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Prove
Proof most often refers to: * Proof (truth), argument or sufficient evidence for the truth of a proposition * Alcohol proof, a measure of an alcoholic drink's strength Proof may also refer to: Mathematics and formal logic * Formal proof, a construct in proof theory * Mathematical proof, a convincing demonstration that some mathematical statement is necessarily true * Proof complexity, computational resources required to prove statements * Proof procedure, method for producing proofs in proof theory * Proof theory, a branch of mathematical logic that represents proofs as formal mathematical objects * Statistical proof, demonstration of degree of certainty for a hypothesis Law and philosophy * Evidence, information which tends to determine or demonstrate the truth of a proposition * Evidence (law), tested evidence or a legal proof * Legal burden of proof, duty to establish the truth of facts in a trial * Philosophic burden of proof, obligation on a party in a dispute to provide s ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Legal Burden Of Proof
In a legal dispute, one party has the burden of proof to show that they are correct, while the other party had no such burden and is presumed to be correct. The burden of proof requires a party to produce evidence to establish the truth of facts needed to satisfy all the required legal elements of the dispute. The burden of proof is usually on the person who brings a claim in a dispute. It is often associated with the Latin maxim ''semper necessitas probandi incumbit ei qui agit'', a translation of which is: "the necessity of proof always lies with the person who lays charges." In civil suits, for example, the plaintiff bears the burden of proof that the defendant's action or inaction caused injury to the plaintiff, and the defendant bears the burden of proving an affirmative defense. The burden of proof is on the prosecutor for criminal cases, and the defendant is presumed innocent. If the claimant fails to discharge the burden of proof to prove their case, the claim will be ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Proof
A mathematical proof is an inferential argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The argument may use other previously established statements, such as theorems; but every proof can, in principle, be constructed using only certain basic or original assumptions known as axioms, along with the accepted rules of inference. Proofs are examples of exhaustive deductive reasoning which establish logical certainty, to be distinguished from empirical arguments or non-exhaustive inductive reasoning which establish "reasonable expectation". Presenting many cases in which the statement holds is not enough for a proof, which must demonstrate that the statement is true in ''all'' possible cases. A proposition that has not been proved but is believed to be true is known as a conjecture, or a hypothesis if frequently used as an assumption for further mathematical work. Proofs employ logic expressed in mathematical symbols ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Complexity
In logic and theoretical computer science, and specifically proof theory and computational complexity theory, proof complexity is the field aiming to understand and analyse the computational resources that are required to prove or refute statements. Research in proof complexity is predominantly concerned with proving proof-length lower and upper bounds in various propositional proof systems. For example, among the major challenges of proof complexity is showing that the Frege system, the usual propositional calculus, does not admit polynomial-size proofs of all tautologies. Here the size of the proof is simply the number of symbols in it, and a proof is said to be of polynomial size if it is polynomial in the size of the tautology it proves. Systematic study of proof complexity began with the work of Stephen Cook and Robert Reckhow (1979) who provided the basic definition of a propositional proof system from the perspective of computational complexity. Specifically Cook and Reckhow ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evidence (law)
The law of evidence, also known as the rules of evidence, encompasses the rules and legal principles that govern the proof of facts in a legal proceeding. These rules determine what evidence must or must not be considered by the trier of fact in reaching its decision. The trier of fact is a judge in bench trials, or the jury in any cases involving a jury. The law of evidence is also concerned with the quantum (amount), quality, and type of proof needed to prevail in litigation. The rules vary depending upon whether the venue is a criminal court, civil court, or family court, and they vary by jurisdiction. The quantum of evidence is the amount of evidence needed; the quality of proof is how reliable such evidence should be considered. Important rules that govern admissibility concern hearsay, authentication, relevance, privilege, witnesses, opinions, expert testimony, identification and rules of physical evidence. There are various standards of evidence, standards sh ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof Theory
Proof theory is a major branchAccording to Wang (1981), pp. 3–4, proof theory is one of four domains mathematical logic, together with model theory, axiomatic set theory, and recursion theory. Jon Barwise, Barwise (1978) consists of four corresponding parts, with part D being about "Proof Theory and Constructive Mathematics". of mathematical logic that represents Mathematical proof, proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. Proofs are typically presented as Recursive data type, inductively-defined data structures such as list (computer science), lists, boxed lists, or Tree (data structure), trees, which are constructed according to the axioms and rule of inference, rules of inference of the logical system. Consequently, proof theory is syntax (logic), syntactic in nature, in contrast to model theory, which is Formal semantics (logic), semantic in nature. Some of the major areas of proof theory include structural proof theory, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Philosophic Burden Of Proof
The burden of proof (Latin: ''onus probandi'', shortened from ''Onus probandi incumbit ei qui dicit, non ei qui negat'') is the obligation on a party in a dispute to provide sufficient warrant for its position. Holder of the burden When two parties are in a discussion and one makes a claim that the other disputes, the one who makes the claim typically has a ''burden of proof'' to justify or substantiate that claim especially when it challenges a perceived ''status quo''. This is also stated in Hitchens's razor, which declares that "what may be asserted without evidence, may be dismissed without evidence." Carl Sagan proposed a related criterion – "extraordinary claims require extraordinary evidence" – which is known as the Sagan standard. While certain kinds of arguments, such as logical syllogisms, require mathematical or strictly logical proofs, the standard for evidence to meet the burden of proof is usually determined by context and community standards and conventions. ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof (truth)
