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Topics referred to by the same term
up provability or provable in Wiktionary, the free dictionary. Provability or provable (and disprovability or disprovable) may refer to: Provability logic
Provable
Prime integer calculated using a primality-proving algorithm
In number theory, a provable prime is an integer that has been calculated to be prime using a primality-proving algorithm. Boot-strapping techniques using
Provable_prime
Limitative results in mathematical logic
theorems of mathematical logic that are concerned with the limits of provability in formal axiomatic theories. These results, published by Kurt Gödel
Gödel's incompleteness theorems
Gödel's_incompleteness_theorems
Computer security method
Provable security refers to any type or level of computer security that can be proved. It is used in different ways by different fields. Usually, this
Provable_security
Fundamental theorem in mathematical logic
that establishes a correspondence between semantic truth and syntactic provability in first-order logic. The completeness theorem applies to any first-order
Gödel's_completeness_theorem
Modal logic
Provability logic is a branch of proof theory and a modal logic, in which the box (or "necessity") operator is interpreted as 'it is provable that'. The
Provability_logic
Determination of whether a given program halts for each input
programming paradigm that restricts the range of programs to those that are provably terminating Walther recursion Size-change termination principle Rogers
Termination_analysis
Branch of mathematical logic
areas of proof theory include structural proof theory, ordinal analysis, provability logic, proof-theoretic semantics, reverse mathematics, proof mining,
Proof_theory
proofs, complexity theory and formal reduction. These functions are called provably secure cryptographic hash functions. To construct these is very difficult
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Theorem on proofs and axiomatic systems
how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is unimaginably long. For example
Gödel's_speed-up_theorem
Quality of an algorithm being correct with respect to a specification
In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness
Correctness (computer science)
Correctness_(computer_science)
American computer scientist (1932–2026)
California since 1971. Before the RISKS mailing list, Neumann was known for the Provably Secure Operating System (PSOS). Neumann worked with Dorothy E. Denning
Peter_G._Neumann
Type of logical system
sound, i.e. all provable statements are true in all models; and complete, i.e. all statements which are true in all models are provable. Although the logical
First-order_logic
Provability logic
is provable in PA that "if P is provable in PA then P is true", then P is provable in PA. If Prov(P) is the assertion that the formula P is provable in
Löb's_theorem
1956 work by philosopher Ludwig Wittgenstein
then it is true that it is provable. And that surely cannot be! And if it is proved, then it is proved that it is not provable. Thus it can only be true
Remarks on the Foundations of Mathematics
Remarks_on_the_Foundations_of_Mathematics
Mathematical function that can be computed by a program
computable is called provably total. The set of provably total functions is recursively enumerable: one can enumerate all the provably total functions by
Computable_function
Summary of a mathematical proof
self-referential formula that, informally, says "I am not provable", and prove that this sentence is neither provable nor disprovable within the theory. Importantly
Proof sketch for Gödel's first incompleteness theorem
Proof_sketch_for_Gödel's_first_incompleteness_theorem
Programming paradigm restricted to provably terminating programs
programming paradigm that restricts the range of programs to those that are provably terminating. Termination is guaranteed by the following restrictions: A
Total_functional_programming
Term in logic and deductive reasoning
property means that every validity (truth) is provable. Together they imply that all and only validities are provable. Most proofs of soundness are trivial.
