NationMaster - Encyclopedia: List of topics in logic

This is a list of topics in logic. Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. ...

Alphabetical list

Abacus logic -- Abduction (logic) -- Abductive validation -- Affine logic -- Affirming the antecedent --Affirming the consequent -- Antecedent -- Antinomy -- Argument form -- Aristotelian logic -- Axiom -- Axiomatic system -- Axiomatization In logic, an abacus is an instrument, often called the logical machine, analogous to the mathematical abacus. ... This article is in need of attention. ... After obtaining results from an inference procedure, we may be left with multiple assumptions, some of which may be contradictory. ... A substructural logic that denies the structural rule of contraction. ... Affirming the antecedent is a valid argument form which proceeds by affirming the truth of the first part (the if part, commonly called the antecedent) of a conditional, and concluding that the second part (the then part, commonly called the consequent) is true. ... Affirming the consequent is a logical fallacy in the form of a hypothetical proposition. ... An antecedent is the first half of a hypothetical proposition. ... Antinomy (Greek anti-, against, plus nomos, law) is a term used in logic and epistemology, which, loosely, means a paradox or unresolvable contradiction. ... In logic, the argument form or test form of an argument results from replacing the different words, or sentences, that make up the argument with letters, along the lines of algebra; the letters represent logical variables. ... Aristotelian logic, also known as syllogistic logic, is the particular type of logic created by Aristotle, primarily in his works Prior Analytics and De Interpretatione. ... In epistemology, an axiom is a self-evident truth upon which other knowledge must rest, from which other knowledge is built up. ... In mathematics, an axiomatic system is any set of axioms from which some or all axioms can be used in conjunction to logically derive theorems. ... In mathematics, axiomatization is the process of defining the basic axiomatic systems from which mathematical theories can be derived. ...

Backward chaining -- Barcan formula -- Biconditional elimination -- Biconditional introduction -- Bivalence and related laws -- Boolean algebra -- Boolean logic Backward chaining is one of the two main methods of reasoning when using inference rules. ... In quantified modal logic, the Barcan formula and the converse Barcan formula state possible relationships between quantifiers and modalities. ... Biconditional elimination allows one to infer a conditional from a biconditional: if ( A ↔ B ) is true, then one may infer one direction of the biconditional, either ( A → B ) or ( B → A ). For example, if its true that Im breathing if and only if Im alive, then it... Biconditional introduction is the inference that, if B follows from A, and A follows from B, then A if and only if B. For example: if Im breathing, then Im alive; also, if Im alive, then Im breathing. ... In logic, the laws of bivalence, excluded middle, and non-contradiction are related, but not the same. ... Wikibooks has more about Boolean logic, under the title Boolean Algebra For a basic intro to sets, Boolean operations, Venn diagrams, truth tables, and Boolean applications, see Boolean logic. ... Boolean logic is a system of syllogistic logic invented by 19th-century British mathematician George Boole, which attempts to incorporate the empty set, that is, a class of non-existent entities, such as round squares, without resorting to uncertain truth values. ...

