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179 relations: Alfred North Whitehead, Ampersand, Argument, Arithmetic, Arity, Associative property, Atomic formula, Augustus De Morgan, Axiom, Axiom schema, Basic Books, Bertrand Russell, Biconditional elimination, Biconditional introduction, Binary relation, Boolean algebra, Boolean algebra (structure), Boolean domain, Boolean function, Boolean satisfiability problem, Boolean-valued function, Calculus ratiocinator, Cardinality of the continuum, Categorical logic, Category (mathematics), Chaff algorithm, Charles Sanders Peirce, Chen Chung Chang, Chrysippus, Clarence Irving Lewis, Combinational logic, Combinatory logic, Commutative property, Completeness (logic), Conceptual graph, Conditional proof, Conjunction elimination, Conjunction introduction, Consistency, Constructive dilemma, Contraposition, De Morgan's laws, Deduction theorem, Destructive dilemma, Disjunction elimination, Disjunction introduction, Disjunctive syllogism, Distributive property, Double negation, DPLL algorithm, ..., Emil Leon Post, Entitative graph, Equational logic, Ernst Schröder, Evert Willem Beth, Exclusive or, Existential graph, Exportation (logic), Expression (mathematics), False (logic), First-order logic, Formal grammar, Formal language, Formal proof, Formal system, Frege's propositional calculus, Function (mathematics), Functional completeness, Gödel, Escher, Bach, George Boole, Gerhard Gentzen, Gottfried Wilhelm Leibniz, Gottlob Frege, Graph (discrete mathematics), Graph traversal, Heyting algebra, Higher-order logic, Hilbert system, Howard Jerome Keisler, Hypothetical syllogism, If and only if, Implicational propositional calculus, Internet Encyclopedia of Philosophy, Interpretation (logic), Intuitionistic logic, Isomorphism, Jan Łukasiewicz, Jean Buridan, Joachim Lambek, John Venn, Latin, Law of excluded middle, Law of noncontradiction, Laws of Form, List of Boolean algebra topics, Logic, Logical conjunction, Logical connective, Logical consequence, Logical disjunction, Logical equivalence, Logical graph, Logical NOR, Logical truth, Ludwig Wittgenstein, Many-valued logic, Material conditional, Material implication (rule of inference), Mathematical logic, Mathematical model, Mereology, Metalanguage, Metamath, Metatheorem, Method of analytic tableaux, Modal logic, Modus ponens, Modus tollens, Natural deduction, Negation, Negation introduction, NP-completeness, Old Dominion University, Operation (mathematics), Order type, Parse tree, Parsing, Partition of a set, Paul of Venice, Peirce's law, Peter Abelard, Peter of Spain, Pointer (computer programming), Possible world, Predicate (mathematical logic), Proof by exhaustion, Proof theory, Proposition, Propositional formula, Propositional variable, Q.E.D., Quantifier (logic), Recursive definition, Robert R. Korfhage, Rule of inference, Satisfiability modulo theories, Second-order logic, Second-order propositional logic, Semantics, Sequent calculus, Set theory, Singular term, Soundness, State of affairs (philosophy), Stoic logic, Stoicism, Substitution (logic), Syllogism, Symmetric difference, Tautology (logic), Tautology (rule of inference), Term logic, Theorem, Tilde, Transposition (logic), Truth, Truth function, Truth table, Truth value, Turnstile (symbol), Uncountable set, Validity, Valuation (logic), Variable (mathematics), Walter Burley, Well-formed formula, William of Sherwood, William Stanley Jevons, Zeroth-order logic. Expand index (129 more) »
Alfred North Whitehead
Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.
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Ampersand
The ampersand is the logogram &, representing the conjunction "and".
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Argument
In logic and philosophy, an argument is a series of statements typically used to persuade someone of something or to present reasons for accepting a conclusion.
