A deductivesystem also called a deductive apparatus of a formal system consists of the axiom s or axiom schema ta and rules of inference that can be used to formal proof derive the theorem s of the system. ref Hunter, Geoffrey, Metalogic An Introduction to the Metatheory of Standard First Order Logic, University of California Pres, 1971 ref Such a deductivesystem is intended to preserve deductive reasoning deductive qualities in the formula mathematical logic formula s that are expressed in the system. Usually the quality we are concerned with is truth as opposed to falsehood. However, other modal logic modalities , such as Theory of justification justification or belief may be preserved instead. In order to sustain its deductive integrity, a deductive apparatus must be definable without reference to any intended interpretation of the language. The aim is to ensure that each line of a Mathematical proof derivation is merely a syntactic consequence of the lines that precede it. There should be no element of any Interpretation logic interpretation of the language that gets involved with the deductive nature of the system. See also Formal grammar Natural deduction Axiomatic system Proof calculus References reflist logic Category Syntactic entities Category Proof theory Category Deduction Category Formal systems el es Sistema deductivo nl Deductief systeem pt Sistema dedutivo ... more details
Unreferenced stub auto yes date December 2009 Orphan date February 2009 A deductive language is a computer programming language in which the program is a collection of predicates facts and rules that connect them. Such a language is used to create knowledge based system s or expert system s which can deduce answers to problems set them by applying the rules to the facts they have been given. An example of a deductive language is Prolog , or it s database query cousin, Datalog . DEFAULTSORT Deductive Language Compu lang stub Category Computer programming Category Databases ... more details
A Deductive database is a database system that can make Deductive reasoning deductions i.e. conclude additional facts based on wiktionary rule rules and facts stored in the deductive database. Datalog is the language typically used to specify facts, rules and queries in deductive databases. Deductive databases have grown out of the desire to combine logic programming with relational database s to construct systems that support a powerful formalism and are still fast and able to deal with very large datasets. Deductive databases are more expressive than relational databases but less expressive than logic programming systems. Deductive databases have not found widespread adoptions outside academia, but some of their concepts are used in today s relational databases to support the advanced features of more recent SQL standards. Citation needed date November 2011 Deductive databases and logic programming Deductive databases reuse a large number of concepts from logic programming rules and facts specified in the deductive database language Datalog look very similar to those in Prolog . However, there are a number of important differences between deductive databases and logic programming Order sensitivity and procedurality in Prolog, program execution depends on the order of rules in the program and on the order of parts of rules these properties are used by programmers to build efficient programs. In database languages like SQL or Datalog , however, program execution is independent of the order of rules and facts. Special predicates In Prolog, programmers can directly influence the procedural evaluation of the program with special predicates such as the Cut logic programming cut , this has no correspondence in deductive databases. Function symbols Logic Programming languages allow Functional predicate function symbols to build up complex symbols. This is not allowed in deductive databases. Tuple oriented processing Deductive databases use set oriented processing while logic ... more details
The deductive mood is an epistemic modality epistemic grammatical mood that indicates that the truth of the statement was deduced from other information, rather than being directly known. ref cite web url http www.sil.org linguistics GlossaryOflinguisticTerms WhatIsDeductiveMood.htm title What is deductive mood? publisher SIL International work Glossary of linguistic terms last Loos first Eugene E. coauthors Susan Anderson Dwight H. Day, Jr. Paul C. Jordan J. Douglas Wingate accessdate 2009 12 28 ref In English, deductive mood is often indicated by the word wikt must must , which is also used for many other purposes. By contrast, some other languages have special words or verb affixes to indicate deductive mood specifically. An example in English language English There s gas in the house Someone must have left the stove on deductive indicated by must References references Grammatical moods Category Grammatical moods Ling morph stub ... more details