Categorical logic -- Categorial logic -- Clocked logic --Cointerpretability --College logic -- Combinatorial logic -- Combinatory logic -- Computability logic -- Conditional -- Conditional proof -- Conjunction elimination --Conjunction introduction -- Conjunctive normal form -- Consequent --Contradiction -- Contrapositive -- Control logic -- Converse (logic) -- Converse Barcan formula -- Cotolerance -- Counterfactual conditional -- Curry's paradox Categorical logic is a branch of category theory within mathematics, adjacent to mathematical logic but in fact more notable for its connections to theoretical computer science. ... Clocked logic (or dynamic logic) is a design methodology in digital logic that was popular in the 1970s and has seen a recent resurgence in the design of high speed digital electronics, particularly computer CPUs. ... In mathematical logic, cointerpretability is a binary relation on formal theories: a formal theory T is cointerpretable in another such theory S, when the language of S can be translated into the language of T in such a way that S proves every formula whose translation is a theorem of... Logic is the study of argument — not angry disagreements or fisticuffs, but instead the giving of reasons to believe things. ... This article is not about combinatory logic, a topic in mathematical logic. ... Combinatory logic is a notation introduced by Moses SchÃ¶nfinkel and Haskell Curry to eliminate the need for variables in mathematical logic. ... Computability logic is a formal theory of computability, introduced by Giorgi Japaridze in 2003. ... In logical calculus of mathematics, the logical conditional (also known as the material implication, sometimes material conditional) is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ... Conditional proof is a proof that takes the form of asserting a conditional, and proving that the premise or antecedent of the conditional necessarily leads to the conclusion. ... In logic, conjunction elimination is the inference that, if the conjunction A and B is true, then A is true, and B is true. ... Conjunction introduction is the inference that, if p is true, and q is true, then the conjunction p and q is true. ... In Boolean logic, Conjunctive Normal Form (CNF) is a method of standardizing and normalizing logical formulas. ... A consequent is the second half of a hypothetical proposition. ... Broadly speaking, a contradiction is an incompatibility between two or more statements, ideas, or actions. ... In predicate logic, the contrapositive (or transposition) of the statement p implies q is not-q implies not-p. ... Control logic is the part of a software architecture that controls what the program will do. ... In logic, if S is a statement of the form P implies Q, then the converse of S is a statement of the form Q implies P. In general, the verity of S says nothing about the verity of its converse. ... In quantified modal logic, the Barcan formula and the converse Barcan formula state possible relationships between quantifiers and modalities. ... In mathematical logic, a cotolerant sequence is a sequence of formal theories such that there are consistent extensions of these theories with each is cointerpretable in . ... A counterfactual conditional (sometimes called a subjunctive conditional) is a logical conditional statement whose antecedent is (ordinarily) taken to be contrary to fact by those who utter it. ... In logic, specifically mathematical logic, Currys paradoxes are a family of logical paradoxes that occur in naive set theory or naive logics. ...

De Morgan's laws -- Deduction theorem -- Deductive reasoning -- Degree of truth -- Denying the antecedent --Disjunction elimination -- Disjunction introduction -- Disjunctive normal form -- Disjunctive syllogism -- Double negative -- Double negative elimination In logic, De Morgans laws (or De Morgans theorem) are rules in formal logic relating pairs of dual logical operators in a systematic manner expressed in terms of negation. ... In mathematical logic, the deduction theorem states that if a formula F is deducible from E then the implication E â†’ F is demonstrable (i. ... In traditional Aristotelian logic, deductive reasoning is inference in which the conclusion is of lesser or equal generality than the premises, as opposed to inductive reasoning, where the conclusion is of greater generality than the premises. ... The degree of truth denotes the extent to which a proposition is true. ... Denying the antecedent is a type of logical fallacy. ... In propositional calculus disjunction elimination is the inference that, if A or B is true, and A entails C, and B entails C, then we may justifiably infer C. The reasoning is simple: since at least one of the statements A and B is true, and since either of them... Disjunction introduction is the logic principle that, if A is true, then its true that either A or B is true. ... In Boolean logic, Disjunctive Normal Form (DNF) is a method of standardizing and normalizing logical formulas. ... A disjunctive syllogism is one valid, simple argument form: A or B If not A Then B In logical operator notation: ¬ where represents the logical assertion. ... A double negative occurs when two or more ways to express negation are used in the same sentence. ... In logic and the propositional calculus, double negative elimination is a rule that states that double negatives can be removed from a proposition without changing its meaning: means the same as: Formally: Â¬ Â¬ A âˆ´ A The rule of double negative introduction states the converse, that double negatives can be added without...

Elimination rule -- End term -- Exclusive nor -- Exclusive or -- Existential fallacy -- Existential quantification In mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. ... The end terms in a categorical syllogism are the major term and the minor term (not the middle term. ... XNOR Logic Gate Symbol Exclusive nor (usual symbol XNOR occasionally XAND <exclusive and>) is a logical operator in Boolean algebra. ... Exclusive disjunction (usual symbol xor) is a logical operator that results in true if one of the operands (not both) is true. ... The existential fallacy is a logical fallacy committed in a categorical syllogism that is invalid because it has two universal premises and a particular conclusion. ... In predicate logic, an existential quantification is the predication of a property or relation to at least one member of the domain. ...