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Arithmetic
Arithmetic (from the Greek ἀριθμός arithmos, "number") is a branch of mathematics that consists of the study of numbers, especially the properties of the traditional operations on them—addition, subtraction, multiplication and division.
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Arity
In logic, mathematics, and computer science, the arity of a function or operation is the number of arguments or operands that the function takes.
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Associative property
In mathematics, the associative property is a property of some binary operations.
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Atomic formula
In mathematical logic, an atomic formula (also known simply as an atom) is a formula with no deeper propositional structure, that is, a formula that contains no logical connectives or equivalently a formula that has no strict subformulas.
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Augustus De Morgan
Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.
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Axiom
An axiom or postulate is a statement that is taken to be true, to serve as a premise or starting point for further reasoning and arguments.
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Axiom schema
In mathematical logic, an axiom schema (plural: axiom schemata or axiom schemas) generalizes the notion of axiom.
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Basic Books
Basic Books is a book publisher founded in 1952 and located in New York, now an imprint of Hachette Books.
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Bertrand Russell
Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 – 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.
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Biconditional elimination
Biconditional elimination is the name of two valid rules of inference of propositional logic.
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Biconditional introduction
In propositional logic, biconditional introduction is a valid rule of inference.
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Binary relation
In mathematics, a binary relation on a set A is a set of ordered pairs of elements of A. In other words, it is a subset of the Cartesian product A2.
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Boolean algebra
In mathematics and mathematical logic, Boolean algebra is the branch of algebra in which the values of the variables are the truth values true and false, usually denoted 1 and 0 respectively.
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Boolean algebra (structure)
In abstract algebra, a Boolean algebra or Boolean lattice is a complemented distributive lattice.
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Boolean domain
In mathematics and abstract algebra, a Boolean domain is a set consisting of exactly two elements whose interpretations include false and true.
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Boolean function
In mathematics and logic, a (finitary) Boolean function (or switching function) is a function of the form ƒ: Bk → B, where B.
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Boolean satisfiability problem
In computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated as SATISFIABILITY or SAT) is the problem of determining if there exists an interpretation that satisfies a given Boolean formula.
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Boolean-valued function
A Boolean-valued function (sometimes called a predicate or a proposition) is a function of the type f: X → B, where X is an arbitrary set and where B is a Boolean domain, i.e. a generic two-element set, (for example B.
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Calculus ratiocinator
The Calculus ratiocinator is a theoretical universal logical calculation framework, a concept described in the writings of Gottfried Leibniz, usually paired with his more frequently mentioned characteristica universalis, a universal conceptual language.
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Cardinality of the continuum
In set theory, the cardinality of the continuum is the cardinality or “size” of the set of real numbers \mathbb R, sometimes called the continuum.
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Categorical logic
Categorical logic is the branch of mathematics in which tools and concepts from category theory are applied to the study of mathematical logic.
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Category (mathematics)
In mathematics, a category (sometimes called an abstract category to distinguish it from a concrete category) is an algebraic structure similar to a group but without requiring inverse or closure properties.
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Chaff algorithm
Chaff is an algorithm for solving instances of the Boolean satisfiability problem in programming.
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Charles Sanders Peirce
Charles Sanders Peirce ("purse"; 10 September 1839 – 19 April 1914) was an American philosopher, logician, mathematician, and scientist who is sometimes known as "the father of pragmatism".
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Chen Chung Chang
Chen Chung Chang is a mathematician who works in model theory.
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Chrysippus
Chrysippus of Soli (Χρύσιππος ὁ Σολεύς, Chrysippos ho Soleus) was a Greek Stoic philosopher.
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Clarence Irving Lewis
Clarence Irving Lewis (April 12, 1883 – February 3, 1964), usually cited as C. I. Lewis, was an American academic philosopher and the founder of conceptual pragmatism.
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Combinational logic
In digital circuit theory, combinational logic (sometimes also referred to as time-independent logic) is a type of digital logic which is implemented by Boolean circuits, where the output is a pure function of the present input only.