Soundness
Concept in mathematical logic
formula in the theory's language, either that formula or its negation is provable. That is, for every sentence φ , {\displaystyle \varphi ,} the theory T
Complete_theory
Hydra game in mathematical logic
all recursive functions that are provably total in " ID ν {\displaystyle {\textrm {ID}}_{\nu }} ", and it is not provable that all hydra games terminate
Buchholz_hydra
Mathematical problem
{\displaystyle {\text{Th}}_{Eq}(\mathrm {HS} )} (that is, the set of identities provable from them in equational logic) is equal to the equational theory of R ≥
Tarski's high school algebra problem
Tarski's_high_school_algebra_problem
Methods of safely sharing general data
computations such that the utility of the statistic is preserved while provably limiting what can be inferred about any individual in the dataset. Another
Differential_privacy
system of provability logic with infinitely many provability modalities. This system has played an important role in some applications of provability algebras
Japaridze's_polymodal_logic
Intelligence of machines
moral agents" and Stuart J. Russell's three principles for developing provably beneficial machines. Active organizations in the AI open-source community
Artificial_intelligence
Hilbert–Bernays-Löb provability conditions, named after David Hilbert, Paul Bernays, and Martin Löb, are a set of requirements for formalized provability predicates
Hilbert–Bernays-Löb provability conditions
Hilbert–Bernays-Löb_provability_conditions
Cryptographic hash function
Hash (VSH) is a provably secure cryptographic hash function invented in 2005 by Scott Contini, Arjen Lenstra, and Ron Steinfeld. Provably secure means that
Very_smooth_hash
Yes-or-no question that cannot ever be solved by a computer
for the "neither provable nor refutable" sense. The usage of "independent" is also ambiguous, however. It can mean just "not provable", leaving open whether
Undecidable_problem
Branch of mathematical logic
provable in weak subsystems of second-order arithmetic when they are restricted. For example, "every field has an algebraic closure" is not provable in
Reverse_mathematics
mathematics. However, many particular instances of it are nevertheless provable in a constructive context as well. The principle was first studied and
Markov's_principle
European collaborative research project
ProCoS ("Provably Correct Systems") was a European ESPRIT initiative of two collaborative computer science research projects and a Working Group, with
ProCoS
Deductive system in set theory
arbitrarily large models containing a large cardinal, this fact will be provable in Ω-logic. The theory involves a definition of Ω-validity: a statement
Ω-logic
Inference rule treating non-provability as falsity
is known as weak negation, in contrast with the strong (i.e. explicit, provable) negation. In Planner, negation as failure could be implemented as follows:
Negation_as_failure
Theorem in mathematical logic
expressible in Peano arithmetic, is not provable in this system. That Ramsey-theoretic claim is, however, provable in slightly stronger systems. This result
Paris–Harrington_theorem
American computer scientist
research centers at UC Berkeley including Algorithms and Specializers for Provably Optimal Implementations with Resilience and Efficiency (ASPIRE), the Parallel
John_Wawrzynek
Type of formal logic
Hence if the accessibility relation R is reflexive and Euclidean, R is provably symmetric and transitive as well. Hence for models of S5, R is an equivalence
Modal_logic
Algebraic structure used in logic
provable (unconditionally) if and only if G is provable from F, that is, if G is a provable consequence of F.) In particular, if F and G are provably
Heyting_algebra
Type of cipher
assumptions regarding their components (such as a block cipher) – is known as provable security. Informally, a block cipher is secure in the standard model if
Block_cipher
Various systems of symbolic logic
meaningful concepts of “constructive truth” (rather than merely validity or provability), are Kurt Gödel’s dialectica interpretation, Stephen Cole Kleene’s realizability
Intuitionistic_logic
Gold mine in Quebec, Canada
in 1988. The LaRonde mining complex has 3.8 million ounces of gold in provable and probable reserves. Previous operations at the LaRonde complex used
LaRonde_mine
Logic statement about a formal system proven in a metalanguage
says that a sentence of the form φ→ψ is provable from a set of axioms A if and only if the sentence ψ is provable from the system whose axioms consist of