Fallacy of distribution -- Fallacy of the four terms -- First-order predicate - First-order predicate calculus - First-order resolution -- Fluidic logic -- Forward chaining -- Free variables and bound variables -- Fuzzy logic A fallacy of distribution is a logical fallacy occurring when an argument assumes there is no difference between a term in the distributive (referring to every member of a class) and collective (referring to the class itself as a whole) sense. ... The fallacy of four terms, also known as quaternio terminorum, is a formal fallacy that is committed in a categorical syllogism that has four terms. ... A first-order predicate is a predicate that takes only individual(s) as argument(s). ... First-order predicate calculus or first-order logic (FOL) permits the formulation of quantified statements such as there exists an x such that. ... In mathematical logic and automated theorem proving, a branch of the traditional artificial intelligence (see GOFAI), resolution is a theorem-proving technique for sentences in propositional logic and first-order logic. ... Fluidic logic , also known as fluidics , is the implementation of Boolean algebra functions using streams of fluid (such as water or air). ... Forward chaining is one of the two main methods of reasoning when using inference rules. ... In mathematics, and in other disciplines involving formal languages, including mathematical logic and computer science, a free variable is a notation for a place or places in an expression, into which some definite substitution may take place, or with respect to which some operation (summation or quantification, to give two... ...

Game semantics Game semantics is an approach to the semantics of logic that bases the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player. ...

Heyting algebra -- Higher-order predicate -- Horn clause -- Hypothetical syllogism In mathematics, Heyting algebras are special partially ordered sets that constitute a generalization of Boolean algebras. ... In mathematics, higher-order logic is distinguished from first-order logic in a number of ways. ... In logic, and in particular in propositional calculus, a Horn clause is a proposition of the general type (p and q and . ... In logic, a hypothetical syllogism is a valid argument of the following form: P → Q. Q → R. Therefore, P → R. In logical operator notation In other words, this kind of argument states that if one implies another, and that other implies a third, then the first implies the third. ...

Iff -- Illicit major -- Illicit minor -- Implicant -- Inductive logic -- Inductive logic programming -- Inference procedure -- Inference rule -- Infinitary logic -- Informal logic -- Intensional statement --Interpretability -- Interpretability logic -- Introduction rule --Intuitionistic linear logic -- Intuitionistic logic -- Invalid proof -- Inverse (logic) â†” â‡” â‰¡ For other possible meanings of iff, see IFF. In mathematics, philosophy, logic and technical fields that depend on them, iff is used as an abbreviation for if and only if. Common alternative phrases to iff or if and only if include Q is necessary and sufficient for P and P... This article may be too technical for most readers to understand. ... Illicit minor is a logical fallacy committed in a categorical syllogism that is invalid because its minor term is undistributed in the minor premise but distributed in the conclusion. ... This article needs to be cleaned up to conform to a higher standard of quality. ... This article is about induction in philosophy and logic. ... Inductive logic programming (ILP) is a machine learning approach, which uses techniques of logic programming. ... An inference procedure is a key component of the knowledge engineering process, sometimes known as abduction. ... In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ... Those unfamiliar with mathematical logic or the concept of ordinals should read these articles first. ... Informal logic is the study of arguments as presented in ordinary language, as contrasted with the presentations of arguments in an artificial (technical) or formal language (see formal logic). ... In logic, an intensional statement-form is a statement-form with at least one instance such that substituting co-extensive expressions into it does not always preserve truth-value. ... The concept of interpretability is one in mathematical logic. ... Interpretability logics comprise a family of modal logics that extend provability logic to describe interpretability and/or various related metamathematical properties and relations such as weak interpretability, Π1-conservativity, cointerpretability, tolerance, cotolerance, arithmetic complexities. ... In mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. ... A variant of linear logic that allows a single, or no more than one, conclusion. ... Intuitionistic logic, or constructivist logic, is the logic used in mathematical intuitionism and other forms of mathematical constructivism. ... In mathematics, there are a variety of spurious proofs of obvious contradictions. ... In logic, if S is a statement of the form P implies Q then the inverse of S is a statement of the form (not P) implies (not Q). ...