Refimprove date May 2010 Wiktionary fallacy A deductive fallacy is defined as a deductive argument that is invalid. The argument itself could have true premise s, but still have a false logical consequence conclusion . ref cite web url http www.nizkor.org features fallacies title Description of Fallacies last Labossiere first Michael year 1995 publisher The Nizkor Project accessdate 2008 09 09 ref Thus, a deductive fallacy is a fallacy where deduction goes wrong, and is no longer a logical process. Logical fallacy The standard Aristotelian logical fallacies are Fallacy of four terms Quaternio terminorum Fallacy of the undistributed middle Fallacy of illicit process of the illicit major major or the illicit minor minor term and Affirmative conclusion from a negative premise . Other logical fallacies include The begging the question self reliant fallacy In philosophy , the term logical fallacy properly refers to a formal fallacy a flaw in the structure of a deductive reasoning deductive logical argument argument , which renders the argument validity invalid . However, it is often used more generally in informal discourse to mean an argument that is problematic for any reason, and thus encompasses informal fallacy informal fallacies as well as formal fallacies valid but soundness unsound claims or poor non deductive argumentation. The presence of a formal fallacy in a deductive argument does not imply anything about the argument s premises or its conclusion see fallacy fallacy . Both may actually be true, or even more probable as a result of the argument e.g. appeal to authority , but the deductive argument is still invalid because the conclusion does not follow from the premises ... is not a deductive one for instance an inductive argument that incorrectly applies principles ..., the deductive fallacy is formed by points that may individually appear logical, but when placed ... 2 relevance fallacies formal fallacy informal fallacy DEFAULTSORT Deductive Fallacy Category Deduction ... more details
wiktionary deductive reasoning Deductive reasoning , also called deductive logic , is the process of reasoning ... 2009 publisher Wadsworth location Belmont, CA isbn 978 0 495 50629 4 pages 578 ref Deductive reasoning involves using given true premises to reach a conclusion that is also true. Deductive reasoning contrasts .... An example of a deductive argument All men are mortal. Socrates is a man. Therefore, Socrates is mortal ... as a man . Deductive reasoning moves from theory to observations or findings. So, in the above example ... form of deductive reasoning. A single Material conditional conditional statement is made, and a hypothesis ... basic form is listed below P Q conditional statement P hypothesis stated Q conclusion deduced In deductive ... conclude that this could be a false statement. Deductive Logic Validity and Soundness Deductive arguments are evaluated in terms of their validity and soundness . It is possible to have a deductive argument ... quarterbacks. This theory of deductive reasoning also known as term logic was developed ... logic . Deductive reasoning can be contrasted with inductive reasoning , in regards to validity ... of thought . Reasoning and Education Typically, deductive reasoning is thought of as a skill that develops without any formal teaching or training. As a result of this belief, deductive skills are not taught ... mathematical proofs which heavily relies on deductive reasoning in high school. Researchers ... for deductive reasoning journal Mathematical Thinking and Learning year 2008 volume 10 issue 2 ... J. P. title Teaching and assessing deductive reasoning skills journal Journal of Experimental Education ... mathematics Insights from psychological research into students ability for deductive reasoning journal ... students who plan on continuing into higher education. Deductive reasoning is a central component ... cite journal last Leighton first J. P. title Teaching and assessing deductive reasoning skills journal ... Defeasible reasoning Decision making Decision theory Fallacy Geometry Hypothetico deductive method ... more details
