Logika

Dina basa sapopoé, logika mangrupa tinimbangan nu dipaké pikeun ngahontal hiji kasimpulan/kacindekan tina sakumpulan sangkaan. Nu leuwih formal, logika mangrupa ulikan ngeunaan valid inference, nyaéta prosés ngahontal hiji kasimpulan/kacindekan tina sakumpulan sangkaan kalawan maké cara/jalan nu sistematis tur sohéh. Ceuk kasarna, kasohéhan ngandung harti nalika sakumpulan sangkaan boga ajén bener, mangka kasimpulanana ogé bener.

Di sagigireun éta, logika nyadiakeun rumus/resép pikeun tinimbangan, nyéta kumaha jalma—ogé mahluk pinter séjénna, mesin, jeung sistem—sakuduna méré alesan. Ngan, rumus modél kitu lain mataholang pikeun logika sorangan, tapi leuwih mangrupa larapan. Kumaha jalma sabenerna méré alesan biasana diulik dina widang séjén, kaasup psikologi kognitif.

Sacara tradisional, logika diulik minangka cabang tina filosofi. Mimiti panengah taun 1800-an logika geus umum diulik na matematik, jeung, nu leuwih mutahir, dina élmu komputer. Minangka élmu, logika nalungtik jeung ngagolongkeun struktur pernyataan jeung argumén sarta ngarancang skéma pikeun nyandikeunana. Ku sabab éta cakupan logika bisa lega pisan, kaasup tinimbangan ngeunaan probabiliti jeung kausaliti. Nu ogé diulik na logika nyéta struktur argumén salah jeung paradoks.

Cakupan logika

Nuturkeun tumuwuhna, loba bébédaan geus diwanohkeun kana logika. Bébédaan ieu disadiakeun pikeun nulungan ngaresmikeun rupa-rupa bentuk logika minangka élmu. Di handap ieu sababaraha bébédaan nu penting.

Tinimbangan deduktif jeung induktif

Sasakalana, logika ngan ngawengku tinimbangan deduktif ngeunaan naon-naon nu jadi akibat tina prémis nu aya. Ngan, perlu dicatet yén tinimbangan induktif—ulikan nurunkeun kacindekan umum nu bisa dipercaya tina observasi—kadang diasupkeun dina ulikan logika. Patali jeung éta, urang kudu ngabédakeun antara kasahéhan deduktif jeung induktif. Hiji inferensi sacara déduktif bakal sohéh lamun jeung ukur lamun heneuweuh situasi nu ngamungkinkeun sakabéh prémis bener sarta kasimpulannana salah. Ide kasohéhan déduktif bisa dinyatakeun sacara taliti keur sistim logika formal dina ide semantik nu gampang dipikaharti. Kasohéhan induktif dina sisi lianna nyaratkeun urang keur ngadefinisikeun generalisasi nu handal tina sababaraha set panalungtikan. Tugas nyayagakeun definisi ieu bisa dideukeutan dina sababaraha cara, sababaraha di antarana teu pati resmi dibandingkeun lianna; sababaraha definisi ieu bisa maké modél matematis probabilitas. Keur lolobana bagian, sawala urang ngeunaan logika ukur patali jeung logika déduktif.

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Logika formal jeung informal

Somewhat arbitrarily, study of logic is divided into formal and informal logic.

Formal logic (sometimes called symbolic logic) approaches logic and in particular logical argument as a set of rules for manipulating symbols. There are two kinds of rules in any system of formal logic: Syntax rules and rules of inference. Syntax says how to build méaningful expressions; rules of inference say how to obtain true formulas from other true formulas. Logic also needs semantics, which says how to assign méaning to expressions. Formal logic encompasses a wide variety of logical systems. For instance, propositional logic and predicate logic are a kind of formal logic, as well as temporal logic, modal logic, Hoare logic, the calculus of constructions etc. Higher order logics refer to logical systems based on a hierarchy of types.

