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Topics referred to by the same term
Look up implication, implicational, implications, implies, or imply in Wiktionary, the free dictionary. Implication may refer to: Logical consequence
Implication
Topics referred to by the same term
Material implication may refer to: Material conditional, a logical connective Material implication (rule of inference), a rule of replacement for some
Material_implication
An implication table is a tool used to facilitate the minimization of states in a state machine. The concept is to start assuming that every state may
Implication_table
The Implication-Realization (I-R) model of melodic expectation was developed by Eugene Narmour as an alternative to Schenkerian analysis centered less
Implication-Realization
Logical connective
implication) is a binary operation commonly used in logic. When the conditional symbol → {\displaystyle \to } is interpreted as material implication,
Material_conditional
Directed graph representing a Boolean expression
In mathematical logic and graph theory, an implication graph is a skew-symmetric, directed graph G = (V, E) composed of vertex set V and directed edge
Implication_graph
Concept in mathematical logic
converse of a categorical or implicational statement is the result of reversing its two constituent statements. For the implication P → Q, the converse is Q
Converse_(logic)
Rule of logical inference
(from Latin 'mode that by affirming affirms'), conditional elimination, implication elimination, or affirming the antecedent, is a deductive argument form
Modus_ponens
formal concept analysis (FCA) implications relate sets of properties (or, synonymously, of attributes). An implication A→B holds in a given domain when
Implication (information science)
Implication_(information_science)
Type of logical contradiction
The paradoxes of material implication are a group of classically true formulae involving material conditionals whose translations into natural language
Paradoxes of material implication
Paradoxes_of_material_implication
Logical connective
In logic and related fields such as mathematics and philosophy, "if and only if" (often shortened as "iff") states that the truth values of two statements
If_and_only_if
American post–World War II art movement
to Washington, DC., and worked together for a while, working at the implications of this kind of painting. In abstract painting during the 1950s and 1960s
Abstract_expressionism
Implicational hierarchy, in linguistics, is a chain of implicational universals. A set of chained universals is schematically shown as in (1): (1) A <
Implicational_hierarchy
Logic problem, AND of pairwise ORs
Alternatively, they may be expressed as a special type of directed graph, the implication graph, which expresses the variables of an instance and their negations
2-satisfiability
System of resource-aware logic
intuitionistic and classical implication can be recovered from linear implication by inserting exponentials: intuitionistic implication is encoded as !A ⊸ B,
Linear_logic
Intelligence in machines
intelligence have increasingly focused on its broader societal and ethical implications. It has been argued AI will become so powerful that humanity may irreversibly
Artificial_intelligence
Emerging technology field
Nanoid robotics (nanorobotics or nanobotics for short) is an emerging technology field creating robots whose components are at or near the scale of a nanometer
Nanorobotics
Conditional statement which is true because the antecedent cannot be satisfied
non-vacuously (since some integers are indeed greater than 5), but some of its implications are only vacuously true: for example, when x is the integer 2, the statement
Vacuous_truth
Kind of non-classical logic
kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related. They may be viewed as a family of substructural
Relevance_logic
Capacity for a sign to have multiple related meanings
of polysemy was developed by B. T. S. Atkins, in the form of lexical implication rules. These are rules that describe how words, in one lexical context
Polysemy
Relationship in which one statement follows from another
Logical consequence (also entailment or logical implication) is a fundamental concept in logic which describes the relationship between statements that
Logical_consequence
Syllogism with conditional premise(s)
the chain argument, chain rule, or the principle of transitivity of implication). The rule may be stated: P → Q , Q → R ∴ P → R {\displaystyle {\frac
Hypothetical_syllogism
Formal statement in logic
avoid paradoxes of material implication. The following statement, for example, is not correctly formalized by material implication: If Bill Gates graduated
Strict_conditional
Various systems of symbolic logic
be used to obtain new formulas: A weakened premise makes for a strong implication, and vice versa. For example, note that if ( ¬ ¬ ψ ) → ϕ {\displaystyle
Intuitionistic_logic
In logic, a statement which is always true
{\displaystyle R} to be true, and so the definition of tautological implication is trivially satisfied. Similarly, if S {\displaystyle S} is a tautology
Tautology_(logic)
Rule of replacement in propositional logic
In classical propositional logic, material implication is a valid rule of replacement that allows a conditional statement to be replaced by a disjunction
Material implication (rule of inference)
