ... more details
Unreferenced date December 2009 A logical schema is a data model of a specific problem domain expressed in terms of a particular data management technology. Without being specific to a particular database management product, it is in terms of either relational tables and columns, object oriented classes, or XML tags. This is as opposed to a conceptual data model , which describes the semantics of an organization without reference to technology, or a physical data model , which describes the particular physical mechanisms used to capture data in a storage medium. The next step in creating a database , after the logical schema is produced, is to create the physical schema . See also Database schema Logical data model Data model DEFAULTSORT Logical Schema Category Data modeling database stub de Schema Informatik ja ru ... more details
Unreferenced date October 2009 In computing , a logical address is the address at which an item memory cell, storage element, network host appears to reside from the perspective of an executing application program . A logical address may be different from the physical address due to the operation of an address translator or mapping function. Such mapping functions may be, in the case of a computer memory architecture, a memory management unit MMU between the CPU and the memory bus, or an address translation layer, e.g., the Data Link Layer , between the hardware and the internetworking protocols Internet Protocol in a computer networking system. Computer memory The physical address of computer memory banks may be mapped to different logical addresses for various purposes. For example, the same physical memory may appear at two different logical addresses and if accessed by the program at one address, data will pass through the CPU cache whereas if it is accessed at the other address, it will bypass the cache. In a system supporting virtual memory , there may actually not be any physical memory mapped to a logical address until an access is attempted. The access triggers special functions of the operating system which reprogram the MMU to map the address to some physical memory, perhaps writing the old contents of that memory to disk and reading back from disk what the memory should contain at the new logical address. In this case, the logical address may be referred to as a virtual address . Computer networking Other uses Logical address or virtual address is also used in IBM IBM s VM Operating system VM operating system and in Virtual Device Location . See also Memory segment Flat memory model memory address FOLDOC DEFAULTSORT Logical Address Category Virtual memory ar ... more details
n sup rounding towards 0 . Because arithmetic right shift differs from logical right shift, many languages ... Java and JavaScript , the arithmetic right shift operator is tt tt whereas the logical right shift ... and logical left shift have the same effect. The programming language s C programming language C , C ... using the logical shift. Example If the bit sequence 0001 0111 decimal 23 were subjected to a logical ... 46 File Rotate left logically.svg thumb left 300px Logical left shift one bit ...to the right would yield 0000 1011 decimal 11 File Rotate right logically.svg thumb left 300px Logical right shift one bit DEFAULTSORT Logical shift Category Binary arithmetic Category Operators programming de Logische ... more details
File Logical hexagon.png thumb 350px right The logical hexagon extends the square of opposition to six statements. The logical hexagon also called the hexagon of opposition is a conceptual model of the relationships between the truth value s of six statement logic statement s. It is an extension of Aristotle s square of opposition . It was discovered independently by both Augustin Sesmat and Robert Blanch . ref http alessiomoretti.perso.sfr.fr NOTLogicalHexagon.html N opposition theory logical hexagon ref This extension consists in introducing two statements Y and U . Y is the Logical conjunction conjunction of the two traditional particulars I and O . Whereas, U is the Logical disjunction disjunction of A and E . Summary of relationships The traditional square of opposition demonstrates two sets of contradictories A and O , and E and I i.e. they cannot both be true and cannot both be false , two contraries A and E i.e. they can both be false, but cannot both be true , and two subcontraries I and O i.e. they can both be true, but cannot both be false according to Aristotle s definitions. However, the logical hexagon provides that U and Y are also contradictory. Interpretations of the logical hexagon The logical hexagon may be interpreted in various ways, including as a model of term logic traditional logic , quantification s, modal logic , order theory , or paraconsistent logic . For instance, the statement A may be interpreted as Whatever x may be, if x is a man, then x is white. x M x W x The statement E may be interpreted as Whatever x may be, if x is a man, then x is non ... The logical hexagon may be interpreted as a model of modal logic such that A is interpreted as necessary and sufficient condition necessity E is interpreted as impossibility I is interpreted as logical ... the square and the hexagon, followed by a logical cube , belong to a regular series of n dimensional objects called logical bi simplexes of dimension n. The pattern also goes even beyond this. ref Moretti ... more details
Unreferenced date December 2009 A logical clock is a mechanism for capturing chronological and causal relationships in a distributed system . Logical clock algorithms of note are Lamport timestamps , which are monotonically increasing software counters. Vector clocks , that allow for total ordering of events in a distributed system. Version vector s, order replicas, according to updates, in an optimistic replicated system. Matrix clocks , an extension of vector clocks that also contains information about other processes views of the system. DEFAULTSORT Logical Clock Category Distributed algorithms de Logische Uhr fr horloge logique pt Rel gios l gicos sr ru ... more details
Citations missing article date January 2008 Infobox Bertrand Russell Wittgenstein Logical atomism is a philosophical belief that originated in the early 20th century with the development of analytic philosophy . Its principal exponents were the British philosopher Bertrand Russell , the early work of his Austrian born pupil and colleague Ludwig Wittgenstein , and his German counterpart Rudolf Carnap . The theory holds that the world consists of ultimate logical facts or atoms that cannot be broken ... 2011 The name for this kind of theory was coined in 1918 by Russell in response to what he called logical ... The Philosophy of Logical Atomism . Russell was much influenced by Ludwig Wittgenstein, as an introductory ... of them ... . The principles of logical atomism Russell referred to his atomistic doctrine as contrary to the tier of the people who more or less follow Hegel PLA 178 . The first principle of logical ... of fictional objects. This theory of descriptions was crucial to logical atomism, as Russell believed ... Russell delivered his lectures on logical atomism, he had lost contact with Wittgenstein. After the First ... Philosophicus , Wittgenstein s own version of Logical Atomism. Although Wittgenstein did not use the expression Logical Atomism , the book espouses most of Russell s logical atomism except for Russell ..., was perhaps even greater long term, especially on Logical Positivism . Like Russell, Wittgenstein eventually rejected Logical Atomism. This rejection culminated in the posthumously published ... Arturn The Philosophy of Betrand Russell , New York, Tudorm 1951. See also G. E. Moore Logical positivism ... reflist External links Sep entry logical atomism Peter Schulte http wwwhomes.uni bielefeld.de ... entries logical atomism Kevin Klement Russell s Logical Atomism http plato.stanford.edu entries wittgenstein atomism Ian Proops Wittgenstein s Logical Atomism Jeff Speaks http www.nd.edu jspeaks mcgill 370 winter2004 russell atomism.htm Russell on logical constructions and logical atomism , McGill ... more details
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