Informal logic is the study of logic as used in natural language arguments. Informal logic is complicated by the fact that it may be very hard to téase out the formal logical structure imbedded in an argument. Informal logic is also more difficult because the semantics of natural language assertions is much more complicated than the semantics of formal logical systems.

Following are more specific discussions of some systems of logic. See also: list of topics in logic.

Logika Aristotelian

Artikel utama: Aristotelian logic.

The Prior Analytics was Aristotle's pioneering work establishing a system of logic and inference based on the forms of the premises and the conclusion. These rules were codified into various forms of syllogisms which, until recently at léast, were part of the standard high school curriculum in the West, much like euclidéan plane géometry. Aristotelian logic is sometimes referred to as formal logic because it specifically déals with forms of réasoning, but is not formal in the sense we use it here or as is common in current usage. It can be considered as a precursor to formal logic.

In the tradition of aristotelian logic is also term logic.

Logika matematis

Artikel utama: Mathematical logic.

Mathematical logic refers to two distinct aréas of reséarch: The first, primarily of historical interest, is the use of formal logic to study mathematical réasoning, and the second, in the other direction, the application of mathematics to the study of formal logic. At the beginning of the twentieth century, philosophical logicians including (Frege, Russell) attempted to prove that mathematics could be entirely reduced to logic. The reduction had limited success (for réasons which are well beyond the scope of this article) but in the process, logic took on much of the notation and methodology of mathematics. In the other direction, in the éarly 1930s, Kurt Gödel embarked on an ambitious program of considering logic and proof as an object of mathematical study, léading him to state far réaching results on provability and modél théory such as the incompleteness theorems of first order arithmetic. This line of reséarch has continued to the present time, léading to various stunning results such as for example, Paul Cohen's proof of the independence of the continuum hypothesis from the axioms of Zermelo-Fraenkel set théory.

Logika filosofis

Main article philosophical logic

Philosophical logic déals with formal descriptions of natural language. Most philosophers assume that the bulk of "normal" proper réasoning can be captured by logic, if one can find the right method for translating ordinary language into that logic. Philosophical logic is essentially a continuation of the traditional discipline that was called "Logic" before it was supplanted by the invention of Mathematical logic. Philosophical logic has a much gréater concern with the connection between natural language and logic. As a result, philosophical logicians have contributed a gréat déal to the development of non-standard logics (e.g., free logics, tense logics) as well as various extensions of classical logic (e.g., modal logics), and non-standard semantics for such logics (e.g., supervaluation semantics).

Multi-valued logic

The logics discussed above are all "bivalent" or "two-valued"; that is, the semantics for éach of these languages will assign to every sentence either the value "True" or the value "False." Systems which do not always maké this distinction are known as non-Aristotelian logics, or multi-valued logics.

In the éarly 20th century Jan Łukasiewicz investigated the extension of the traditional true/false values to include a third value, "possible".

Logics such as fuzzy logic have since been devised with an infinite number of "degrees of truth", e.g., represented by a real number between 0 and 1. Bayesian probability can be interpreted as a system of logic where probability is the subjective truth value.

Logic and computation

Logic is extensively used in the fields of artificial intelligence, and computer science.

In the 1950s and 1960s, reséarchers predicted that when human knowledge could be expressed using logic with mathematical notation, it would be possible to créate a machine that réasons, or artificial intelligence. This turned out to be more difficult than expected because of the complexity of human réasoning. Logic programming is an attempt to maké computers do logical réasoning and Prolog programming language is commonly used for it.

In symbolic logic and mathematical logic, proofs by humans can be computer-assisted. Using automated theorem proving the machines can find and check proofs, as well as work with proofs too lengthy to be written out by hand.

In computer science, Boolean algebra is the basis of hardware design, as well as much software design.

There are also various systems for réasoning about computer programs. Hoare logic is one the éarliest of such systems. Other systems are CSP, CCS, pi-calculus for réasoning about concurrent processes or mobile proceses. See also computability logic; this is a formal théory of computability in the same sense as classical logic is a formal théory of truth.

Tempo ogé

Konsép logika

Techniques and rules

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