Material_implication_(rule_of_inference)
Concerns and policies regarding the biophysical environment
Environmental impact of paper Environmental impact of pesticides Environmental implications of nanotechnology Environmental impact of shipping Environmental impact
Environmental_issues
Branch of logic
system. The deduction theorem of classical logic relates conjunction and implication: A ∧ B ⊢ C iff A ⊢ B ⇒ C {\displaystyle A\wedge B\vdash C\quad {\mbox{iff}}\quad
Bunched_logic
Type of logical formula
programming, where it is common to write definite clauses in the form of an implication: (p ∧ q ∧ ... ∧ t) → u In fact, the resolution of a goal clause with
Horn_clause
Rule of logical inference
contraposition to the premise which is a material implication. For example: If P, then Q. (premise – material implication) If not Q, then not P. (derived by contraposition)
Modus_tollens
Formal proof
Transformation rules Propositional calculus Rules of inference (List) Implication introduction / elimination (modus ponens) Biconditional introduction /
Conditional_proof
Property involving two mathematical operations
→ R ) ) Distribution of implication ( P → ( Q ↔ R ) ) ⇔ ( ( P → Q ) ↔ ( P → R ) ) Distribution of implication over equivalence ( P →
Distributive_property
Spanish spy (1936–2023)
1936 – 3 May 2023) was a Spanish spy and businessman best known for his implication in several corruption scandals and the faking of his own death in the
Francisco_Paesa
Question that has a built-in supposition
presuppositions (often with loaded language—having an unspoken and often emotive implication), it is known as a loaded question. For example, a classic loaded question
Complex_question
Symbol connecting formulas in logic
examples. Common connectives include negation, disjunction, conjunction, implication, and equivalence. In standard systems of classical logic, these connectives
Logical_connective
Rule of replacement in propositional logic
used are material implication, De Morgan's law, and the associative property of disjunction. Due to the use of material implication in the first two steps
Exportation_(logic)
Logical connective
connective which is the negation of converse implication (equivalently, the negation of the converse of implication). Converse nonimplication is notated P ↚
Converse_nonimplication
of non-classical logics designed to exclude the paradoxes of material implication. The characteristic that separates connexive logic from other non-classical
Connexive_logic
Information conveyed verbally yet not literally
this is an implicated premise. The hearer can now draw the contextual implications that +> Susan needs to be cheered up. +> Peter wants me to ring Susan
Implicature
Fuzzy logic concept
interpreted by a t-norm, the residuum plays the role of implication (often called R-implication). If ⇒ {\displaystyle \Rightarrow } is the residuum of
T-norm
Pair of logical equivalences
understood by setting up models using Kripke semantics. Three out of the four implications of de Morgan's laws hold in intuitionistic logic. Specifically, we have
De_Morgan's_laws
Slang term used for a young person
age of consent for sexual activity and usually appears older, with the implication that a person above the age of consent might find them sexually attractive
Jailbait
Miles Laboratories sedative patent medicine (1884–ca.1970)
was absorbed into Bayer). The name is a cognate of 'Nerve', and the implication was that the material worked to calm nervousness. The original form of
Nervine
Point in time when the maximum rate of petroleum extraction is reached
unprecedented risk management problem." To avoid the serious social and economic implications a global decline in oil production could entail, the Hirsch report emphasized
Peak_oil
Proof strategy for showing a collection of statements are equivalent
English it is also sometimes called a cycle of implications, closed chain inference, or circular implication; however, it should be distinguished from circular
Ringschluss
System of logic in mathematics and philosophy
connectives of Łukasiewicz logic are → {\displaystyle \rightarrow } ("implication"), and the constant ⊥ {\displaystyle \bot } ("false"). Additional connectives
Łukasiewicz_logic
Version of classical propositional calculus that uses only one connective
logic, the implicational propositional calculus is a version of classical propositional calculus that uses only one connective, called implication or conditional
Implicational propositional calculus
Implicational_propositional_calculus
Study of general and fundamental questions
biology, examining their fundamental concepts, methods, assumptions, and implications. Philosophy is related to and informs many other fields, such as law
Philosophy
Unproven computational hardness assumption
However, if the exponential time hypothesis fails, it would have no implication for the P versus NP problem. A padding argument proves the existence
Exponential_time_hypothesis
Severe malnutrition due to energy deficiency
muscle mass, and increased visceral fat. Moreover, there are metabolic implications including reduced insulin sensitivity and impaired glucose metabolism
Marasmus
19th-century English proverb
advocating for the daily consumption of apples. By extension, the broader implication is "if one eats healthful foods, one will remain in good health and will
An apple a day keeps the doctor away