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Combinatory logic
Combinatory logic is a notation to eliminate the need for quantified variables in mathematical logic.
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Commutative property
In mathematics, a binary operation is commutative if changing the order of the operands does not change the result.
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Completeness (logic)
In mathematical logic and metalogic, a formal system is called complete with respect to a particular property if every formula having the property can be derived using that system, i.e. is one of its theorems; otherwise the system is said to be incomplete.
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Conceptual graph
Conceptual graphs (CGs) are a formalism for knowledge representation.
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Conditional proof
A conditional proof is a proof that takes the form of asserting a conditional, and proving that the antecedent of the conditional necessarily leads to the consequent.
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Conjunction elimination
In propositional logic, conjunction elimination (also called and elimination, ∧ elimination, or simplification) is a valid immediate inference, argument form and rule of inference which makes the inference that, if the conjunction A and B is true, then A is true, and B is true.
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Conjunction introduction
Conjunction introduction (often abbreviated simply as conjunction and also called and introduction) is a valid rule of inference of propositional logic.
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Consistency
In classical deductive logic, a consistent theory is one that does not contain a contradiction.
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Constructive dilemma
Constructive dilemma is a valid rule of inference of propositional logic.
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Contraposition
In logic, contraposition is an inference that says that a conditional statement is logically equivalent to its contrapositive.
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De Morgan's laws
In propositional logic and boolean algebra, De Morgan's laws are a pair of transformation rules that are both valid rules of inference.
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Deduction theorem
In mathematical logic, the deduction theorem is a metatheorem of propositional and first-order logic.
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Destructive dilemma
Destructive dilemma is the name of a valid rule of inference of propositional logic.
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Disjunction elimination
In propositional logic, disjunction elimination (sometimes named proof by cases, case analysis, or or elimination), is the valid argument form and rule of inference that allows one to eliminate a disjunctive statement from a logical proof.
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Disjunction introduction
Disjunction introduction or addition (also called or introduction) is a rule of inference of propositional logic and almost every other deduction system.
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Disjunctive syllogism
In classical logic, disjunctive syllogism (historically known as modus tollendo ponens (MTP), Latin for "mode that affirms by denying") is a valid argument form which is a syllogism having a disjunctive statement for one of its premises.
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Distributive property
In abstract algebra and formal logic, the distributive property of binary operations generalizes the distributive law from boolean algebra and elementary algebra.
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Double negation
In propositional logic, double negation is the theorem that states that "If a statement is true, then it is not the case that the statement is not true." This is expressed by saying that a proposition A is logically equivalent to not (not-A), or by the formula A ≡ ~(~A) where the sign ≡ expresses logical equivalence and the sign ~ expresses negation.
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DPLL algorithm
In computer science, the Davis–Putnam–Logemann–Loveland (DPLL) algorithm is a complete, backtracking-based search algorithm for deciding the satisfiability of propositional logic formulae in conjunctive normal form, i.e. for solving the CNF-SAT problem.
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Emil Leon Post
Emil Leon Post (February 11, 1897 – April 21, 1954) was an American mathematician and logician.
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Entitative graph
An entitative graph is an element of the diagrammatic syntax for logic that Charles Sanders Peirce developed under the name of qualitative logic beginning in the 1880s, taking the coverage of the formalism only as far as the propositional or sentential aspects of logic are concerned.
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Equational logic
First-order equational logic consists of quantifier-free terms of ordinary first-order logic, with equality as the only predicate symbol.
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Ernst Schröder
Friedrich Wilhelm Karl Ernst Schröder (25 November 1841 in Mannheim, Baden, Germany – 16 June 1902 in Karlsruhe, Germany) was a German mathematician mainly known for his work on algebraic logic.
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Evert Willem Beth
Evert Willem Beth (7 July 1908 – 12 April 1964) was a Dutch philosopher and logician, whose work principally concerned the foundations of mathematics.
