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Set of logical formulae containing all formulae able to be deduced from itself
formulae, the deductive closure of T {\displaystyle T} is its smallest superset that is deductively closed. The deductive closure of a theory T
Deductive_closure
Form of reasoning
Deductive reasoning is the process of drawing valid inferences. An inference is valid if its conclusion follows logically from its premises, meaning that
Deductive_reasoning
Statement supporting a conclusion
or justified and must be relevant to the conclusion. The premises of deductively valid arguments provide the strongest support: if the premises are true
Premise
Topics referred to by the same term
Epistemic closure, a principle in epistemology Deductive closure, a principle in logic Cognitive closure, a principle in philosophy of mind Closure: A Short
Closure
Smallest transitive relation containing a given binary relation
transitive closure on distributed systems based on the MapReduce paradigm. Ancestral relation Deductive closure Reflexive closure Symmetric closure Transitive
Transitive_closure
Method of logical reasoning
an argument is supported not with deductive certainty, but at best with some degree of probability. Unlike deductive reasoning (such as mathematical induction)
Inductive_reasoning
Analysis of facts to form a judgment
appear white from my viewing angle, so sheep are white. Contrast with the deductive statement: Some sheep are white on at least one side. Kerry S. Walters
Critical_thinking
Study of the properties of logical systems
of mathematical logic that is known as model theory, and the study of deductive systems is the branch that is known as proof theory. A formal language
Metalogic
ambiguity, or faulty inference. In deductive reasoning, a formal fallacy renders an argument invalid. In non-deductive reasoning, fallacious reasoning may
List_of_fallacies
Text for clarification; one of four rhetorical modes
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Description
Logically self-contradictory statement
Fallacy – Argument that uses faulty reasoning Formal fallacy – Faulty deductive reasoning due to a logical flaw Impossible object – Type of optical illusion
Paradox
Overview of and topical guide to logic
Metalinguistic variable Deductive system Metatheorem Metatheory Interpretation Absorption law Clause (logic) Deductive closure Distributive property Entailment
Outline_of_logic
Two types of knowledge, justification, or argument
Abductive reasoning Abstract and concrete Analytic–synthetic distinction Deductive reasoning Inductive reasoning Off the verandah Relativized a priori Tabula
A_priori_and_a_posteriori
Relationship between objects
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Reference
Semi-decision algorithm for transforming a set of equations
(⟶E) is its rewrite closure, and (⁎⟷E) is the equivalence closure of (⟶E). For a set R of rewrite rules, its deductive closure (⁎⟶R ∘ ⁎⟵R) is the set
Knuth–Bendix completion algorithm
Knuth–Bendix_completion_algorithm
Conformity to reality
observation and experimentation, whereas the formal sciences rely on deductive reasoning from fundamental principles. Many religious traditions regard
Truth
Academic discipline
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Logic_in_computer_science
List of symbols used to express logical relations
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_logic_symbols
Real or apparent mutual contradiction between two ideas that exposes their misconceptions
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Antinomy
Class of formal logics
Frege–Russell logic is the intensively studied and most widely used class of deductive logic. Classical logic has had much influence on analytic philosophy.