An_apple_a_day_keeps_the_doctor_away
Device that measures proper acceleration
ISSN 2510-523X. Kröger, Jacob Leon; Raschke, Philip (January 2019). "Privacy implications of accelerometer data: a review of possible inferences". Proceedings
Accelerometer
Situation in which one cannot avoid a problem because of contradictory constraints
applied to loopholes and quirks of the military system, always with the implication that rules are inaccessible to and slanted against those lower in the
Catch-22_(logic)
Relationship between programs and proofs
of the combinators could be seen as axiom-schemes for intuitionistic implicational logic. In 1958, he observes that a certain kind of proof system, referred
Curry–Howard_correspondence
Diverse clade of specialized reptiles
Caseosaurus crosbyensis from the Late Triassic of Texas, USA and its implications for early dinosaur evolution". Acta Palaeontologica Polonica. 63. doi:10
Dinosaur
Universally-occurring linguistic pattern
(opposite: statistical, often called tendencies) and implicational (opposite: non-implicational). Absolute universals apply to every known language and
Linguistic_universal
Algebraic structure used in logic
and greatest element 1) equipped with a binary operation a → b called implication such that (c ∧ a) ≤ b is equivalent to c ≤ (a → b). In a Heyting algebra
Heyting_algebra
Resistance to German occupation in WWII
several forms: Asserting the legitimacy of the exiled government, and by implication the lack of legitimacy of Vidkun Quisling's pro-Nazi regime and Josef
Norwegian_resistance_movement
Common Greek noun for knowledge
and philosophies in the Greco-Roman world. It is best known for its implication within Gnosticism, where it signifies a spiritual knowledge or insight
Gnosis
Some application areas may also have particularly important ethical implications, like healthcare, education, criminal justice, or the military. Machine
Ethics of artificial intelligence
Ethics_of_artificial_intelligence
Unsourced material may be challenged and removed. Find sources: "Ethical implications in contracts" – news · newspapers · books · scholar · JSTOR (May 2026)
Ethical implications in contracts
Ethical_implications_in_contracts
Canadian journalist and author (born 1963)
Pushkin Industries. Gladwell's writings often deal with the unexpected implications of research in the social sciences, such as sociology and psychology
Malcolm_Gladwell
Mathematical logic concept
contrapositives are logically equivalent, we need to understand when material implication is true or false. P → Q {\displaystyle P\to Q} This is only false when
Contraposition
Logical paradox
although the problem continues to be discussed in relation to theories of implication and modal logic. In the story, Uncle Joe and Uncle Jim are walking to
Barbershop_paradox
Generalized belief about people
likely to reflect reality. Although stereotypes generally have negative implications, they may also be positive or neutral. They can also be broken down into
Stereotype
Fictional character from A Clockwork Orange
DeLarge, a reference to Alex calling himself Alexander The Large (the implication being that he possesses oversized genitals; as well as a punning reference
Alex_(A_Clockwork_Orange)
Format for expressing RDF statements in HTML documents
Beautiful, Tormented Machine". Building Interoperable Web Metadata "RDFa – Implications for Accessibility – Standards Schmandards". "Web Data Commons – RDFa
RDFa
State of a person who has never engaged in sexual intercourse
interpersonal relationships. Although virginity has social implications and had significant legal implications in some societies in the past, it has no legal consequences
Virginity
Decline in oil production
Oil depletion is the decline in petroleum production of a well, oil field, or geographic area. Earth's natural oil supply is effectively fixed because
Oil_depletion
Methods for indexing the Internet
Back-of-the-book-style web indexes may be called "web site A-Z indexes". The implication with "A-Z" is that there is an alphabetical browse view or interface
Web_indexing
Erotic practices involving domination and sadomasochism
person, for example, by being whipped, purely recreationally, without any implication of being psychologically dominated, and submissives may be ordered to
BDSM
or method. The listing documents the occurrence of a death, making no implications regarding wrongdoing or justification on the part of the person killed
List of unarmed African Americans killed by law enforcement officers in the United States
List_of_unarmed_African_Americans_killed_by_law_enforcement_officers_in_the_United_States
prior films, rather than for the performance specifically nominated. The implication is that the winning performance was inferior to the recipient's prior
Legacy_Oscar
Attack model against cryptographic hash functions
collision resistance does imply preimage resistance (by a provisional implication). Conversely, a second-preimage attack implies a collision attack (trivially
Preimage_attack
Title given to military organizations
is a title given to military organizations at various times, with the implication of an emergency or reserve force raised for local defense. The term "home
Home_guard
Science fiction genre that focuses on technological use of life studies
focuses on biotechnology. It is derived from cyberpunk, but focuses on the implications of biotechnology rather than mechanical cyberware and information technology