Johnston diagram Johnston diagrams, which look similar to Euler or Venn diagrams, illustrate formal propositional logic in a visual manner. ...

Karnaugh map The Karnaugh map, also known as a Veitch diagram (K-map or KV-map for short), is a tool to facilitate management of Boolean algebraic expressions. ...

Law of excluded middle -- Law of non-contradiction -- Laws of logic -- Laws of Form -- Linear logic -- Logic -- Logic gate -- Logical argument -- Logical assertion -- Logical biconditional -- Logical conditional --Logical conjunction -- Logical disjunction -- Logical equivalence -- Logical fallacy -- Logical language -- Logical nand -- Logical nor -- Logical operator -- Logicism -- Logic programming In logic, the law of excluded middle (tertium non datur in Latin) states that for any proposition P, it is true that (P âˆ¨ Â¬P). ... In logic, the law of noncontradiction judges as false any proposition P asserting that both proposition Q and its denial, proposition not-Q, are true at the same time and in the same respect. In the words of Aristotle, One cannot say of something that it is and that it... These laws of classical logic are valid in propositional logic and any boolean algebra. ... The phrase Laws of Form refers to either of two things: The book, hereinafter abbreviated LoF: G. Spencer-Brown, 1979. ... In mathematical logic, linear logic is a type of substructural logic that denies the structural rules of weakening and contraction. ... Logic, from Classical Greek Î»ÏŒÎ³Î¿Ï‚ (logos), originally meaning the word, or what is spoken, (but coming to mean thought or reason) is most often said to be the study of arguments, although the exact definition of logic is a matter of controversy among philosophers. ... A logic gate is an arrangement of controlled switches used to calculate operations using Boolean logic in digital circuits. ... An argument is an attempt to demonstrate the truth of an assertion called a conclusion, based on the truth of a set of assertions called premises. ... The logical assertion is a statement that asserts that a certain premise is true, and is useful for statements in proof. ... In logical calculus of mathematics, logical biconditional is a logical operator connecting two statements to assert, p if and only if q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ... In propositional calculus, or logical calculus in mathematics, the logical conditional is a binary logical operator connecting two statements, if p then q where p is a hypothesis (or antecedent) and q is a conclusion (or consequent). ... AND Logic Gate In mathematics, logical conjunction (usual symbol and) is a logical operator that results in false if either of the operands is false. ... OR logic gate In mathematics, logical disjunction (usual symbol or) is a logical operator that results in true if either of the operands is true. ... In logic, statements p and q are logically equivalent if they have the same logical content. ... A logical fallacy is an error in logical argument which is independent of the truth of the premises. ... Engineered languages, sometimes called engelangs, are constructed languages devised to test or prove some hypothesis about how languages work or might work. ... NAND Logic Gate The Sheffer stroke, |, is the negation of the conjunction operator. ... NOR Logic Gate Logical nor (not or), joint denial, or Webb-operation is a boolean logic operator which produces a result that is the inverse of logical or. ... In logical calculus, logical operators or logical connectors serve to connect statements into more complicated compound statements. ... Logicism is one of the schools of thought in the philosophy of mathematics, putting forth the theory that mathematics is an extension of logic and therefore some or all mathematics is reducible to logic. ... Logic programming is a programming paradigm that is claimed to be declarative (i. ...