Metatheorem
and additionally maintains that "It seems entirely plausible, while not provable, that 700,000 German military personnel listed as missing actually died
German prisoners of war in the Soviet Union
German_prisoners_of_war_in_the_Soviet_Union
Non-contradiction of a theory
and ⟨ A ⟩ {\displaystyle \langle A\rangle } the set of closed sentences provable from A {\displaystyle A} under some (specified, possibly implicitly) formal
Consistency
Impossible task in computing
viewed as asking for an algorithm to decide whether a given statement is provable using the rules of logic. In 1936, Alonzo Church and Alan Turing published
Entscheidungsproblem
Field of knowledge
numbers, there are theorems that are true (that is provable in a stronger system), but not provable inside the system. This approach to the foundations
Mathematics
Index of articles associated with the same name
set with certain properties. Without such an axiom, such a set might not provably exist. Important countability axioms for topological spaces include: sequential
Axiom_of_countability
theories to coincide. For example, if A is provable in Heyting arithmetic (HA), then AB is also provable in HA. Moreover, if A is a Σ01-formula, then
Friedman_translation
Secure communication method
to be strong has not to date been formally proved. In contrast, QKD has provable security based on information theory, and forward secrecy. The main drawback
Quantum_key_distribution
The mathematical statements discussed below are provably independent of ZFC (the canonical axiomatic set theory of contemporary mathematics, consisting
List of statements independent of ZFC
List_of_statements_independent_of_ZFC
Mathematical models of strategic interactions
combinatorial structures (like chess, go, or backgammon) for which no provable optimal strategies have been found. The practical solutions involve computational
Game_theory
Object-oriented programming principle
Subtype Requirement: Let ϕ ( x ) {\displaystyle \phi (x)} be a property provable about objects x {\displaystyle x} of type T. Then ϕ ( y ) {\displaystyle
Liskov_substitution_principle
Computation model defining an abstract machine
Entscheidungsproblem, or 'decision problem' (whether every mathematical statement is provable or disprovable). Turing machines proved the existence of fundamental limitations
Turing_machine
Form of political manipulation
will reinforce the two-party system. Additionally, while this method is provably fair to the two parties creating the districts, it is not necessarily fair
Gerrymandering
Damages assessed in order to punish the defendant for outrageous conduct
ordre public. Because they are usually paid in excess of the plaintiff's provable injuries, punitive damages are awarded only in special cases, usually under
Punitive_damages
Systematic method for producing proofs
is a systematic method for producing proofs in some proof calculus of (provable) statements. There are several types of proof calculi. The most popular
Proof_procedure
American philosopher and logician (1940–1996)
expressing "This sentence is provable" (as opposed to the Gödel sentence, "This sentence is not provable") was provable and hence true. Martin Löb showed
George_Boolos
definition "¬φ is provable". If Theorem 1 holds, and φ is not satisfiable in any structure, then ¬φ is valid in all structures and therefore provable, thus φ is
Original proof of Gödel's completeness theorem
Original_proof_of_Gödel's_completeness_theorem
Play by William Shakespeare
discussed their plans.[citation needed] This interpretation is not fully provable; however, the motivating role of ambition for Macbeth is universally recognised
Macbeth
Method in mathematical logic
(informally) "This sentence is not provable", Rosser's trick uses a formula that says "If this sentence is provable, there is a shorter proof of its negation"
Rosser's_trick
American musician and activist (born 1941)
fear of doing because we know who we are and what we are, and it's easily provable through a DNA test. If Buffy did that, that's one thing that could clear
Buffy_Sainte-Marie
Set theory concept
much work has been done in determining what relations between them are provable, and constructing models of set theory for various consistent configurations
Cardinal characteristic of the continuum
Cardinal_characteristic_of_the_continuum
Number that is not a ratio of integers