Biopunk
2015 UK Supreme Court contract law case
(Jersey) Ltd [2015] UKSC 72 is an English contract law case, concerning the implication of terms in commercial contracts, and business tenancies agreed between
Marks and Spencer plc v BNP Paribas Securities Services Trust Company (Jersey) Ltd
Marks_and_Spencer_plc_v_BNP_Paribas_Securities_Services_Trust_Company_(Jersey)_Ltd
Folk story and cautionary tale
tradition in which a vagina is said to contain teeth, with the associated implication that sexual intercourse might result in injury, emasculation, or castration
Vagina_dentata
Sexual fixation on non-human animals
and sociology the word "zoophilia" is sometimes used without sexual implications. Being fond of animals in general, or as pets, is accepted in Western
Zoophilia
research activities that anticipate and address ethical, legal and social implications (ELSI) or aspects (ELSA) of emerging sciences, notably genomics and nanotechnology
Ethical, Legal and Social Aspects research
Ethical,_Legal_and_Social_Aspects_research
Type of consonant used in many spoken languages
Americanist phonetic notation is ⟨y⟩. If it is necessary to avoid the implication that the approximant is spread as its vocalic equivalent [i] is, it may
Voiced_palatal_approximant
Relationship between language and human evolution
modern human behavior, but there is little agreement about the facts and implications of this connection. The shortage of direct, empirical evidence has caused
Origin_of_language
Time period of 1000 years
beginning on any date. Millennia sometimes have religious or theological implications (see millenarianism). The word millennium derives from the Latin mille
Millennium
relationship in Information retrieval. This formalization is a logical implication with an attached measure of uncertainty. Rijsbergen proposes that the
Uncertain_inference
Person who holds values of ancient Romans
to embody the values of ancient Roman civilization – values which, by implication, became extinct on their death. It has been used to describe a number
Last_of_the_Romans
Penis-like object
"phallic symbol"). Such symbols often represent fertility and cultural implications that are associated with the male sexual organ, as well as the male orgasm
Phallus
Rhetoric used to influence an audience
exploit stereotypes. Loaded words and phrases have significant emotional implications and involve strongly positive or negative reactions beyond their literal
Loaded_language
Early sample or model built to test a concept or process
left by a blow, then by a stamp struck by a die (note "typewriter"); by implication a scar or mark; by analogy a shape i.e. a statue, (figuratively) style
Prototype
Unsolved problem in computer science
problem in computational theory, a proof either way would have profound implications for mathematics, cryptography, algorithm research, artificial intelligence
P_versus_NP_problem
Non-member of science fiction fandom
belong to a particular group, according to the members of that group; the implication is that such persons, lacking imagination, are concerned solely with
Mundane
Nonsensical speech or writing
rough equivalent of nonsense, folderol, balderdash, or claptrap. The implication is that the criticized expression or proposition lacks substance or congruence
Gibberish
Urban legend
urban legend and stories of such feats are viewed as tall tales. The implication that rural citizens seek such entertainment due to lack of alternatives
Cow_tipping
English Army officer and politician
Oliver Cromwell during the Commonwealth.[citation needed] Following his implication in the Rye House Plot in 1683, Armstrong was hanged, drawn and quartered
Thomas Armstrong (English politician)
Thomas_Armstrong_(English_politician)
1966, that describe fragments of the propositional calculus involving implication known as BCI and BCK logics. An algebra (in the sense of universal algebra)
BCK_algebra
2005 book by T. Colin Campbell and Thomas M. Campbell II
Most Comprehensive Study of Nutrition Ever Conducted and the Startling Implications for Diet, Weight Loss and Long-term Health is a book by T. Colin Campbell
The_China_Study
Topics referred to by the same term
refers to: Crossword puzzle, a word game Economic puzzle, where the implication of theory is inconsistent with observed economic data Jigsaw puzzle,
Puzzle_(disambiguation)
Symbolic logic system
formulated using the same syntax as intuitionistic propositional logic, with implication → {\displaystyle \to } , conjunction ∧ {\displaystyle \land } , disjunction
Minimal_logic
Topics referred to by the same term
who is younger than the age of consent for sexual activity, with the implication that an older person might find them sexually attractive. Jailbait or
Jailbait_(disambiguation)
Hypothesis of barriers to forming interstellar civilizations
development on the Kardashev scale, allowing few or no species through. One implication of this argument is that the more probable it is that other life could
Great_Filter
Figure of speech describing an impossible event
figure of speech so hyperbolic that it describes an impossibility. The implication of such a phrase is that the circumstances in question (the adynaton
When_pigs_fly
travel, tourism, insurance
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
IMPLICATION
travel, tourism, insurance