Major premise -- Major term -- Mathematical logic -- Mereology -- Metalogic -- Middle term -- Minor premise -- Modal logic -- Modus ponens -- Modus tollens -- Multi-valued logic The major premise in a categorical syllogism is the premise whose terms are the syllogisms major term and middle term. ... The major term is the predicate term of the conclusion of a categorical syllogism. ... Mathematical logic is a discipline within mathematics, studying formal systems in relation to the way they encode intuitive concepts of proof and computation as part of the foundations of mathematics. ... Mereology is the branch of logic, mathematics and metaphysics dealing with part-whole relationships. ... The metalogic of a system of logic is the formal proof supporting its soundness. ... The middle term is the term that occurs in both premises (but not in the conclusion) of a categorical syllogism. ... In a categorical syllogism, the minor premise is the premise whose terms are the syllogisms minor term and middle term. ... A modal logic, or (less commonly) intensional logic, is a logic that deals with sentences that are qualified by modalities such as can, could, might, may, must, possibly, necessarily, eventually, etc. ... In Logic, Modus ponens (Latin: mode that affirms) is a valid, simple argument form (often abbreviated to MP): If P, then Q. P. Therefore, Q. or in logical operator notation: P â†’ Q P âŠ¢ Q where âŠ¢ represents the logical assertion. ... Modus tollens (Latin: mode that denies) is the formal name for indirect proof or proof by contrapositive, often abbreviated to MT. It can also be referred to as denying the consequent. ... Multi-valued logics are logical calculi in which there are more than two possible truth values. ...

Naive set theory -- Natural deduction -- Necessary and sufficient -- Negation -- Non-Aristotelian logic -- Nonfirstorderizability -- Non-monotonic logic -- Non sequitur (logic) Naive set theory1 is distinguished from axiomatic set theory by the fact that the former regards sets as collections of objects, called the elements or members of the set, whereas the latter regards sets only as that which satisfies certain axioms. ... In mathematical logic, natural deduction is the name given to a class of foundational approaches for two key concepts in logic, propositions and proofs. ... In logic, the words necessary and sufficient describe relations that hold between propositions or states of affairs, if one is conditional on the other. ... This article needs to be cleaned up to conform to a higher standard of quality. ... The term non-Aristotelian logic, sometimes shortened to null-A, is a term popularised by A. E. van Vogt and deriving from Alfred Korzybskis General Semantics. ... In formal logic, nonfirstorderizability is the inability of an expression to be adequately captured in standard first-order logic. ... A non-monotonic logic is a formal logic whose consequence relation is not monotonic. ... Non sequitur is Latin for it does not follow. ...

Open sentence -- Ordered logic In the jargon of the new mathematics of the 1960s, an open sentence is a sentence in which there are specific numbers which, when used to replace the variables, will allow the resulting expression to evaluate to true. ... Noncommutative logic is the name given to a family of substructural logics in which the exchange rule is inadmissible. ...

Paraconsistent logics -- Paradox -- Pierce's law -- Plural quantification --Polish notation -- Polysyllogism --Predicate -- Principia Mathematica -- Principle of bivalence -- Proof theory -- Proposition -- Propositional calculus -- Provability logic A paraconsistent logic is a non-trivial logic which allows inconsistencies. ... Listen to this article Â· (info) This audio file was created from the revision dated 2005-07-07, and does not reflect subsequent edits to the article. ... Peirces law in logic is named after the philosopher and logician Charles Sanders Peirce. ... In mathematics and logic, plural quantification is the theory that an individual variable x may take on plural, as well as singular values. ... Polish notation, also known as prefix notation, is a method of mathematical expression. ... A polysyllogism, sometimes called multi-premise syllogism, is a string of any number of syllogisms such that the conclusion of one is a premise for the next, and so on. ... In mathematics, a predicate is a relation. ... The Principia Mathematica is a three-volume work on the foundations of mathematics, written by Alfred North Whitehead and Bertrand Russell and published in 1910-1913. ... In logic, the principle of bivalence states that for any proposition P, either P is true or P is false. ... Proof theory, studied as a branch of mathematical logic, represents proofs as formal mathematical objects, facilitating their analysis by mathematical techniques. ... Proposition is a term used in logic to describe the content of assertions. ... In mathematical logic the propositional calculus or sentential calculus is a formal deduction system whose atomic formulas are propositional variables. ... Provability logic, or the logic of provability, is a modal logic where the necessity operator is interpreted as provability in a reasonably rich formal theory such as Peano arithmetic. ...

