Other uses Philosophy sidebar Logic from the Greek wiktionary logik ref possessed of reason ... Digital, Inc isbn 978 0 385 42533 9 page 238 ref Logic is used in most intellectual activities ... . In philosophy, the study of logic is applied in most major areas metaphysics , ontology ... language . ref name stanford logic onthology Logic is also studied in argumentation theory . ref cite ... Illinois University Press year 1983 isbn 978 0809310500 ref Logic was studied in several ancient ... Greece . In the West, logic was established as a formal discipline by Aristotle , who gave it a fundamental place in philosophy. The study of logic was part of the classical Trivium education trivium , which also included grammar and rhetoric. Logic is often divided into three parts, inductive reasoning , abductive reasoning , and deductive reasoning . The study of logic rquote right Upon this first ... of inquiry. Charles Sanders Peirce , First Rule of Logic The concept of Argument form logical form is central to logic, it being held that the validity of an argument is determined by its logical form, not by its content. Traditional syllogism Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics. Informal logic is the study of natural language Logical argument arguments . The study of fallacies is an especially important branch of informal logic. The dialogues ... logic. Mathematical formalism Formal logic is the study of inference with purely formal content. An inference ... of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands ... Analytics ref In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuance of natural language. Symbolic logic is the study of symbolic abstractions ... modern treatment, see cite book first A. G. last Hamilton title Logic for Mathematicians publisher ... more details
saved book title Logic and Metalogic subtitle cover image cover color Logic and Metalogic Main article Logic History History of logic Topics in logic Term logic Aristotelian logic Propositional calculus Predicate logic Modal logic Informal logic Mathematical logic Algebraic logic Multi valued logic Fuzzy logic Metatheory Metalogic Philosophical logicLogic in computer science Controversies in logic Principle of bivalence Paradoxes of material implication Paraconsistent logic Is logic empirical? Category Wikipedia books on logicLogic Category Wikipedia books on computer science ... more details
Unreferenced stub auto yes date December 2009 Strict logic is essentially synonymous with Relevance logic relevant logic , though it can be characterized proof theory proof theoretically as ordinary logic without weakening , or linear logic with Idempotency of entailment contraction . See also Substructural logic DEFAULTSORT Strict Logic Category Substructural logicLogic stub ... more details
In mathematics, logic can refer to consistent theory logiclogic , an infinitary extension of first order logiclogic , a deductive system in set theory developed by Hugh Woodin mathdab ... more details
Dynamic Logic may mean In theoretical computer science, dynamic logic modal logic is a modal logic for reasoning about dynamic behaviour In digital electronics, dynamic logic digital electronics is a technique used for clocked combinatorial circuit design A different concept proposed by Leonid Perlovsky disambig ... more details
Binary logic could refer to any two valued logic , especially in social sciences classical propositional logic propositional two valued logic, also called boolean logic in engineering, which is the logical foundation of digital electronics circuits implementing boolean logic see logic gate s an English Rock band active from 1989 1992 famous for their use of synthesisers in tandem with guitar based harmonies. Should not to be confused with binary numeral system . dab ... more details
In mathematical logic , a logical system has the erasure property if and only if no subset of the propositions can be added to another subset of the propositions to refute a consequence. For instance, if proposition A means the store is open from 8 00 to 22 00 and proposition B means except Tuesdays , the system AB does not have erasure. See also Monotonic logic in mathematical logic http plato.stanford.edu entries peirce logic Peirce s Logic at the Stanford Encyclopedia of Philosophy mathlogic stub Category Mathematical logic ... more details
Wiktionarypar logicLogic may refer to Logic , the study of the principles and criteria of valid inference and demonstration Mathematical logic , a branch of mathematics that grew out of symbolic logic Philosophical logicLogic may also refer to Entertainment A Logic Named Joe , a science fiction short story by Murray Leinster using his given name, Will F. Jenkins first published in the March 1946 issue of Astounding Science Fiction Lamont LOGiC Coleman, a musician who collaborated on rapper Jim Jones fifth studio album, Capo album Capo album 2011 on E1 Music Science and technology Digital logic , a class of digital circuits characterized by the technology underlying its logic gates Software Dolby Pro Logic , also known as Pro Logic, a surround sound processing technology Logic Pro , a MIDI sequencer and Digital Audio Workstation application, part of Logic Studio Logic Studio , a music production suite by Apple Inc. See also Logarithm disambig el he ko nl Logica doorverwijspagina ja ... more details