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Exclusive or
Exclusive or or exclusive disjunction is a logical operation that outputs true only when inputs differ (one is true, the other is false).
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Existential graph
An existential graph is a type of diagrammatic or visual notation for logical expressions, proposed by Charles Sanders Peirce, who wrote on graphical logic as early as 1882, and continued to develop the method until his death in 1914.
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Exportation (logic)
Exportation is a valid rule of replacement in propositional logic.
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Expression (mathematics)
In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.
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False (logic)
In logic, false or untrue is the state of possessing negative truth value or a nullary logical connective.
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First-order logic
First-order logic—also known as first-order predicate calculus and predicate logic—is a collection of formal systems used in mathematics, philosophy, linguistics, and computer science.
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Formal grammar
In formal language theory, a grammar (when the context is not given, often called a formal grammar for clarity) is a set of production rules for strings in a formal language.
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Formal language
In mathematics, computer science, and linguistics, a formal language is a set of strings of symbols together with a set of rules that are specific to it.
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Formal proof
A formal proof or derivation is a finite sequence of sentences (called well-formed formulas in the case of a formal language), each of which is an axiom, an assumption, or follows from the preceding sentences in the sequence by a rule of inference.
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Formal system
A formal system is the name of a logic system usually defined in the mathematical way.
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Frege's propositional calculus
In mathematical logic Frege's propositional calculus was the first axiomatization of propositional calculus.
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Function (mathematics)
In mathematics, a function was originally the idealization of how a varying quantity depends on another quantity.
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Functional completeness
In logic, a functionally complete set of logical connectives or Boolean operators is one which can be used to express all possible truth tables by combining members of the set into a Boolean expression.
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Gödel, Escher, Bach
Gödel, Escher, Bach: An Eternal Golden Braid, also known as GEB, is a 1979 book by Douglas Hofstadter.
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George Boole
George Boole (2 November 1815 – 8 December 1864) was a largely self-taught English mathematician, philosopher and logician, most of whose short career was spent as the first professor of mathematics at Queen's College, Cork in Ireland.
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Gerhard Gentzen
Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician.
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Gottfried Wilhelm Leibniz
Gottfried Wilhelm (von) Leibniz (or; Leibnitz; – 14 November 1716) was a German polymath and philosopher who occupies a prominent place in the history of mathematics and the history of philosophy.
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Gottlob Frege
Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.
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Graph (discrete mathematics)
In mathematics, and more specifically in graph theory, a graph is a structure amounting to a set of objects in which some pairs of the objects are in some sense "related".
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Graph traversal
In computer science, graph traversal (also known as graph search) refers to the process of visiting (checking and/or updating) each vertex in a graph.
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Heyting algebra
In mathematics, a Heyting algebra is a bounded lattice (with join and meet operations written ∨ and ∧ and with least element 0 and greatest element 1) equipped with a binary operation a → b of implication such that c ∧ a ≤ b is equivalent to c ≤ a → b. From a logical standpoint, A → B is by this definition the weakest proposition for which modus ponens, the inference rule A → B, A ⊢ B, is sound.
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Higher-order logic
In mathematics and logic, a higher-order logic is a form of predicate logic that is distinguished from first-order logic by additional quantifiers and, sometimes, stronger semantics.
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Hilbert system
In logic, especially mathematical logic, a Hilbert system, sometimes called Hilbert calculus, Hilbert-style deductive system or Hilbert–Ackermann system, is a type of system of formal deduction attributed to Gottlob FregeMáté & Ruzsa 1997:129 and David Hilbert.
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Howard Jerome Keisler
Howard Jerome Keisler (born 3 December 1936) is an American mathematician, currently professor emeritus at University of Wisconsin–Madison.
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Hypothetical syllogism
In classical logic, hypothetical syllogism is a valid argument form which is a syllogism having a conditional statement for one or both of its premises.
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If and only if
In logic and related fields such as mathematics and philosophy, if and only if (shortened iff) is a biconditional logical connective between statements.