expansion that terminates or repeats must be a rational number. These are provable properties of rational numbers and positional number systems and are not
Irrational_number
Proof by Alan Turing
that there is no general method which tells whether a given formula U is provable in K [Principia Mathematica]". Turing followed this proof with two others
Turing's_proof
Blockchain protocol
permissionless and permissioned blockchains. Ouroboros was published as "the first provable secure PoS consensus protocol". It was postulated by an academic team led
Ouroboros_(protocol)
Unreproducible object used in digital security
attacks. Using a fuzzy extractor or the fuzzy commitment scheme that are provably suboptimal in terms of storage and privacy leakage amount or using nested
Physical_unclonable_function
They showed that a certain finitistic theorem in Ramsey theory is not provable in Peano arithmetic (PA). Given a set s ⊆ N {\displaystyle s\subseteq \mathbb
Kanamori–McAloon_theorem
Philosophical problem-solving principle
natural laws, and the constancy of natural law. Rather than depend on provability of these axioms, science depends on the fact that they have not been
Occam's_razor
Type of timestamping
1007/11751595_43. ISBN 978-3-540-34075-1. Buldas, Ahto; Saarepera, Märt (2004). On Provably Secure Time-Stamping Schemes. Lecture Notes in Computer Science. Vol. 3329
Linked_timestamping
Indian mathematician (born 1956)
listed as an ISI highly cited researcher. He invented one of the first provably polynomial time algorithms for linear programming, which is generally referred
Narendra_Karmarkar
Decidable first-order theory of the natural numbers with addition
sentence in the language of Presburger arithmetic, whether that sentence is provable from the axioms of Presburger arithmetic. The asymptotic running-time computational
Presburger_arithmetic
Formula for the derivative of a ratio of functions
{\displaystyle h'(x)={\frac {f'(x)g(x)-f(x)g'(x)}{(g(x))^{2}}}.} It is provable in many ways by using other derivative rules. Given h ( x ) = e x x 2 {\displaystyle
Quotient_rule
Quantum computing protocol
entropy. Recently, researchers have built on classical shadow to devise provably efficient classical machine learning algorithms for a wide range of quantum
Classical_shadow
Axiom of set theory
paradox exists." Such conditional statements are provable in ZF when the original statements are provable from ZF and the axiom of choice. As discussed above
Axiom_of_choice
Cryptographic hash function
MuHASH implies solving the discrete logarithm problem. MuHASH is thus a provably secure hash, i.e. we know that finding a collision is at least as hard
Elliptic_curve_only_hash
1967 missing person case in Malaysia
massive nature of the search made it almost certain (and even arguably provable mathematically) that just because it was the "biggest land search in Malaysian
Disappearance_of_Jim_Thompson
Mathematical theory
Σ1-sound (or 1-consistent, in another terminology) if every Σ01-sentence provable in T is true in the standard model of arithmetic N (i.e., the structure
Ω-consistent_theory
Process of repeating items in a self-similar way
it is a provable proposition. If a proposition can be derived from true reachable propositions by means of inference rules, it is a provable proposition
Recursion
Expression associated with political misinformation established in 2017
during the interview with Chuck Todd to explain why Spicer would "utter a provable falsehood", Conway stated that Spicer was giving "alternative facts". Todd
Alternative_facts
Propositions that are demonstrably, necessarily or self-evidently true
possibility of something's being true. Apodictic judgments are clearly provable or logically certain. For instance, "Three plus one equals four" is apodictic
Apodicticity
Universal network for provably efficient communication
The fat tree network is a universal network for provably efficient communication. It was invented by Charles E. Leiserson of the MIT in 1985. k-ary n-trees
Fat_tree
English actor and musician (born 1987)
vehemently denied the allegations, describing them as "unverified and provably untrue". As a result, filming of the series White Gold was temporarily
Ed_Westwick
Illegal usage of copyrighted works
infringing products, and award damages. Some jurisdictions only allow actual, provable damages, and some, like the United States, allow for large statutory damage
Copyright_infringement
Phase transition in machine learning
