Other uses Philosophy sidebar Logic from the Greek wiktionary logik ref possessed of reason ... . Logic is used in most intellectual activities, but is studied primarily in the disciplines of philosophy , mathematics , semantics , and computer science . Logic examines general forms which argument s may take, which forms are valid, and which are fallacies . In philosophy, the study of logic ... of valid inference s within some formal language . ref name stanford logic onthology Logic is also ... ref Logic was studied in several ancient civilizations, including India , ref For example, Nyaya ... at 2200 years. ref and Ancient Greece Greece . Logic was established as a discipline by Aristotle , who gave it a fundamental place in philosophy. The study of logic was part of the classical Trivium education trivium . Logic is often divided into two parts, inductive reasoning and deductive reasoning . Nature The concept of Argument form logical form is central to logic, it being held that the validity ... Aristotelian syllogistic logic and modern symbolic logic are examples of formal logics. Informal logic ... important branch of informal logic. The dialogues of Plato ref cite book author Plato authorlink ... isbn 0 14 015040 4 ref are good examples of informal logic. Mathematical formalism Formal logic is the study ... study of logic. Modern formal logic follows and expands on Aristotle. ref cite book author Aristotle ... Library year 2001 isbn 0 375 75799 6 chapter Posterior Analytics ref In many definitions of logic ... of informal logic vacuous, because no formal logic captures all of the nuance of natural language. Symbolic logic is the study of symbolic abstractions that capture the formal features of logical ... A. G. last Hamilton title Logic for Mathematicians publisher Cambridge University Press year 1980 isbn 0 521 29291 3 ref Symbolic logic is often divided into two branches propositional logic and predicate logic . Mathematical logic is an extension of symbolic logic into other areas, in particular to the study ... 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 ... more details
Dynamic logic may mean In modal logic, dynamic logic modal logic is a modal logic for reasoning about dynamic behaviour in digital electronics, dynamic logic digital logic is used for circuit design disambig ... more details
Symbolic logic may refer to First order logic , a system of formal logic Mathematical logic , a field of mathematics mathdab Category Logic ... 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
Unreferenced date December 2006 For the subject in computer programming dynamic logic modal logic In integrated circuit design, dynamic logic or sometimes clocked logic is a design methodology logic family in Digital circuit digital logic that was popular in the 1970s and has seen a recent resurgence ... . Dynamic logic is distinguished from so called static logic in that it uses a clock signal in its implementation of combinational logic circuits. The usual use of a clock signal is to synchronize transitions in sequential logic circuits, and for most implementations of combinational logic a clock signal is not even needed. Terminology In the context of logic design, the term dynamic logic is more commonly used as compared to clocked logic , as it makes clear the distinction between this type of design and static logic . To additionally confuse the matter, clocked logic is sometimes used as a synonym for sequential logic . This usage is nonstandard and should be avoided. Static versus dynamic logic Advert section date October 2010 The largest difference between static and dynamic logic is that in dynamic logic, a clock signal is used to evaluate combinational logic . However, to truly comprehend the importance of this distinction, the reader will need some background on static logic. In most types of logic design, termed static logic , there is at all times some mechanism to drive the output either high or low. In many of the popular logic styles, such as Transistor transistor logic ... not qualify as distinct from static logic. In contrast, in dynamic logic , there is not always a mechanism ... high or low during distinct parts of the clock cycle. Dynamic logic requires a minimum clock rate .... Static logic has no minimum clock rate the clock can be paused indefinitely. While it may seem ... CPUs use dynamic logic ref http www.anandtech.com show 1647 11 ref , only CPUs designed with fully ... logic, when properly designed, can be over twice as fast as static logic. It uses only the faster ... more details
dablink Not to be confused with intensional logic with an s rather than a t in the initial word . Intentional Logic A Logic Based on Philosophical Realism is a book by Henry Babcock Veatch published in 1952. book stub Category Philosophy books Category Logic literature ... more details
Unreferenced stub auto yes date December 2009 Strict logic is essentially synonymous with 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 mathematical logic and rewriting system s, terms are expressions which can be obtained from variable logic variables and function symbol logic function symbols . Terms serve to denote objects. See also Term first order logic Mathlogic stub Category Mathematical logic Category Rewriting systems ... more details