Classical_logic
List of statements that appear to contradict themselves
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_paradoxes
Study of correct reasoning
includes both formal and informal logic. Formal logic is the study of deductively valid inferences or logical truths. It examines how conclusions follow
Logic
Precisely specified semantic version of a statement
argument valid or cogent. All logical form arguments are either inductive or deductive. Inductive logical forms include inductive generalization, statistical
Logical_form
Bearer of truth values
support is found in deductively valid arguments, in which the conclusion cannot be false if the premises are true. To study deductive validity, logicians
Proposition
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Schrödinger_logic
One or more words used to refer to something
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Name
Formal systems of logic that significantly differ from standard logical systems
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Non-classical_logic
Terms to describe a conditional relationship between two statements
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Necessity_and_sufficiency
American political philosopher (1938–2002)
Nozick's theory of knowledge is his rejection of the principle of deductive closure. This principle states that if S knows X and S knows that X implies
Robert_Nozick
German polymath (1646–1716)
inherently relational. Leibniz's 1690 discovery of his algebra of concepts (deductively equivalent to the Boolean algebra) and the associated metaphysics, are
Gottfried_Wilhelm_Leibniz
Concept of focusing on form over concept
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Formalism_(philosophy)
Inference seeking the simplest and most likely explanation
beginning in the latter half of the 19th century. Abductive reasoning, unlike deductive reasoning, yields a plausible conclusion but does not definitively verify
Abductive_reasoning
Concept of philosophy and logic used to express modal claims
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Possible_world
Idea that knowledge comes only/mainly from sensory experience
generalizations from experience; mathematical inference, generally conceived as deductive [and a priori] in nature, Mill set down as founded on induction. Thus
Empiricism
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
XOR-SAT
Logical incompatibility between two or more propositions
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Contradiction
Statement that attaches a meaning to a term
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Definition
Logic founded on unproven premises
formal fallacy (an argument that is defective because it uses an incorrect deductive step). Rather, it is usually a type of informal fallacy that is logically
Begging_the_question
Statement that is true regardless of the truth or falsity of its constituent propositions
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Logical_truth
Establishment of a theorem using inference from the axioms
qualify as part of a proof, it must be the result of applying a rule of the deductive apparatus (of some formal system) to the previous well-formed formulas
Formal_proof
Branch of logic
approach vs. the critical thinking approach the viability of the inductive/deductive dichotomy the ethics of argumentation and logical criticism the problem
Informal_logic
Study of mathematics itself
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Metamathematics
Semantic distinction in philosophy
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Analytic–synthetic distinction
Analytic–synthetic_distinction
Logical formalism using combinators instead of variables
{\displaystyle X,A\not \vdash B} by the deduction theorem, thus the deductive closure of X ∪ { A } {\displaystyle X\cup \{A\}} is an element Y ∈ W {\displaystyle
Combinatory_logic
Branch of mathematics that studies sets
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Set_theory
Use of logic to perform or reason about computation
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Computational_logic
Rules used for constructing, or transforming the symbols and words of a language
consists of a formal language together with a deductive apparatus (also called a deductive system). The deductive apparatus may consist of a set of transformation
Syntax_(logic)
Number measuring the chance an event occurs
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Probability
Argument whose conclusion must be true if its premises are
In logic, specifically in deductive reasoning, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true
Validity_(logic)
Term used to model separate circumstances that cannot exist together
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Impossible_world
Assumed context surrounding an utterance
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Presupposition
Sufficient evidence/argument for truth
part of a formal proof, it must be the result of applying a rule of the deductive apparatus of some formal system to the previous well-formed formulae in
Proof_(truth)
About mathematical functions
Tarski, Alfred (1946). Introduction to Logic and to the Methodology of Deductive Sciences (1995 ed.). Courier Dover. ISBN 0-486-28462-X. {{cite book}}:
History of the function concept
History_of_the_function_concept
In logic, a statement which is always true
also possible to define a deductive system (i.e., proof system) for propositional logic, as a simpler variant of the deductive systems employed for first-order
Tautology_(logic)
Template that specifies one or more axioms
finitely axiomatizable if there is a finite set of sentences whose deductive closure is exactly the theory. An axiom schema may be finitely describable
Axiom_schema
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List of Boolean algebra topics
List_of_Boolean_algebra_topics
Term in linguistics
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Autonomy_of_syntax
Study of the semantics, or interpretations, of formal and natural languages
logic. Term logic is an attempt to modernize Aristotle's logic: find deductive systems in the spirit of Aristotle's syllogisms, but with the generality
Semantics_(logic)
Steps in reasoning
contradict it, even though the latter (falsifications) is more informative for deductive reasoning. This is demonstrated by the Watson selection task. Another
Inference
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_logicians
Mathematical operator