Hu, Wei (2023). "Dichotomy of Early and Late Phase Implicit Biases Can Provably Induce Grokking". arXiv:2311.18817 [cs.LG]. Chizat, Lenaic; Oyallon, Edouard;
Grokking_(machine_learning)
2014 documentary film by Amy J. Berg
2015). "Hollywood Sex Abuse Accuser's Lawyers Admit Filing "Untrue and Provably False" Claims". The Hollywood Reporter. Retrieved April 13, 2018. Johnson
An_Open_Secret
Task to construct a program meeting a formal specification
computer science, program synthesis is the task to construct a program that provably satisfies a given high-level formal specification. In contrast to program
Program_synthesis
Topics referred to by the same term
language or its negation is provable Gödel's completeness theorem, correspondence between semantic truth and syntactic provability in first-order logic Gödel's
Completeness
American computer scientist
speculation". "Randomized Rounding And Discrete Ham-Sandwich Theorems: Provably Good Algorithms for Routing and Packing Problems". UC Berkeley. Retrieved
Prabhakar_Raghavan
Israeli American computer scientist (born 1959)
Turing Award along with Silvio Micali for having "pioneered the field of provable security, which laid the mathematical foundations that made modern cryptography
Shafi_Goldwasser
Property of cryptographic hash functions
integer factorization or discrete logarithm). Those functions are called provably secure. A family of functions {hk : {0, 1}m(k) → {0, 1}l(k)} generated
Collision_resistance
Military term for a captive of the enemy
Rüdiger Overmans maintains that it seems entirely plausible, while not provable, that one million died in Soviet custody. He also believes that there were
Prisoner_of_war
In mathematics, a statement that has been proven
stated in Peano arithmetic, but is proved to be not provable in Peano arithmetic. However, it is provable in some more general theories, such as Zermelo–Fraenkel
Theorem
Reasoning for mathematical statements
all axiomatic systems can generate certain undecidable statements not provable within the system. The definition of a formal proof is intended to capture
Mathematical_proof
Axiom set used in first-order logic
language is either provable or disprovable from the axioms, and we have an algorithm which decides for any given sentence whether it is provable or not. Early
Tarski's_axioms
Symbol in mathematical logic
means that S is provable from T. This usage is demonstrated in the article on propositional calculus. The syntactic consequence of provability should be contrasted
Turnstile_(symbol)
Concept in mathematics
if every formula from Γ {\displaystyle \Gamma } provable in T 2 {\displaystyle T_{2}} is also provable in T 1 {\displaystyle T_{1}} . Note that a conservative
Conservative_extension
Social-cultural system
story that is important for the group, whether or not it is objectively or provably true. Examples include the resurrection of their real-life founder Jesus
Religion
how to find explicit examples of statements in formal systems that are provable in that system but whose shortest proof is absurdly long. For example,
List of long mathematical proofs
List_of_long_mathematical_proofs
Method of proof in mathematics
some principle that is not constructively provable, then the statement itself cannot be constructively provable. For example, a particular statement may
Constructive_proof
Term in mathematical logic
in a decision problem.) A theory T is independent if no axiom in T is provable from the remaining axioms in T. A theory for which there is an independent
Independence (mathematical logic)
Independence_(mathematical_logic)
Chronological legal documentation process
transfer of evidence from person to person be documented and that it be provable that nobody else could have accessed that evidence. It is best to keep
Chain_of_custody
PROVABLE
PROVABLE
PROVABLE
PROVABLE
Boy/Male
Indian
Stream
Boy/Male
Tamil
Lokpradeep | லோகபà¯à®°à®¤à¯€à®ª
Gautam Buddha
Male
German
 Low German short form of Latin Johan, JAN means "God is gracious." Compare with another form of Jan.
Girl/Female
Muslim
Pure
Surname or Lastname
English
English : perhaps a variant of Hadaway, itself a variant of Hathaway. Compare Hardaway.
Boy/Male
Muslim
Forgiver
Girl/Female
Indian
Ghee
Male
English
(×ַלï‹×Ÿ) Variant spelling of English Allon, ALON means "oak tree."
Girl/Female
English, Finnish, German, Italian, Swedish
Powerful in Battle; Battle-mighty
Boy/Male
Hindu, Indian, Kannada, Malayalam, Marathi
One Adorned with Knowledge of the Vedas
PROVABLE
PROVABLE
PROVABLE
PROVABLE
PROVABLE
a.
Capable of being proved; demonstrable.