Quantification -- Quantum logic -- Quod erat demonstrandum In language and logic, quantification is a construct that specifies the extent of validity of a predicate, that is the extent to which a predicate holds over a range of things. ... In mathematical physics and quantum mechanics, quantum logic can be regarded as a kind of propositional logic suitable for understanding the apparent anomalies regarding quantum measurement, most notably those concerning composition of measurement operations of complementary variables. ... This page includes English translations of several Latin phrases and abbreviations such as . ...

Reductio ad absurdum -- Relevant logic -- Rule of inference Reductio ad absurdum (Latin for reduction to the absurd, traceable back to the Greek Î·Ì” ÎµÎ¹Ï‚ Î¬Ï„Î¿Ï€Î¿Î½ Î±Ï€Î±Î³Ï‰Î³Î·, reduction to the impossible, often used by Aristotle) is a type of logical argument where we assume a claim for the sake of argument, arrive at an absurd result, and then conclude the original assumption must... Relevance logic, also called relevant logic, is any of a family of non-classical substructural logics that impose certain restrictions on implication. ... In logic, especially in mathematical logic, a rule of inference is a scheme for constructing valid inferences. ...

Satisfiability -- Scholastic logic -- Second-order predicate -- Self-reference -- Sequent -- Sequent calculus -- Sequential logic -- Singular term -- Soundness -- Square of opposition -- Strict conditional -- Strict implication -- Strict logic -- Structural rule -- Sufficient condition -- Syllogism -- Syllogistic fallacy The Boolean satisfiability problem (SAT) is a decision problem considered in complexity theory. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ... A second-order predicate is a predicate that takes a first-order predicate as an argument. ... A self-reference occurs when an object refers to itself. ... In proof theory, a sequent is a formalized statement of provability that is frequently used when specifying calculi for deduction. ... In proof theory and mathematical logic, the sequent calculus is a widely known deduction system for first-order logic (and propositional logic as a special case of it). ... In digital circuit theory, sequential logic is a type of logic circuit whose output depends not only on the present input but also on the history of the input. ... There is no really adequate definition of singular term. ... (This article discusses the soundess notion of informal logic. ... The Square of Opposition is a term from the study of Aristotelian logic or Term Logic in which the logical relationship between various types of sentences is spelled out. ... In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic. ... In logic, a strict conditional is a material conditional that is acted upon by the necessity operator from modal logic. ... Essentially synonymous with relevant logic, though it can be characterized proof-theoretically as ordinary logic without weakening, or linear logic with contraction See also Relevant logic Linear logic Substructural logic Proof theory ... In proof theory, a structural rule is an inference rule that does not refer to any logical connective, but instead operates on the judgements or sequents directly. ... In logic, the words necessary and sufficient describe relations that hold between propositions or states of affairs, if one is conditional on the other. ... In traditional logic, a syllogism is an inference in which one proposition (the conclusion) follows of necessity from two others (known as premises). ... Syllogistic fallacies are logical fallacies that occur in syllogisms. ...

Tautology -- Temporal logic -- Term -- Term logic -- Ternary logic -- Theorem -- Tolerance -- Trilemma --Truth -- Truth condition -- Truth function -- Truth value -- Type theory In logic, a tautology is a statement which is true by its own definition. ... In logic, the term temporal logic is used to describe any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time. ... In traditional logic, term came to mean a referring expression, but only through the Latin terminus - margin, (so that terms were terminal for analysis). in Project management - deadline Figures of speech and shorthands are called terms of language. ... Traditional logic, also known as term logic, is a loose term for the logical tradition that originated with Aristotle and survived broadly unchanged until the advent of modern predicate logic in the late nineteenth century. ... Ternary logic is a multi-valued logic in which there are three truth values indicating true, false and unknown. ... A theorem is a proposition that has been or is to be proved on the basis of explicit assumptions. ... In mathematical logic, a tolerant sequence is a sequence ,..., of formal theories such that there are consistent extensions ,..., of these theories with each interpretable in . ... A trilemma is similar to a dilemma, but with three options from which a choice must be made. ... When someone sincerely agrees with an assertion, they are claiming that it is the truth. ... In semantics, truth conditions are what obtain precisely when a sentence is true. ... In logic a truth function is a connective for which the truth value is determined systematically by the values of the statements it connects. ... In logic, a truth value, or truth-value, is a value indicating to what extent a statement is true. ... At the broadest level, type theory is the branch of mathematics and logic that concerns itself with classifying entities into collections called types. ...