In mathematics, a closure operator on a set S is a function cl : P ( S ) → P ( S ) {\displaystyle \operatorname {cl} :{\mathcal {P}}(S)\rightarrow {\mathcal
Closure_operator
Logical operator in modal logic
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Modal_operator
Capacity for consciously making sense of things
Reasoning may be subdivided into forms of logical reasoning, such as deductive reasoning, inductive reasoning, and abductive reasoning. Aristotle drew
Reason
Application of logical methods to philosophical problems
Stanford University. Retrieved 4 December 2021. Magnus, P. D. (2005). "1.4 Deductive validity". Forall X: An Introduction to Formal Logic. Victoria, BC, Canada:
Philosophical_logic
Method in formal logic
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Condensed_detachment
Process of changing beliefs to take into account a new piece of information
{\displaystyle K+P} is the deductive closure of K ∪ { P } {\displaystyle K\cup \{P\}} . The AGM postulates for revision are: Closure: K ∗ P {\displaystyle
Belief_revision
Concept in model theory
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Interpretation_(model_theory)
Formal study of linguistic meaning
alternative "Steve invited Anne and Mary". Formal logic studies the laws of deductive reasoning, focusing on entailment relations between premises and conclusions
Formal semantics (natural language)
Formal_semantics_(natural_language)
Formal statement in logic
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Strict_conditional
American philosopher
A. Warfield, Oxford University Press, 2010. Audi, Robert (1995). "Deductive Closure, Defeasibility and Scepticism: A Reply to Feldman". The Philosophical
Richard_Feldman_(philosopher)
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Gödel_logic
Study of the scope and nature of logic
the form of arguments, expressed in a formal language, and focuses on deductive inferences. Informal logic, on the other hand, addresses a much wider
Philosophy_of_logic
Academic field of logic and rhetoric
Books: "The most lasting legacy of the work is its break with formal, deductive logic and its introduction of Stephen Toulmin's model of argument to undergraduate
Argumentation_theory
Relationship where one statement follows from another
language L {\displaystyle {\mathcal {L}}} , either by constructing a deductive system for L {\displaystyle {\mathcal {L}}} or by formal intended semantics
Logical_consequence
Reasoning for mathematical statements
A mathematical proof is a deductive argument for a mathematical statement, showing that the stated assumptions logically guarantee the conclusion. The
Mathematical_proof
proof of the conclusion. deductive consequence See syntactic consequence. deductive validity 1. The property of a deductive argument where, if the premises
Glossary_of_logic
Problem of determining if a Boolean formula could be made true
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Boolean satisfiability problem
Boolean_satisfiability_problem
Theorem in mathematical logic
first-order logic is the strongest logic (satisfying certain conditions, e.g. closure under classical negation) having both the (countable) compactness property
Lindström's_theorem
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_women_logicians
Type of logical system
theories, predicates may be interpreted as sets of sets. There are many deductive systems for first-order logic which are both sound, i.e. all provable
First-order_logic
Theorem in set theory
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Schröder–Bernstein_theorem
Entities that are said to be either true or false
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Truth-bearer
Type of argument
schemes can include inferences based on different types of reasoning—deductive, inductive, abductive, probabilistic, etc. The study of argumentation
Argumentation_scheme
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List of mathematical logic topics
List_of_mathematical_logic_topics
One of six schools of Hindu philosophy
statements), and in philosophical discourse. Inference in Indian logic is ‘deductive and inductive’, ‘formal as well as material’. In essence, it is the method
Nyaya
Subfield of mathematics
mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include usage of logic to characterize correct
Mathematical_logic
Theorem in set theory
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Kőnig's_theorem_(set_theory)
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_set_theory_topics
Type of diagrammatic notation for logic
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Randolph_diagram
Concept in mathematical logic
be omitted from the definition. If T {\displaystyle T} is furthermore deductively closed, completeness reduces to the concise condition that exactly one
Complete_theory
NP-complete variant of the Boolean satisfiability problem
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
1-in-3-SAT
mathematical theories are, like those of physics and biology, hypothetico-deductive: pure mathematics therefore turns out to be much closer to the natural
Philosophy_of_mathematics
are preserved in the works of Plato and Aristotle, and the idea of a deductive system was probably known in the Pythagorean school and the Platonic Academy
History_of_logic
Logical theory
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Trivialism
American philosopher (born 1941)
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Bas_van_Fraassen
American philosopher
Philosophical Studies article, "Skepticism, Relevant Alternatives, and Deductive Closure". "Mrs. William Stine". The Morning Call. 29 December 1977. Retrieved
Gail_Stine
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
List_of_rules_of_inference
Concept in logic
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Substitution_(logic)
Nyāya text
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Tarka-Sangraha
Sanskrit treatise by Gangesa
propositions Antecedent Consequent Contradiction Paradox Antinomy Deduction Deductive closure Definition Description Dichotomy Entailment Linguistic Form Induction
Tattvachintamani
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
Girl/Female
American, Arabic, Australian, Christian, English, French, Greek, Hebrew, Indian, Persian, Sanskrit
Dark Haired Beauty; Night; Divine Play; From the Island; Night Beauty; Lovelorn; Seductive
Girl/Female
African, Arabic, Australian, French, German, Hebrew, Indian, Kenyan, Spanish, Swahili, Tamil
Gentle; Delicate; Gentleness is her Soul; Lovelorn; Seductive
Female
Chinese
flattering and seductive.