Other uses Closure disambiguation Peter D. Klein , in the second edition of The Cambridge Dictionary of Philosophy , defines closure mathematics closure as follows blockquote A set mathematics set of objects, var O var , is said to exhibit closure or to be closed under a given closure operator operation , var R var , provided that for every object, var x var , if var x var is a member of var O var and var x var is var R var related to any object, var y var , then var y var is a member of var O var . links not in original blockquote In propositional calculus propositional logic , the set of all propositions exhibits deductive closure if set var O var is the set of propositions, and operation var R var is logical entailment math vdash math , then provided that proposition var p var is a member of var O var and var p var is var R var related to var q var i.e., p math vdash math q , var q var is also a member of var O var . In the philosophical branch of epistemology , many philosophers have and continue to debate whether particular subsets of propositions&mdash especially ones ascribing knowledge or justification of a belief to a subject&mdash are closed under deduction. Epistemic closure It is not the case that knowledge is closed under deduction that is, if person var S var knows var p var , and var p var entails var q var , then var S var knows var q var sometimes called the straight principle . ref name stanford Luper, Steven. The Epistemic Closure Principle. Stanford Encyclopedia of Philosophy . Dec 31, 2001. http plato.stanford.edu entries closure epistemic CloPri accessed November 2, 2006 . ref A subject may not actually believe var q var , for example, regardless of whether he or she is justified or warranted. Thus, one might instead say that knowledge is closed under known deduction if, while knowing var p var , var S var believes var q var because var S var knows that var p var entails var q var , then var S var knows var q var . ref name stanford ... more details
Multiple issues disputed March 2008 POV March 2008 The hypothetico deductive model or method , first so named by William Whewell , ref William Whewell 1837 History of the Inductive Sciences ref ref William Whewell 1840 , Philosophy of the Inductive Sciences ref is a proposed description of scientific method . According to it, scientific inquiry proceeds by formulating a hypothesis in a form that could conceivably be falsified by a test on observable data. A test that could and does run contrary to predictions of the hypothesis is taken as a Falsifiability falsification of the hypothesis. A test that could but does not run contrary to the hypothesis corroborates the theory. It is then proposed to compare the explanatory value of competing hypotheses by testing how stringently they are corroborated by their predictions. Quotation2 From the long tradition of empiricism we have inherited the hypothetico deductive model of scientific research . p.86 Brody, Thomas A. 1993 , The Philosophy Behind Physics , Springer Verlag, ISBN 0 387 55914 0 . Luis De La Pe a and Peter E. Hodgson, eds. Qualification of corroborating evidence is sometimes raised as philosophically problematic. The raven paradox is a famous example. The hypothesis that all ravens are black would appear to be corroborated by observations of only black ravens. However, all ravens are black is Logical equivalence logically equivalent to all non black things are non ravens this is the contraposition form of the original implication ... Knowledge , pp. 30, 360. ref Despite the philosophical questions raised, the hypothetico deductive ... statement of the hypothetico deductive method ref Peter Godfrey Smith 2003 Theory and Reality ... references Related subjects Confirmation bias Deductive nomological Explanandum Explanandum and explanans ... Deductive reasoning Inductive reasoning Analogy philosophy of science DEFAULTSORT Hypothetico Deductive Model Category Scientific method Category Philosophy of science Category Conceptual models ... more details
The deductive nomological model or D N model is a Formal science formalized Citation needed date March 2011 view of science scientific explanation in natural language . It characterizes scientific explanations primarily as deductive reasoning deductive arguments with at least one natural law statement among its premises. Nomological comes from the Greek word nomos nomos , i.e., law. Background The D N model is known by many names, including the covering law model , the subsumption theory , Hempel s model , the Hempel Oppenheim model , and the Popper Hempel model of explanation Niiniluoto, 1995 . Its introduction in the philosophical literature is part of a broad general discussion about the nature of scientific explanation i.e., what it is, what it should be, etc. . The D N model is taught implicitly in schools, and approximates our pre theoretical conception of science, which many non experts hold. It was initially formalized by Carl Hempel and Paul Oppenheim in their article Studies in the Logic of Explanation 1948 . A sketch of it can be found in Karl Popper s Logic of Scientific Discovery 1934 . Formalization The model offers the following account of scientific explanation , where an explanation is set out as a formalized argument Let p be the explanandum the statement that describes the phenomenon or phenomena to be explained. Let s sub 1 sub . . . s sub n sub be the explanans the statements that explain the statement P . In the D N model, at least one of the statements s sub i sub must be a law like statement Citation needed date March 2011 a problematic concept, but initially thought to be captured by term logic universal affirmatives , i.e., statements of the form ... constitutes a correct deductive nomological explanation of p s sub 1 sub . . . s sub n sub ... 2011 See also Related subjects Explanandum Explanandum and explanans Hypothetico deductive model ... Deductive reasoning Inductive reasoning References and further reading cite journal last Hempel ... more details