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Implicational propositional calculus
In mathematical logic, the implicational propositional calculus is a version of classical propositional calculus which uses only one connective, called implication or conditional.
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Internet Encyclopedia of Philosophy
The Internet Encyclopedia of Philosophy (IEP) is a scholarly online encyclopedia, dealing with philosophy, philosophical topics, and philosophers.
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Interpretation (logic)
An interpretation is an assignment of meaning to the symbols of a formal language.
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Intuitionistic logic
Intuitionistic logic, sometimes more generally called constructive logic, refers to systems of symbolic logic that differ from the systems used for classical logic by more closely mirroring the notion of constructive proof.
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Isomorphism
In mathematics, an isomorphism (from the Ancient Greek: ἴσος isos "equal", and μορφή morphe "form" or "shape") is a homomorphism or morphism (i.e. a mathematical mapping) that can be reversed by an inverse morphism.
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Jan Łukasiewicz
Jan Łukasiewicz (21 December 1878 – 13 February 1956) was a Polish logician and philosopher born in Lwów, a city in the Galician kingdom of Austria-Hungary.
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Jean Buridan
Jean Buridan (Latin: Johannes Buridanus; –) was an influential 14th century French philosopher.
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Joachim Lambek
Joachim "Jim" Lambek (5 December 1922 – 23 June 2014) was Peter Redpath Emeritus Professor of Pure Mathematics at McGill University, where he earned his Ph.D. degree in 1950 with Hans Zassenhaus as advisor.
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John Venn
John Venn, FRS, FSA, (4 August 1834 – 4 April 1923) was an English logician and philosopher noted for introducing the Venn diagram, used in the fields of set theory, probability, logic, statistics, and computer science.
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Latin
Latin (Latin: lingua latīna) is a classical language belonging to the Italic branch of the Indo-European languages.
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Law of excluded middle
In logic, the law of excluded middle (or the principle of excluded middle) states that for any proposition, either that proposition is true or its negation is true.
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Law of noncontradiction
In classical logic, the law of non-contradiction (LNC) (also known as the law of contradiction, principle of non-contradiction (PNC), or the principle of contradiction) states that contradictory statements cannot both be true in the same sense at the same time, e.g. the two propositions "A is B" and "A is not B" are mutually exclusive.
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Laws of Form
Laws of Form (hereinafter LoF) is a book by G. Spencer-Brown, published in 1969, that straddles the boundary between mathematics and philosophy.
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List of Boolean algebra topics
This is a list of topics around Boolean algebra and propositional logic.
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Logic
Logic (from the logikḗ), originally meaning "the word" or "what is spoken", but coming to mean "thought" or "reason", is a subject concerned with the most general laws of truth, and is now generally held to consist of the systematic study of the form of valid inference.
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Logical conjunction
In logic, mathematics and linguistics, And (∧) is the truth-functional operator of logical conjunction; the and of a set of operands is true if and only if all of its operands are true.
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Logical connective
In logic, a logical connective (also called a logical operator, sentential connective, or sentential operator) is a symbol or word used to connect two or more sentences (of either a formal or a natural language) in a grammatically valid way, such that the value of the compound sentence produced depends only on that of the original sentences and on the meaning of the connective.
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Logical consequence
Logical consequence (also entailment) is a fundamental concept in logic, which describes the relationship between statements that hold true when one statement logically follows from one or more statements.
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Logical disjunction
In logic and mathematics, or is the truth-functional operator of (inclusive) disjunction, also known as alternation; the or of a set of operands is true if and only if one or more of its operands is true.
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Logical equivalence
In logic, statements p and q are logically equivalent if they have the same logical content.
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Logical graph
A logical graph is a special type of diagramatic structure in any one of several systems of graphical syntax that Charles Sanders Peirce developed for logic.
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Logical NOR
In boolean logic, logical nor or joint denial is a truth-functional operator which produces a result that is the negation of logical or.