Hybrid logic refers to a number of extensions to propositional logic propositional modal logic with more expressive power, though still less than first order logic . In formal logic , there is a trade off between expressiveness and computational tractability how easy it is to computer compute automated reasoning reason with logical languages . The history of hybrid logic began with Arthur Prior s work in tense logic. ref cite web url http plato.stanford.edu entries logic hybrid title Hybrid Logic author Torben Bra ner date 2008 work Stanford Encyclopedia of Philosophy accessdate 1 February 2011 ref Unlike ordinary modal logic, hybrid logic makes it possible to refer to states possible worlds in formulas. This is achieved by a class of formulas called nominals , which are true in exactly one state, and by the use of the operator, which is defined as follows sub i sub p is true iff if and only if p is true in the unique state named by the nominal i i.e., the state where i is true . Hybrid logics with extra or other operators exist, but is more or less standard. Hybrid logics have many features in common with temporal logic s which use nominal like constructs to denote specific points in time , and they are a rich source of ideas for researchers in modern modal logic. They also have applications in the areas of feature logic , model theory , proof theory , and the logical analysis of natural language . It is also deeply connected to description logic because the use of nominals allows one to perform assertional ABox reasoning, as well as the more standard terminological TBox reasoning. References reflist Further reading P. Blackburn. 2000. Representation, reasoning and relational structures a hybrid logic manifesto. Logic Journal of the IGPL , 8 3 339 365. External links http hylo.loria.fr Hybrid Logics Home Page http plato.stanford.edu entries logic hybrid Stanford Encyclopedia of Philosophy entry on Hybrid Logic Category Modal logiclogic stub ... more details
Orphan date November 2006 Logic Spectacles , Thomas Carlyle s name for eyes that can discern only the external relations of things, but not the inner nature of them. Nuttall philo stub Category Concepts in logic ... more details
Logic system may refer to A type of Formal system Logic System, a musical project of Japanese composer and programmer Hideki Matsutake disambig ... more details
The following outline is provided as an overview of and topical guide to logicLogic &ndash formal science of using reason , considered a branch of both philosophy and mathematics . Logic investigates ... and through the study of arguments in natural language . The scope of logic can therefore ... . One of the aims of logic is to identify the correct or validity valid and incorrect or fallacy fallacious ... . Foundations of logic Main Philosophy of logic Analytic synthetic distinction Antinomy A priori and a posteriori ... Quantification Reason Reasoning Reference Semantics Strict conditional Syntax logic Truth Truth value Validity Philosophical logic Philosophical logic &ndash Informal logic and critical thinking Informal logic &ndash Critical thinking &ndash Argumentation theory &ndash Argument &ndash Argument ... Narrative logic &ndash Occam s razor &ndash Opinion &ndash Practical syllogism &ndash Precision questioning ... credibility &ndash Source criticism &ndash Theory of justification &ndash Topical logic &ndash Vagueness ... Ultrafinitism Fallacies Main List of fallacies Fallacy &ndash In logic and rhetoric, this is usually ... logic Formal logic &ndash Mathematical logic, symbolic logic and formal logic are largely, if not completely ... Main Table of logic symbols Symbol formal Variable mathematics Logical variables Propositional variable Predicate variable Literal mathematical logic Literal Metavariable Logical constant s Logical ... Types of propositions Main Proposition Analytic proposition Axiom Atomic sentence Clause logic Contingency ... Sentence mathematical logic Sequent Statement logic Tautology logic Tautology Theorem Rules ... logic Conversion logic De Morgan s laws Destructive dilemma Disjunction elimination Disjunction introduction Disjunctive syllogism Double negative elimination Generalization logic Hypothetical syllogism ... Principle of contradiction Resolution logic Simplification Transposition logic Formal theories Main Theory mathematical logic Formal proof List of first order theories Expressions in an object ... more details