Notability Books date January 2010 Primary sources date January 2010 Radiohead and Philosophy Fitter Happier More Deductive is a book edited by Brandon W. Forbes and George A. Reisch, published as Volume 38 in the Popular Culture and Philosophy series of the Open Court Publishing Company . It is a collection of philosophical insights into various aspects of Radiohead s music, by a varied group of academics and other writers, including David Dark , Tim Footman and Mark Greif . References http radioheadandphilosophy.com Radiohead and Philosophy website http www.opencourtbooks.com books n radiohead.htm Open Court Publishing Company Book Review http www.opencourtbooks.com podcast.htm Podcast of Selected Chapters Category Radiohead ... more details
The System can refer to Any system Any system of government , law , or bureaucracy political system . The phrase in this usage can carry negative connotations. Systema , a Russian martial art Das System , a derogatory term used by the NSDAP Nazis to denote contemptuously the Weimar Republic . In media The System band , an American synth pop duo founded in 1982 The System film The System film , a 1964 British film The System satellite radio , a channel on WorldSpace satellite radio Derren Brown The System The System , a 2008 TV special starring Derren Brown The System , a book on chess by Hans Berliner The System , a comic book by Peter Kuper The System , a song by punk band The Black Pacific See also System disambiguation disambig ... more details
In mathematics , System T can refer to A theory of arithmetic in all finite types use in G del s Dialectica interpretation An axiom system of modal logic SIA ... more details
Other uses Image System boundary.svg thumb right 250px A schematic representation of a closed system and its boundary A system from Latin syst ma , in turn from Greek language Greek lang grc syst ma, whole compounded of several parts or members, system , literary composition ref http www.perseus.tufts.edu ... or interdependent components forming an integrated whole. A system is a set of Element mathematics ..., energy, information, or data Systems have interconnectivity the various parts of a system have ... of functions The term system may also refer to a set of rules that governs structure and or behavior. History The word system in its meaning here, has a long history which can be traced back to Plato ... more ancient times, as it derives from the verb sun stemi , uniting, putting together. System means ..., before Descartes, there was no system . Plato had no system . Aristotle had no system . Marshall ... American Library, New York, 1967, p. 288 . In the 19th century the first to develop the concept of a system ... . In 1824 he studied the system which he called the working substance , i.e. typically a body of water vapor, in steam engines, in regards to the system s ability to do work when heat is applied ... systems surroundings and began to use the term working body when referring to the system. One ... to the concept of a system was done by Norbert Wiener and Ross Ashby who pioneered the use of mathematics ... to Cybernetics , Chapman & Hall. ref In the 1980s the term complex adaptive system was coined at the interdisciplinary .... System concepts Environment and boundaries Systems theory views the world as a complex system of interconnected parts. We scope a system by defining its Boundary topology boundary this means choosing which entities are inside the system and which are outside part of the environment systems environment . We then make simplified representations Scientific modelling models of the system in order ... and or the behavior of the system. Natural and human made systems There are natural and human made ... more details