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Logical truth
Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.
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Ludwig Wittgenstein
Ludwig Josef Johann Wittgenstein (26 April 1889 – 29 April 1951) was an Austrian-British philosopher who worked primarily in logic, the philosophy of mathematics, the philosophy of mind, and the philosophy of language.
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Many-valued logic
In logic, a many-valued logic (also multi- or multiple-valued logic) is a propositional calculus in which there are more than two truth values.
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Material conditional
The material conditional (also known as material implication, material consequence, or simply implication, implies, or conditional) is a logical connective (or a binary operator) that is often symbolized by a forward arrow "→".
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Material implication (rule of inference)
In propositional logic, material implication is a valid rule of replacement that allows for a conditional statement to be replaced by a disjunction in which the antecedent is negated.
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Mathematical logic
Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.
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Mathematical model
A mathematical model is a description of a system using mathematical concepts and language.
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Mereology
In philosophy and mathematical logic, mereology (from the Greek μέρος meros (root: μερε- mere-, "part") and the suffix -logy "study, discussion, science") is the study of parts and the wholes they form.
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Metalanguage
Broadly, any metalanguage is language or symbols used when language itself is being discussed or examined.
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Metamath
Metamath is a language for developing strictly formalized mathematical definitions and proofs accompanied by a proof checker for this language and a growing database of thousands of proved theorems covering conventional results in logic, set theory, number theory, group theory, algebra, analysis, and topology, as well as topics in Hilbert spaces and quantum logic.
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Metatheorem
In logic, a metatheorem is a statement about a formal system proven in a metalanguage.
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Method of analytic tableaux
In proof theory, the semantic tableau (plural: tableaux, also called 'truth tree') is a decision procedure for sentential and related logics, and a proof procedure for formulae of first-order logic.
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Modal logic
Modal logic is a type of formal logic primarily developed in the 1960s that extends classical propositional and predicate logic to include operators expressing modality.
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Modus ponens
In propositional logic, modus ponens (MP; also modus ponendo ponens (Latin for "mode that affirms by affirming") or implication elimination) is a rule of inference.
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Modus tollens
In propositional logic, modus tollens (MT; also modus tollendo tollens (Latin for "mode that denies by denying") or denying the consequent) is a valid argument form and a rule of inference.
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Natural deduction
In logic and proof theory, natural deduction is a kind of proof calculus in which logical reasoning is expressed by inference rules closely related to the "natural" way of reasoning.
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Negation
In logic, negation, also called the logical complement, is an operation that takes a proposition P to another proposition "not P", written \neg P (¬P), which is interpreted intuitively as being true when P is false, and false when P is true.
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Negation introduction
Negation introduction is a rule of inference, or transformation rule, in the field of propositional calculus.
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NP-completeness
In computational complexity theory, an NP-complete decision problem is one belonging to both the NP and the NP-hard complexity classes.
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Old Dominion University
Old Dominion University, also known as ODU, is a public, co-educational research university located in Norfolk, Virginia, United States, with two satellite campuses in the Hampton Roads area.
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Operation (mathematics)
In mathematics, an operation is a calculation from zero or more input values (called operands) to an output value.
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Order type
In mathematics, especially in set theory, two ordered sets X,Y are said to have the same order type just when they are order isomorphic, that is, when there exists a bijection (each element matches exactly one in the other set) f: X → Y such that both f and its inverse are strictly increasing (order preserving i.e. the matching elements are also in the correct order).
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Parse tree
A parse tree or parsing tree or derivation tree or concrete syntax tree is an ordered, rooted tree that represents the syntactic structure of a string according to some context-free grammar.
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Parsing
Parsing, syntax analysis or syntactic analysis is the process of analysing a string of symbols, either in natural language, computer languages or data structures, conforming to the rules of a formal grammar.
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Partition of a set
In mathematics, a partition of a set is a grouping of the set's elements into non-empty subsets, in such a way that every element is included in one and only one of the subsets.