A proof is sufficient evidence or a sufficient argument for the truth of a proposition. The concept applies in a variety of disciplines, with both the nature of the evidence or justification and the criteria for sufficiency being area-dependent. In the area of oral and written communication such as conversation, dialog, rhetoric, etc., a proof is a persuasive perlocutionary speech act, which demonstrates the truth of a proposition. In any area of mathematics defined by its assumptions or axioms, a proof is an argument establishing a theorem of that area via accepted rules of inference starting from those axioms and from other previously established theorems. The subject of logic, in particular proof theory, formalizes and studies the notion of formal proof. In some areas of epistemology and theology, the notion of justification plays approximately the role of proof, while in jurisprudence the corresponding term is evidence, with "burden of proof" as a concept common to both ph ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Evidence
Evidence for a proposition is what supports this proposition. It is usually understood as an indication that the supported proposition is true. What role evidence plays and how it is conceived varies from field to field. In epistemology, evidence is what justifies beliefs or what makes it rational to hold a certain doxastic attitude. For example, a perceptual experience of a tree may act as evidence that justifies the belief that there is a tree. In this role, evidence is usually understood as a private mental state. Important topics in this field include the questions of what the nature of these mental states is, for example, whether they have to be propositional, and whether misleading mental states can still qualify as evidence. In phenomenology, evidence is understood in a similar sense. Here, however, it is limited to intuitive knowledge that provides immediate access to truth and is therefore indubitable. In this role, it is supposed to provide ultimate justifications for ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Statistical Proof
Statistical proof is the rational demonstration of degree of certainty for a proposition, hypothesis or theory that is used to convince others subsequent to a statistical test of the supporting evidence and the types of inferences that can be drawn from the test scores. Statistical methods are used to increase the understanding of the facts and the proof demonstrates the validity and logic of inference with explicit reference to a hypothesis, the experimental data, the facts, the test, and the odds. Proof has two essential aims: the first is to convince and the second is to explain the proposition through peer and public review. The burden of proof rests on the demonstrable application of the statistical method, the disclosure of the assumptions, and the relevance that the test has with respect to a genuine understanding of the data relative to the external world. There are adherents to several different statistical philosophies of inference, such as Bayes theorem versus the likelih ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Prepress Proof
A contract proof usually serves as an agreement between customer and printer and as a color reference guide for adjusting the press before the final press run. Most contract proofs are a prepress proof. The primary goal of proofing is to serve as a tool for customer verification that the entire job is accurate. Prepress proofing (also known as off-press proofing) is a cost-effective way of providing a visual copy without the expense of creating a press proof. If errors are found during the printing process on press, correcting them can prove very costly to one or both parties involved. Press time is the most expensive part of print media. The main objective of proofing is to produce either a soft or hard copy of what the final product will look like on press. Hard-copy proofing usually involves ink-jet printing or other technologies (i.e. Laminate Proof) to produce high-quality one-off copies of the production artwork. Soft proofing usually involves highly color accurate wide-gam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof (2005 Film)
''Proof'' is a 2005 American drama film directed by John Madden and starring Gwyneth Paltrow, Anthony Hopkins, Jake Gyllenhaal, and Hope Davis. The screenplay was written by Rebecca Miller and David Auburn, based on Auburn's Pulitzer Prize-winning play of the same name. Plot The plot alternates between events immediately following the death of Robert, a brilliant mathematician at the University of Chicago whose genius was undone by crippling mental illness, and flashbacks revealing the life he shared with his daughter Catherine. Catherine is also a mathematician and was once a promising student at Northwestern University, but she struggles with living in her father's shadow and balancing her demanding studies with caring for her father, as well as the fear that she may have inherited his mental illness. At home, Robert clings to sanity by constantly bombarding Catherine with complex mathematical problems. In the opening scene Robert startles Catherine while she watches TV in th ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Proof (1991 Film)
''Proof'' is a 1991 Australian romantic comedy-drama film written and directed by Jocelyn Moorhouse. The film stars Hugo Weaving, Geneviève Picot and Russell Crowe. The film was released in Australia on 15 August 1991. It was chosen as "Best Film" at the 1991 Australian Film Institute Awards, along with five other awards, including Moorhouse for Best Director, Weaving for Best Leading Actor, and Crowe for Best Supporting Actor. Plot The story concerns the tribulations of Martin, a blind photographer. Through a series of flashbacks, Martin is shown as a child, distrustful of his own mother. She describes to him the garden outside his bedroom window. She tells him that someone is raking leaves, but he can't hear the sound and angrily decides she is lying to him. This childhood experience strongly affects Martin as an adult, as he anticipates that sighted people will take advantage of his blindness to lie to him, or worse yet, pity him. He has become a resentful, vaguely bitter ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