Wiktionarypar logicLogic may refer to Science and technology 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 logic Digital logic , a class of digital circuits characterized by the technology underlying its logic gates Software Logic Studio , a music production suite by Apple Inc. Logic Pro , a MIDI sequencer and Digital Audio Workstation application, part of Logic Studio Dolby Pro Logic , also known as Pro Logic, a surround sound processing technology See also Logarithm disambig el he ko nl Logica doorverwijspagina ja ... 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 Should not to be confused with binary numeral system . dab ... 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
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
For the subject in digital circuit s also known as clocked logic dynamic logic digital logic Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs and later .... Language Modal logic is characterized by the modal operator s math Box p math box p asserting that math ... is possibly the case. Dynamic logic extends this by associating to every action math a , math the modal operators math a , math and math langle a rangle , math , thereby making it a multimodal logic ... exists , math quantifiers. Dynamic logic permits compound actions built up from smaller actions. While ... s regular expression operators are a good match to modal logic. Given actions math a , math and math ... but does terminate. Axioms These operators can be axiomatized in dynamic logic as follows, taking as already given a suitable axiomatization of modal logic including such axioms for modal operators ... n generalized to arbitrary actions math a , math . Derivations The modal logic axiom math a p equiv ... between implication and inference is the same in dynamic logic as in any other logic whereas the implication ... the dynamic nature of dynamic logic moves this distinction out of the realm of abstract axiomatics ... 1, and therefore is not valid. Derived rules of inference As for modal logic, the inference rules modus ponens and necessitation suffice also for dynamic logic as the only primitive rules it needs, as noted above. However, as usual in logic, many more rules can be derived from these with the help of the axioms. An example instance of such a derived rule in dynamic logic is that if kicking a broken ... is broken, dynamic logic expresses this inference as math b to k b vdash b to k b , math , having as premise ... x , math is 8 to begin with, or 6.5, whence this proposition is not a theorem of dynamic logic ... referential opacity of modal logic in the case when a modality can interfere with a substitution. When ... manner of first order logic to obtain Peano s celebrated axiom math Phi 0 land forall i Phi ... 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
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 is 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 ie. 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
In electronic design , logic design is a step in the standard design cycle in which the functional design of an electronic circuit is converted into the representation which captures Boolean algebra logiclogic operations , arithmetic operations , control flow , etc. A common output of this step is RTL description . Logic design is commonly followed by the circuit design step. ref Naveed Sherwani, Algorithms for VLSI Physical Design Automation ref Logic Operations Image Baops.gif right thumb 450px Various representations of Boolean operations Logic Operations usually consist of boolean AND, OR, XOR and NAND operations, and are the most basic forms of operations in an electronic circuit. Arithmetic Operations Arithmetic operations are usually implemented with the use of logic operators. Circuits such as a binary multiplier or a binary adder are examples of more complex binary operations that can be implemented using basic logic operators. References reflist Category Electronic design logic stub ... more details
Infobox Software name Logic Express logo Deleted image removed Image Logic Express.png 48px Logic Express icon screenshot caption developer Apple Computer latest release version 9.1.3 latest release date 2010 10 28 operating system Mac OS X genre MIDI Music sequencer Sequencer Digital Audio Workstation license Proprietary software Proprietary website http www.apple.com logicexpress apple.com logicexpress Logic Express is a light version of Logic Pro , a MIDI music sequencer sequencer and digital audio workstation software application maintained by Apple Computer Apple that runs on the Mac OS X platform. It was announced on 15 January 2004 for release in March 2004. Logic Pro and Express share most functionality and the same interface. Logic Express is limited to two channel stereo mixdown, while Logic Pro can handle multichannel surround sound Logic Express also lacks support for TDM DAE systems, high end Audio Control Surface control surfaces and Distributed Audio Processing. Both can handle up to 255 audio tracks, depending on system performance CPU , hard disk throughput and seek time . Logic Express 8 comes with 36 software instruments and 73 effect plug ins, including almost all of those in the Logic Pro Package. Those that it doesn t include are Sculpture, a physical modelling ... can upgrade it to Logic Express. See also Logic Studio Logic Pro Logic Control Audio Units Core ... Logic Pro 6 & Logic Express 6. Retrieved January 16, 2004. http www.apple.com pr library 2004 ... logicexpress Official Logic Express home page http www.apple.com logicexpress resources Logic Express Resources Reviews http audio production software review.toptenreviews.com apple logic express review.html Review of Logic Express 9 Top Ten Reviews Apple software Category MIDI Category Digital audio workstation software Category Mac OS only software made by Apple Inc. mac software stub es Logic Express is Logic Express it Logic Express ja Logic Express ... 