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Paul of Venice
Paul of Venice (or Paulus Venetus; 1369–1429) was a Roman Catholic scholastic philosopher, theologian, and realist logician and metaphysician of the Hermits of the Order of Saint Augustine.
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Peirce's law
In logic, Peirce's law is named after the philosopher and logician Charles Sanders Peirce.
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Peter Abelard
Peter Abelard (Petrus Abaelardus or Abailardus; Pierre Abélard,; 1079 – 21 April 1142) was a medieval French scholastic philosopher, theologian, and preeminent logician.
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Peter of Spain
Peter of Spain (Petrus Hispanus; Portuguese and Pedro Hispano; century) was the author of the Tractatus, later known as the Summulae Logicales, an important medieval university textbook on Aristotelian logic.
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Pointer (computer programming)
In computer science, a pointer is a programming language object that stores the memory address of another value located in computer memory.
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Possible world
In philosophy and logic, the concept of a possible world is used to express modal claims.
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Predicate (mathematical logic)
In mathematical logic, a predicate is commonly understood to be a Boolean-valued function P: X→, called the predicate on X. However, predicates have many different uses and interpretations in mathematics and logic, and their precise definition, meaning and use will vary from theory to theory.
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Proof by exhaustion
Proof by exhaustion, also known as proof by cases, proof by case analysis, complete induction, or the brute force method, is a method of mathematical proof in which the statement to be proved is split into a finite number of cases or sets of equivalent cases and each type of case is checked to see if the proposition in question holds.
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Proof theory
Proof theory is a major branchAccording to Wang (1981), pp.
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Proposition
The term proposition has a broad use in contemporary analytic philosophy.
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Propositional formula
In propositional logic, a propositional formula is a type of syntactic formula which is well formed and has a truth value.
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Propositional variable
In mathematical logic, a propositional variable (also called a sentential variable or sentential letter) is a variable which can either be true or false.
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Q.E.D.
Q.E.D. (also written QED and QED) is an initialism of the Latin phrase quod erat demonstrandum meaning "what was to be demonstrated" or "what was to be shown." Some may also use a less direct translation instead: "thus it has been demonstrated." Traditionally, the phrase is placed in its abbreviated form at the end of a mathematical proof or philosophical argument when the original proposition has been restated exactly, as the conclusion of the demonstration or completion of the proof.
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Quantifier (logic)
In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.
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Recursive definition
A recursive definition (or inductive definition) in mathematical logic and computer science is used to define the elements in a set in terms of other elements in the set (Aczel 1978:740ff).
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Robert R. Korfhage
Robert Roy Korfhage (December 2, 1930 – November 20, 1998) was an American computer scientist, famous for his contributions to information retrieval and several textbooks.
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Rule of inference
In logic, a rule of inference, inference rule or transformation rule is a logical form consisting of a function which takes premises, analyzes their syntax, and returns a conclusion (or conclusions).
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Satisfiability modulo theories
In computer science and mathematical logic, the satisfiability modulo theories (SMT) problem is a decision problem for logical formulas with respect to combinations of background theories expressed in classical first-order logic with equality.
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Second-order logic
In logic and mathematics second-order logic is an extension of first-order logic, which itself is an extension of propositional logic.
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Second-order propositional logic
A second-order propositional logic is a propositional logic extended with quantification over propositions.
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Semantics
Semantics (from σημαντικός sēmantikós, "significant") is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics.
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Sequent calculus
Sequent calculus is, in essence, a style of formal logical argumentation where every line of a proof is a conditional tautology (called a sequent by Gerhard Gentzen) instead of an unconditional tautology.
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Set theory
Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.
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Singular term
A singular term is a paradigmatic referring device in a language.
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Soundness
In mathematical logic, a logical system has the soundness property if and only if every formula that can be proved in the system is logically valid with respect to the semantics of the system.