Girl/Female
American, Arabic, Hebrew
Night; Lovelorn; Seductive
Boy/Male
English American
From the raven farm. TV detective character Renington Steele. Surname.
Girl/Female
American, Arabic, Australian, British, Danish, English, Greek, Hebrew, Latin
Night; Night Beauty; Feminine of Lyle; From the Island; Variant of Delilah; Form of Lilac; Bluish; Languishing; Lovelorn; Seductive
Girl/Female
Muslim
Depictive
Male
Japanese
(1-妖一, 2-陽一, 3-洋一, 4-与一) Japanese name YOICHI means "bewitching/seductive first (son)," 2) "clear/sun/pride first (son)," 3) "foreign/ocean first (son)," and 4) "participating first (son)."
Girl/Female
African, American, Arabic, Danish, Finnish, French, German, Hebrew, Indian, Iranian, Irish, Italian, Muslim, Parsi, Sindhi, Swedish, Tamil
Dark as Night; Black; Night; Night Beauty; Nocturnal; Dark-haired Beauty; Lovelorn; Seductive; Name of a Saint; Dark Haired
Girl/Female
African, American, Arabic, Assamese, Australian, British, Danish, English, French, German, Greek, Hebrew, Hindu, Indian, Iranian, Jamaican, Latin, Muslim, Parsi, Persian, Polish, Sanskrit, Sindhi, Swahili, Tamil
Good; Night; Feminine of Lyle; Seductive; Dark Beauty; Lily; Purity; Pleasure; Sport; Pastime; Delicate; Playful; Divine Drama
Girl/Female
Afghan, African, American, Arabic, Danish, Egyptian, Finnish, Hebrew, Hindu, Indian, Jamaican, Modern, Muslim, Swahili, Swedish, Tamil
Dark Beauty; Wine; Intoxication; Night Beauty; Born at Night; Seductive
Girl/Female
French, German, Latin, Spanish
Smooth; Seductive; Flattering; Blond
Boy/Male
Indian, Sanskrit
Not Defective; Healthy; Whole
Girl/Female
Arabic, Muslim
Depictive
Girl/Female
Hindu, Indian, Tamil, Telugu
Initiation; Concentration; God's Name; Dedicative
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
Boy/Male
Arabic, Muslim, Parsi
Funny
Girl/Female
Anglo, British, English
Noble
Boy/Male
Hindu, Indian, Telugu
Love; Lovable Person
Girl/Female
American, Australian, British, English, Irish, Jamaican
Cushion; Pillow; Helpful; Helper
Boy/Male
Scottish
True and bold. Also 'bald'. Introduced from England and Germany during the Norman conquest, the...
Male
Hungarian
 Hungarian form of German Emmerich, IMRE means "work-power." Compare with another form of Imre.
Surname or Lastname
English
English : variant of Allum.
Boy/Male
Indian
Rock
Boy/Male
Celtic American English Irish Scottish
Stranger.
Boy/Male
Hindu
Another name of Ganesh, Warrior
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
DEDUCTIVE CLOSURE
adv.
By deduction; by way of inference; by consequence.
a.
Wanting in something; incomplete; lacking a part; deficient; imperfect; faulty; -- applied either to natural or moral qualities; as, a defective limb; defective timber; a defective copy or account; a defective character; defective rules.
n.
Subtraction; deduction.
a.
Seductive.
a.
Facilitating induction; susceptible of being acted upon by induction; as certain substances have a great inductive capacity.
adv.
By deduction.
n.
A detective.
a.
Lacking some of the usual forms of declension or conjugation; as, a defective noun or verb.
a.
Inductive.
adv.
In a seductive manner.
a.
Tending to lead astray; apt to mislead by flattering appearances; tempting; alluring; as, a seductive offer.
a.
Tending to educate; that gives education; as, an educative process; an educative experience.
n.
Act of deducting or taking away; subtraction; as, the deduction of the subtrahend from the minuend.
a.
Operating by induction; as, an inductive electrical machine.
n.
That which is deducted; the part taken away; abatement; as, a deduction from the yearly rent.
n.
A reductive agent.
a.
Fitted for, or skilled in, detecting; employed in detecting crime or criminals; as, a detective officer.
a.
Sweet speaking; persuasive; seductive.
a.
Leading to inferences; proceeding by, derived from, or using, induction; as, inductive reasoning.
a.
Of or pertaining to deduction; capable of being deduced from premises; deducible.