Minimal logic , or minimal calculus , is a Mathematical logic symbolic logic system originally developed by Ingebrigt Johansson . It is a variant of intuitionistic logic that rejects not only the classical logic classical law of excluded middle as intuitionistic logic does , but also the principle of explosion ex falso quodlibet . Just like intuitionistic logic, minimal logic can be formulated in a language using , , , logical implication implication , logical conjunction conjunction , logical disjunction disjunction and falsum as the basic logical connective connectives , treating A as an abbreviation for A . In this language it is axiomatized by the positive fragment i.e., formulas using only , , of intuitionistic logic, with no additional axioms or rules about . Thus minimal logic is a subsystem of intuitionistic logic, and it is strictly weaker as it does not derive the ex falso quodlibet principle math neg A,A vdash B math however, it derives its special case math neg A,A vdash neg B math . Adding the ex falso axiom math neg A to A to B math to minimal logic results in intuitionistic logic, and adding the double negation law math neg neg A to A math to minimal logic results in classical logic. Minimal logic is closely related to simply typed lambda calculus via the Curry Howard isomorphism , ie. the typing derivation s of simply typed lambda terms are isomorphic to natural deduction proofs in minimal logic. References Ingebrigt Johansson Johansson, Ingebrigt , 1936, http www.numdam.org numdam bin item?id CM 1937 4 119 0 Der Minimalkalkul, ein reduzierter intuitionistischer Formalismus . Compositio Mathematica 4 , 119 136. Logic mathlogic stub Category Non classical logic Category Constructivism mathematics Category Systems of formal logic fr Logique minimale uk ... more details
Inappropriate tone date March 2011 Philosopher Susan Haack uses the term deviant logic to describe certain non classical logic non classical systems of logic . In these logics, the Set mathematics set of well formed formula s generated equals the set of well formed formulas generated by classical logic. the set of theorem s generated is different from the set of theorems generated by classical logic. The set of theorems of a deviant logic can differ in any possible way from classical logic s set ... logic developed by Poles Polish logician and mathematician Jan ukasiewicz . Under this system, any theorem necessarily dependent on classical logic s principle of bivalence would fail to be valid. The term first appears in Chapter 6 of Willard Van Orman Quine W.V.O. Quine s Philosophy of Logic ... logics Haack also described what she calls a quasi deviant logic. These logics are different ... of the set of well formed formulas generated by classical logic. the set of theorems generated is a proper superset of the set of theorems generated by classical logic, both in that the quasi deviant logic generates novel theorems using well formed formulas held in common with classical logic, as well ... formed formulas generated by classical logic. the set of theorems generated is a proper superset of the set of theorems generated by classical logic, but only in that the novel theorems generated by the extended logic are only a result of novel well formed formulas. Some systems of modal logic meet this definition. In such systems, any novel theorem would not parse in classical logic due to modal ... logic, the impetus behind extended logics is normally only to provide a supplement to it. Two decades ... of a philosophical position, Deviant Logic retains its significance. References Haack, S. 1996 . Deviant Logic, Fuzzy Logic Beyond the Formalism . Chicago The University of Chicago Press. First appeared in 1974 as Deviant Logic , published by Cambridge University Press. The 1996 edition includes ... more details
Transaction logic is an extension of predicate logic with both declarative and procedural semantics that describe state changes in logic programming over dynamic database s. First proposed in the early 1990s by Anthony J. Bonner and Michael Kifer, transaction logic allows for the amalgamation property amalgamation of features including hypothetical updating, nondeterminism , and artificial intelligence via behaviors of object oriented databases. ref Bonner and Kifer 1995 , abstract ref Bonner and Kifer have offered a proof of completeness for a Serial Horn program implementation of transaction logic. ref Bonner and Kifer 1995 , 6. Proof Theory and appendix E ref A prototype of transaction logic has been implemented in XSB XSB Prolog . ref nowiki ftp ftp.cs.toronto.edu pub goku transaction logic XSB Prototype3 nowiki ref Notes references References Bonner, Anthony J. and Michael Kifer 1995 Transaction logic programming , Computer Systems Research Institute Technical Report CSRI 323 revision of CSRI 270 of 1992 , University of Toronto. Category Logic programming languages comp sci theory stub ... more details
Affine logic is a substructural logic whose proof theory rejects the structural rule of Idempotency of entailment contraction . It can also be characterized as linear logic with weakening . The name affine logic is associated with linear logic , to which it differs by allowing the weakening rule. Jean Yves Girard introduced the name as part of the geometry of interaction semantics of linear logic, which characterises linear logic in terms of linear algebra here he alludes to affine transformation s on vector spaces. ref Jean Yves Girard , 1997. http www.seas.upenn.edu sweirich types archive 1997 98 msg00134.html Affine . Message to the TYPES mailing list. ref The logic predated linear logic. V. N. Grishin used this logic in 1974, ref Grishin, 1974, and later, Grishin, 1981. ref after observing that Russell s paradox cannot be derived in a set theory without contraction, even with an unbounded comprehension