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State of affairs (philosophy)
In philosophy, a state of affairs (Sachverhalt), also known as a situation, is a way the actual world must be in order to make some given proposition about the actual world true; in other words, a state of affairs (situation) is a truth-maker, whereas a proposition is a truth-bearer.
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Stoic logic
Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece.
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Stoicism
Stoicism is a school of Hellenistic philosophy founded by Zeno of Citium in Athens in the early 3rd century BC.
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Substitution (logic)
Substitution is a fundamental concept in logic.
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Syllogism
A syllogism (συλλογισμός syllogismos, "conclusion, inference") is a kind of logical argument that applies deductive reasoning to arrive at a conclusion based on two or more propositions that are asserted or assumed to be true.
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Symmetric difference
In mathematics, the symmetric difference, also known as the disjunctive union, of two sets is the set of elements which are in either of the sets and not in their intersection.
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Tautology (logic)
In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.
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Tautology (rule of inference)
In propositional logic, tautology is one of two commonly used rules of replacement.
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Term logic
In philosophy, term logic, also known as traditional logic, syllogistic logic or Aristotelian logic, is a loose name for an approach to logic that began with Aristotle and that was dominant until the advent of modern predicate logic in the late nineteenth century.
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Theorem
In mathematics, a theorem is a statement that has been proven on the basis of previously established statements, such as other theorems, and generally accepted statements, such as axioms.
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Tilde
The tilde (in the American Heritage dictionary or; ˜ or ~) is a grapheme with several uses.
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Transposition (logic)
In propositional logic, transposition is a valid rule of replacement that permits one to switch the antecedent with the consequent of a conditional statement in a logical proof if they are also both negated.
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Truth
Truth is most often used to mean being in accord with fact or reality, or fidelity to an original or standard.
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Truth function
In logic, a truth function is a function that accepts truth values as input and produces a truth value as output, i.e., the input and output are all truth values.
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Truth table
A truth table is a mathematical table used in logic—specifically in connection with Boolean algebra, boolean functions, and propositional calculus—which sets out the functional values of logical expressions on each of their functional arguments, that is, for each combination of values taken by their logical variables (Enderton, 2001).
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Truth value
In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.
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Turnstile (symbol)
In mathematical logic and computer science the symbol \vdash has taken the name turnstile because of its resemblance to a typical turnstile if viewed from above.
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Uncountable set
In mathematics, an uncountable set (or uncountably infinite set) is an infinite set that contains too many elements to be countable.
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Validity
In logic, an argument is valid if and only if it takes a form that makes it impossible for the premises to be true and the conclusion nevertheless to be false.
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Valuation (logic)
In logic and model theory, a valuation can be.
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Variable (mathematics)
In elementary mathematics, a variable is a symbol, commonly an alphabetic character, that represents a number, called the value of the variable, which is either arbitrary, not fully specified, or unknown.
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Walter Burley
Walter Burley (or Burleigh) (c. 1275–1344/5) was a medieval English scholastic philosopher and logician with at least 50 works attributed to him.
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Well-formed formula
In mathematical logic, propositional logic and predicate logic, a well-formed formula, abbreviated WFF or wff, often simply formula, is a finite sequence of symbols from a given alphabet that is part of a formal language.
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William of Sherwood
William of Sherwood or William Sherwood, with numerous variant spellings, was a medieval English scholastic philosopher, logician, and teacher.
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William Stanley Jevons
William Stanley Jevons FRS (1 September 1835 – 13 August 1882) was an English economist and logician.
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Zeroth-order logic
Zeroth-order logic is first-order logic without variables or quantifiers.
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Redirects here:
Classical propositional logic, Exportation in logic, Propositional Calculus, Propositional calculi, Propositional logic, Sentance logic, Sentence logic, Sentential calculus, Sentential logic, Truth-functional propositional calculus, Truth-functional propositional logic.
References
[1] https://en.wikipedia.org/wiki/Propositional_calculus