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 of theorems as a proper subset , superset, or fully exclusive set. A notable example of this is the trivalent 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 W.V.O. Quine s Philosophy of Logic , New Jersey Prentice ... also described what she calls a quasi deviant logic. These logics are different from pure deviant logics ... 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 as novel theorems using ... 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 operators. While deviant and quasi deviant logics are typically proposed as rivals to classical logic, the impetus behind ... Logic, Fuzzy Logic Beyond the Formalism . Chicago The University of Chicago Press. Category Non classical logiclogic stub ... more details
Image Unilog111 enter1 copie.jpg thumb right 450px Universal logic is the field of logic that is concerned with giving an account of what features are common to all logical structures. Universal logic is to logic what universal algebra is to algebra . The term universal logic was introduced in the 1990s by Swiss logician Jean Yves B ziau , but the field has arguably existed for many decades. Some of the works of Alfred Tarski in the early twentieth century, for example, can be regarded as fundamental contributions to universal logic. The First World Congress and School on Universal Logic took place in Montreux, Switzerland in early 2005. Participants included Jean Yves B ziau B ziau , Dov Gabbay , Saul Kripke , and David Makinson . The term universal logic has also been used by some logicians e.g. Richard Sylvan and Ross Brady to mean a logic that is applicable in all situations even impossible ones. Resources B ziau, J. Y. ed . 2005. http www.springer.com birkhauser mathematics book 978 3 7643 8353 4 Logica Universalis Towards a General Theory of Logic . Basel Birkh user Verlag. ISBN 3 7643 7259 1 Brady, R. 2006. Universal Logic . Stanford CSLI Publications. ISBN 1 57586 255 7. A journal dedicated to Universal Logic http www.birkhauser science.com LU Logica Universalis . A book series dedicated to Universal Logic http www.springer.com series 7391 Studies in Universal Logic . External links http www.uni log.org UNILOG 05 First World Congress and School on Universal Logic http www.uni log.org UNILOG 07 Second World Congress and School on Universal Logic http www.uni log.org UNILOG 10 Third World Congress and School on Universal Logiclogic stub Category Logic ... 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
selfref This article refers to a book. For the mathematical concept also called Polish logic, see Polish notation . Polish Logic is an anthology of papers by several authors, including Kazimierz Ajdukiewicz , published in 1967 and covering the period 1920&ndash 1939. The work focus on the contributions of Polish logician s, more particularly, mathematical logic ians, to modern logic . Library of Congress cataloging data LC Control No. 67106639 Type of Material Book Print, Microform, Electronic, etc. Personal Name McCall, Storrs, comp. Main Title Polish logic, 1920 1939 papers by Ajdukiewicz and others Published Created Oxford, Clarendon P., 1967. Description 2 viii, 406 p. 23 cm. Subjects Logic, Symbolic and mathematical Addresses, essays, lectures. LC Classification BC135 .M18 Category History of logic Category 1967 books Category Logic books mathematics lit stub ... 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. 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 Mathematical constructivism Category Systems of formal logic fr Logique minimale uk ... more details
Infobox Software name Logic Studio logo screenshot caption developer Apple Inc. latest release version 9.0 latest release date 2009 07 23 operating system Mac OS X genre Music production license Proprietary software Proprietary website http www.apple.com logicstudio apple.com logicstudio Logic Studio is a music production suite by Apple Inc. The first version of Logic Studio was unveiled on September 12, 2007. Components Apple Loops Utility used to create custom Music loop loops . Compressor software Compressor 3.5 Video compression video and Audio compression data audio data compression application Impulse Response Utility used to create custom convolution reverb s Logic Pro Logic Pro 9 Mainstage software MainStage 2 application for live performances Plug ins & Sounds Soundtrack Pro Soundtrack Pro 3 WaveBurner WaveBurner 1.6 CD Audio mastering mastering application br style clear both Logic Studio Apple software Category Digital audio workstation software Category Mac OS only software made by Apple Inc. Category Software synthesizers Mac software stub de Logic Studio ko it Logic Studio ja Logic Studio ru Logic Studio zh Logic Studio ... 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 passing 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 ... more details
Encyclopedia
top