axiom . ref Cf. Frederic Fitch s demonstrably consistent set theory ref Likewise, the logic formed the basis of a decidable subtheory of predicate logic , called Direct logic Ketonen & Wehrauch, 1984 Ketonen & Bellin, 1989 . Affine logic can be embedded into linear logic by rewriting the affine arrow math A rightarrow B math as the linear arrow math A circ B otimes top math . Whereas full linear logic i.e. propositional linear logic with multiplicatives, additives and exponentials is undecidable, full affine logic is decidable. Affine logic forms the foundation of ludics . Notes references References V.N. Grishin, 1974. A nonstandard logic and its application to set theory, Russian . Studies in Formalized Languages and Nonclassical Logics Russian , 135 171. Izdat, Nauka, Moskow. . V.N. Grishin, 1981. Predicate and set theoretic calculi based on logic without contraction ... on Direct Logic. In Linear Logic and its Implementation . See also Strict logic and relevant logic Category Substructural logiclogic stub ... more details
Defeasible logic is a non monotonic logic proposed by Donald Nute to formalize defeasible reasoning . In defeasible logic, there are three different types of propositions strict rules specify that a fact is always a consequence of another defeasible rules specify that a fact is typically a consequence of another undercutting defeaters specify exceptions to defeasible rules. A priority ordering over the defeasible rules and the defeaters can be given. During the process of deduction, the strict rules are always applied, while a defeasible rule can be applied only if no defeater of a higher priority specifies that it should not. See also Common sense Non monotonic logic Default logic Defeasible reasoning References D. Nute 1994 . Defeasible logic. In em Handbook of logic in artificial intelligence and logic programming em , volume 3 Nonmonotonic reasoning and uncertain reasoning, pages 353 395. Oxford University Press. G. Antoniou, D. Billington, G. Governatori, and M. Maher 2001 . Representation results for defeasible logic. em ACM Transactions on Computational Logic em , 2 2 255 287. Category Logic programming Category Non classical logic philo stub compu AI stub es L gica retractable fr Logique d faisable zh ... more details
Provability logic is a modal logic , in which the box or necessity operator is interpreted as it is provable that . The point is to capture the notion of a proof predicate of a reasonably rich formal theory , such as Peano arithmetic . There are a number of provability logics, some of which are covered in the literature mentioned in the References section. The basic system is generally referred to as GL for Kurt G del G del Martin Hugo L b L b or L or K4W. It can be obtained by adding the modal version of L b s theorem to the logic K or K4 . It was pioneered by Robert M. Solovay in 1976. Since then until his death in 1996 the prime inspirer of the field was George Boolos . Significant contributions to the field have been made by Sergei Artemov, Lev Beklemishev, Giorgi Japaridze , Dick de Jongh , Franco Montagna, Vladimir Shavrukov, Albert Visser and others. Interpretability logic s present natural extensions of provability logic. See also Interpretability logic Kripke semantics References George Boolos , The Logic of Provability . Cambridge University Press, 1993. http www.csc.villanova.edu japaridz Giorgi Japaridze and Dick de Jongh, http www.csc.villanova.edu japaridz Text prov.pdf The logic of provability . In Handbook of Proof Theory , S. Buss, ed. Elsevier, 1998, pp. 475 546 ... www.phil.uu.nl preprints preprints PREPRINTS preprint234.pdf Provability logic . In http dx.doi.org 10.1007 1 4020 3521 7 3 Handbook of Philosophical Logic , D. Gabbay and F. Guenthner, eds., vol. 13, 2nd ed., pp. 189 360. Springer, 2005. Per Lindstr m , Provability logic a short introduction . Theoria 62 1996 , pp. 19 61. Craig Smory ski, Self reference and modal logic . Springer, Berlin, 1985. Robert M. Solovay , Provability Interpretations of Modal Logic , Israel Journal of Mathematics, Vol. 25 1976 287 304. http plato.stanford.edu entries logic provability Provability logic , from the Stanford Encyclopedia of Philosophy . Category Modal logic Category Proof theory logic stub es L gica demostrativa ... more details
A logic probe is a hand held pen like test probe used for analyzing and troubleshooting the logical states Boolean logic Boolean 0 or 1 of a digital circuit. While most are powered by the circuit under test, some devices use batteries. They can be used on either Transistor transistor logic TTL transistor transistor logic or CMOS complementary metallic oxide semiconductor integrated circuit devices. There are usually three differently colored LED s on the probe s body Red and green LEDs indicate high and low states respectively An amber LED indicates a pulse as used in a NOID Light to test for pulses to fuel injectors on a electronically controlled fuel injection vehicle The pulse detecting electronics usually has a pulse stretcher circuit so that even very short pulses become visible on the amber LED. A control on the logic probe allows either the capture and storage of a single event or continuous running. Image Logic