refimprove date April 2010 System L is a natural deductive logic developed by John Lemmon E.J. Lemmon . Derived from Patrick Suppes Suppes method, it represents natural deduction proofs as sequences of justified steps. Description of the deductivesystem The syntax of proof is governed by nine primitive rules The Rule of Assumption A Modus Ponendo Ponens MPP The Rule of Double Negation DN The Rule of Conditional Proof CP The Rule of introduction I The Rule of elimination E The Rule of introduction I The Rule of elimination E Reductio Ad Absurdum RAA In system L, a proof has a definition with the following conditions has a finite sequence of well formed formula s or wffs each line of it is justified by a rule of the system L the last line of the proof is what is intended, and this last line of the proof uses only the premises which were given, if any. If no premise is given, the sequent is called theorem. Therefore, the definition of a theorem in system L is a theorem is a sequent that can be proved in system L, using an empty set of assumptions. Examples An example of the proof of a sequent Modus tollens Modus Tollendo Tollens in this case class wikitable align center bgcolor FFEBAD colspan 4 p q , q p Modus Tollendo Tollens MTT Assumption number Line number Formula wff Lines in use and Justification bgcolor bbffbb 1 bgcolor bbffbb 1 bgcolor bbffbb p q bgcolor bbffbb A bgcolor bbffbb 2 bgcolor bbffbb 2 bgcolor bbffbb q bgcolor bbffbb A bgcolor bbffbb 3 bgcolor bbffbb 3 bgcolor bbffbb p bgcolor bbffbb A for RAA bgcolor bbffbb 1,3 bgcolor bbffbb 4 bgcolor bbffbb q bgcolor bbffbb 1,3,MPP bgcolor bbffbb 1,2,3 bgcolor bbffbb 5 bgcolor bbffbb q q bgcolor bbffbb 2,4, I bgcolor bbffbb 1,2 bgcolor bbffbb 6 bgcolor bbffbb p bgcolor bbffbb 3,5,RAA align center bgcolor BBBBFF colspan ... by its inputs. See also Deductivesystem s External links Pelletier, Jeff, http www.sfu.ca jeffpell ... bgcolor BBBBFF colspan 4 Q.E.D Each rule of system L has its own requirements for the type of input ... more details
In information technology a reasoning system is any software application , hardware device or combination of software and hardware whose computational function is to generate conclusions from available knowledge using logic logical techniques of Deductive reasoning deduction , Inductive reasoning induction or other forms of Reason Logical reasoning methods and argumentation reasoning . Reasoning systems are a subset of a broader category of Intelligent system intelligent systems . They play an important role in the practical implementation knowledge engineering and artificial intelligence . A reasoning system manipulates previously acquired knowledge in order to generate new knowledge. Knowledge is typically represented symbolically as informational facts and propositional statements that capture assertions, assumptions, beliefs and other premises. Sub symbolic Connectionism connectionist knowledge representations may also be used e.g., trained Neural network neural nets . Reasoning systems ... significant variation in terms of Formal system systems of logic and formality. Most reasoning systems ... reasoning systems employ deductive reasoning to draw Inference inferences from available knowledge ... chaining , respectively. Although reasoning systems widely support deductive inference, some ... uncertainty . This is important when building situated Distributed Multi Agent Reasoning System reasoning ... approaches to handling uncertainty. These include the use of Expert system Certainty factors certainty ... system This section provides a non exhaustive and informal categorisation of common types of reasoning system. These categories are not discreet. They overlap to a significant degree and share ... on formal logic, and has wide application across many disciplines. Expert systems Expert system ... Production system production systems to support forward or backward chaining. Each rule production ... A Procedural Reasoning System procedural reasoning system PRS uses reasoning techniques to select ... more details
mathematical logic , a Hilbert system , sometimes called Hilbert calculus or Hilbert&ndash Ackermann system , is a type of system of Deductive reasoning formal deduction attributed to Gottlob Frege ref name M t & Ruzsa 1997 M t & Ruzsa 1997 129 ref and David Hilbert . These deductivesystem ...In mathematical physics , Hilbert system is an infrequently used term for a physical system described ... called Hilbert Lewis system s, are generally axiomatised with two additional rules, the necessitation ... the Hilbert system in such a way that its rules of inference contain only Judgment mathematical ... of the deduction system In a Hilbert style deduction system, a formal deduction is a finite sequence ... that logic. We describe here a Hilbert system with nine axioms and just the rule modus ponens ... to math and only the quantifier math forall math . Later we show how the system can be extended ... the propositional system to axiomatise classical predicate logic . Likewise, these three rules extend system for intuitionstic propositional logic with P1 3 and P4i to intuitionistic predicate logic ... extensions It is common to include in a Hilbert