probe new.jpg right 100px thumb A low cost logic probe When the logic probe is either connected to an invalid logic level a fault condition or a tri state logic tri stated output or not connected at all, none of the LEDs lights up. Another control on the logic probe allow selection of either TTL or CMOS family logic. This is required as these families have different thresholds for V sub IH sub and V sub IL sub . Some logic probes have a separate audible tone for each of the logical states. An oscillating signal causes the probe to alternate between high state and low state tones. A logic probe is a cheap, versatile and convenient digital test instrument, but can test only a single signal at a time. When many logic levels need to be observed or recorded simultaneously, a logic analyzer is used. External links http www.swansontec.com sprobe.html Schematic of a Simple Logic Tester Category Electronic test equipment Category Digital electronics Category Measuring instruments electronics stub cs Logick sonda de Logiktester es Sonda l gica ... more details
Classical logic identifies a class of formal logic s that have been most intensively studied and most widely used. The class is sometimes called standard logic as well. ref name BunninYu2004 cite book ... 0679 5 page 266 ref ref name Gamut1991 cite book author L. T. F. Gamut title Logic, language, and meaning, Volume 1 Introduction to Logic url http books.google.com books?id Z0KhywkpolMC&pg PA156 year ... logic . In D.M. Gabbay, C.J. Hogger, and J.A. Robinson, Eds , Handbook of Logic in Artificial Intelligence and Logic Programming , volume 2, chapter 2.6. Oxford University Press. ref Law of the excluded ... discussions of classical logic normally only include propositional logic propositional and first order logic first order logics. ref Shapiro, Stewart 2000 . Classical Logic. In Stanford Encyclopedia ... plato.stanford.edu entries logic classical ref ref name haack Susan Haack Haack, Susan , 1996 . Deviant Logic, Fuzzy Logic Beyond the Formalism . Chicago The University of Chicago Press. ref The intended semantics of classical logic is bivalence bivalent . With the advent of algebraic logic it became ... semantics for classical propositional logic , the truth values are the elements of an arbitrary Boolean .... Examples of classical logics Aristotle s Organon introduces his theory of syllogism s, which is a logic ... within the syllogistic framework. George Boole s algebraic reformulation of logic, his system of Boolean logic The first order logic found in Gottlob Frege s Begriffsschrift . Non classical logics Main Non classical logic Computability logic is a semantically constructed formal theory of computability, as opposed to classical logic, which is a formal theory of truth integrates and extends classical, linear and intuitionistic logics. Many valued logic , including fuzzy logic , which rejects the law ... logic rejects the law of the excluded middle, double negative elimination, and the De Morgan s laws Linear logic rejects idempotency of entailment as well Modal logic extends classical logic with Truth ... more details
Unreferenced stub auto yes date December 2009 In logic , the comprehension of an object is the totality of intension s, that is, attributes, characters, marks, properties, or qualities, that the object possesses, or else the totality of intensions that are pertinent to the context of a given discussion. This is the correct technical term for the whole collection of intensions of an object, but it is common in less technical usage to see intension used for both the composite and the primitive ideas. See also Extension semantics Extension Extensional definition Intension Intensional definition DEFAULTSORT Comprehension LogicLogic stub Category Concepts in logic ... more details
F logic frame data structure frame Logic programming logic is a knowledge representation and ontology language . F logic combines the advantages of conceptual modeling with object oriented, frame based ... of a logic based language. Features include, among others, object identity, complex objects, inheritance ... computer science encapsulation . F logic stands in the same relationship to object oriented programming as classical predicate calculus stands to relational database programming. F logic was developed ... . F logic was originally developed for deductive databases, but is now most frequently used for semantic technologies, especially the Semantic Web . F logic is considered as one of the formalisms for Ontology information science ontologies , but description logic DL is more popular and accepted, so as the DL based Web Ontology Language OWL . A development environment for F logic was developed in the NeOn ... answering and semantic search . Prior to the version 4 of Protege ontology editor, F Logic is supported as one of the two kinds of ontology. F logic syntax Classes and individuals may be defined in F logic as follows man person. woman person. brad man. angelina woman. This states, that men and women ... to represent axioms in the F logic in the following manner man X < person X AND NOT woman ... logic based ontology formalism the semantics of F logic are normally that of a closed world assumption as opposed to DL s open world assumption . Also, F logic is generally Undecidable problem undecidable , whereas the SHOIN SHOIN description logic that Web Ontology Language OWL DL is based on is decidable. However it is possible to represent more expressive statements in F logic that are not possible with description logics. F logic based Languages http flora.sourceforge.net FLORA 2 is an extension of F logic with HiLog and transaction logic. http dbis.informatik.uni freiburg.de index.php?project ... 771 papers flogic.pdf Paper on F logic, from 1995 Category Knowledge representation Category ... more details
Unreferenced date December 2009 Logic Control is a control surface originally designed by Emagic in cooperation with Mackie . History Logic Control was designed by Emagic as a dedicated control surface for their Logic Pro Logic Digital Audio Workstation software . It was manufactured by Mackie, but distributed by Emagic. About 6 months later, Mackie introduced a physically identical product called Mackie Control which included support for most major DAW applications, but not Logic. The Emagic Logic Control was still available and would only work with Logic. Later, Mackie Control s firmware was revised to include compatibility with Logic. The name of the Mackie Control was changed to Mackie Control Universal MCU . Out of the box, MCU included Lexan overlays with different button legends to support control of other DAWs such as Pro Tools and Cubase. Description Logic Control and now MCU allows to control almost all of Logic s parameters with its hardware faders, buttons and V Pots knobs . Its touch sensitive, motorized faders react to track automation. All transport functions and wheel scrubbing are also available. The unit also controls plug in parameters. Visual feedback including current parameters being edited, parameter values, project location SMPTE time code or bars beats divisions ticks are conveyed by a two line LCD and red 7 segment led displays. See also Logic Pro Mackie Category Computer peripherals Category Electronic musical instruments Category Music hardware ... more details
Cleanup date August 2009 Noncommutative logic is an extension of linear logic which combines the commutative connectives of linear logic with the noncommutative multiplicative connectives of the Joachim ... Hopf algebra s. Noncommutativity in logic By extension, the term noncommutative logic is also ... to a presentation of this acceptance of the term. The oldest noncommutative logic is the Lambek calculus ... of Jean Yves Girard s linear logic there have been several new noncommutative logics proposed, namely the cyclic linear logic of David Yetter, the pomset logic of Christian Retore, and the noncommutative logics BV and NEL studied in the calculus of structures . Noncommutative logic is sometimes called ordered logic , since it is possible with most proposed noncommutative logics to impose a total ... logics do not support such an order, such as Yetter s cyclic linear logic. Note also that while ... the first noncommutative logic in his 1958 paper Mathematics of Sentence Structure to model the combinatory ... formalisms of computational linguistics . Cyclic linear logic David Yetter proposed a weaker structural rule in place of the exchange rule of linear logic, yielding cyclic linear logic. Sequents of cyclic linear logic form a ring, and so are invariant under rotation, where multipremise rules ... ? and of linear logic, allowing nonlinear structural rules to be used together with exchange. Pomset logic Pomset logic was proposed by Christian Retore in a semantic formalism with two dual sequential operators existing together with the usual tensor product and par operators of linear logic, the first logic proposed to have both commutative and noncommutative operators. A sequent calculus for the logic was given, but it lacked a cut elimination theorem instead the sense of the calculus ... this explanation concurs with the difficulty of designing sequent systems for pomset logic that have ... in which linear logic with the mix rule appears as a subsystem. Structads Structads are an approach ... more details
A logic board is the Apple Inc. Apple equivalent of a motherboard . ref name Engadget Cite web url http www.engadget.com 2006 07 08 apple sneaks new logic board into whining macbook pros title Apple sneaks new logic board into whining MacBook Pros accessdate 2008 10 23 author Paul Miller format 2006 publisher Engadget ref The term logic board was coined back in the 1980s, when the compact Macs at the time had two separate circuit components. The term logic board stuck over the years of Macintosh manufacturing, even in the non all in one Macs. A longtime practice for Apple when an existing model was upgraded was to offer a logic board upgrade where a user could bring their computer into an Apple dealer and have the old logic board replaced with the new one, along with other upgrades necessary to bring their computer in line with the new model s specs. The old logic board would be kept by the dealer as a trade in. See also Motherboard Analog board References reflist Category Macintosh internals ... more details
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