style deduction system only axioms for implication ... in the extended system if and only if is derivable in the original system. When fully extended, a Hilbert style system will resemble more closely a system of natural deduction . Existential quantification ... no deductive power, in the sense that a deduction using the new deduction rules can be converted into a deduction ... A. Tarski, Logic, semantics, metamathematics, Oxford, 1956 ref The original system by Gottlob ... calculus . Bertrand Russell Russell and Alfred North Whitehead Whitehead also suggested a system with five ... system then correspond to combinator terms in combinatory logic. See also Curry Howard ... isbn 0 7204 2103 9 See in particular Chapter IV Formal System pp. 69&ndash 85 wherein Kleene presents ... style deduction system restricted to propositional calculus . DEFAULTSORT Hilbert System ... more details
X System or System X may refer to System X IBM System x , server platform System X album System X computing , supercomputer System X telephony , digital switching platform X System Esperanto orthography X system in Esperanto orthography SIGSALY , secure voice transmission system sometimes called X System Taito X System , arcade system board X Window System disambig ... more details
In artificial intelligence , an expert system is a computer system that emulates the decision making ... Chuks , School of Science Education, Expert system a catalyst in educational development in Nigeria The ability of this system to explain the reasoning process through back traces ... provides an additional ... Korelsky, Benoit Lavoie A new approach to expert system explanations ref ref http www.pcmag.com ... Crevier 1993 pp 145 62, 197 203 ref An expert system has a unique structure, different from traditional Programming programs . It is divided into two parts, one fixed, independent of the expert system the inference engine, and one variable the knowledge base. To run an expert system, the engine ... and Agbo Okechuku Chuks , School of Science Education, Expert system a catalyst in educational ... Conversational Programming System conversational . ref Cite doi 10.1145 505282.505285 ref ref cite ..., Rule Based Expert System Shell example of code using the Prolog rule based expert system shell ref that is to say a software structure ready to receive any expert system and to run it. It integrates ..., 2007, Extensions of Deductive Concept in Logic Programing and Some Applications the defects of PROLOG system the expansion concerning Horn clauses, escaping negation treatment as definite failure ... offered expert system courses and two thirds of the Fortune 1000 companies applied the technology in daily ... the wheel, expert system shells were created that had more specialized features for building large ..., with MS DOS operating system. Its low price started to multiply users and opened a new market for computing ... market, showing that AI technology was not mature. In 1986, a new expert system generator ... Service build your own expert system Intelligence Service is a development environment for expert ... to develop its own expert system ref ref http www.tree logic.com Articles 01, 20seul 20IS 20fait 20de .... Software architecture The rule base or knowledge base In expert system technology, the knowledge base ... more details
Mirror System may refer to Mirror System , a spin off project from System 7 band System 7 Steve Hillage & Miquette Giraudy Mirror System album Mirror System , their first album disambig ... more details
saved book title System subtitle cover image System boundary.svg cover color DarkGoldenRod System Main article System Study of systems Systems theory Systems science Characteristics of systems Abstraction Structure Behavior Interconnectivity System concepts Boundary topology Boundary Environment systems Environment Scientific modelling Open system systems theory Open system Closed system Types of systems Conceptual system Physical system Social structure Category Wikipedia books on systems System ... more details
System 8 may mean Mac OS 8 , a late 1990s version of the Macintosh operating system Copland operating system Copland , an unreleased operating system disambig ... more details
Single system may refer to Single system image , a concept in cluster computing Single system interpretation , a concept in Marxist theory Single system recording , a concept in film production disambig ... more details
L system may refer to L system or Lindenmayer systems in biology L carrier AT&T Transcontinental Cable System Taito L System arcade system board An alternative name for Chicago L mass transit system The main system of transport for tyrosine across biological cell membranes and the Blood brain barrier Blood Brain Barrier . disambig ... more details
Encyclopedia
top