Unification -- Universal quantification -- Uniqueness quantification In mathematical logic, in particular as applied to computer science, a unification of two terms is a join (in the lattice sense) with respect to a specialisation order. ... In predicate logic, universal quantification is an attempt to formalise the notion that something (a logical predicate) is true for everything, or every relevant thing. ... In predicate logic and technical fields that depend on it, uniqueness quantification, or unique existential quantification, is an attempt to formalise the notion of something being true for exactly one thing, or exactly one thing of a certain type. ...

Vacuous truth -- Validity -- Venn diagram Informally, a logical statement is vacuously true if it is true but doesnt say anything; examples are statements of the form everything with property A also has property B, where there is nothing with property A. It is tempting to dismiss this concept as vacuous or silly. ... This article discusses validity in logic, for the term in the social sciences see validity (psychometric). ... Venn diagrams, Euler diagrams (pronounced oiler) and Johnston diagrams are similar-looking illustrations of set, mathematical or logical relationships. ...

Famous logicians

See also: list of logicians A logician is a person, such as a philosopher or mathematician, whose topic of scholarly study is logic. ...

George Boole [], (November 2, 1815 Lincoln, Lincolnshire, England â€“ December 8, 1864 Ballintemple, County Cork, Ireland) was a mathematician and philosopher. ... Abraham Robinson (October 6, 1918 - April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were incorporated into mathematics. ... Gerhard Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. ... Luitzen Egbertus Jan Brouwer (February 27, 1881 - December 2, 1966), usually cited as L. E. J. Brouwer, was a Dutch mathematician, a graduate of the University of Amsterdam, who worked in topology, set theory, measure theory and complex analysis. ... Haskell Brooks Curry (September 12, 1900 - September 1, 1982) was an American mathematician and logician. ... Friedrich Ludwig Gottlob Frege Friedrich Ludwig Gottlob Frege (November 8, 1848 â€“ July 26, 1925) was a German mathematician, logician, and philosopher who is regarded as a founder of both modern mathematical logic and analytic philosophy. ... Alonzo Church (June 14, 1903 â€“ August 11, 1995) was an American mathematician and logician who was responsible for some of the foundations of theoretical computer science. ... Jacques Herbrand (February 12, 1908 - July 27, 1932) was a French mathematician who was born in Paris, France and died in La Bérarde, Isère, France. ... This article needs cleanup. ... John Barkley Rosser Sr. ... Gerhard Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician. ... Jean-Yves Girard is a French mathematician working in proof theory. ... David Hilbert I was dreaming about a colony of spiders that lived behind a chair in my living room. ... Kurt GÃ¶del Kurt GÃ¶del [kurt gÃ¸Ëdl], (April 28, 1906 â€“ January 14, 1978) was a logician, mathematician, and philosopher of mathematics. ... Francis William Lawvere is a mathematician who is known for his work in category theory and the philosophy of mathematics. ... William Stanley Jevons (September 1, 1835 - August 13, 1882), English economist and logician, was born in Liverpool. ... Stephen Cole Kleene (January 5, 1909 â€“ January 25, 1994) was an American mathematician whose work at the University of Wisconsin-Madison helped lay the foundations for theoretical computer science. ... Alfred Tarski (January 14, 1901 in Warsawâ€“October 26, 1983 in Berkeley, USA) was a Polish logician considered to be one of the greatest logicians of all time in a manner after Aristotle, Gottlob Frege, and Kurt GÃ¶del. ... Albert Thoralf Skolem (May 23, 1887 - March 23, 1963) was a Norwegian mathematician. ... Saharon Shelah (×©×”×¨×Ÿ ×©×œ×—, born July 3, 1945 in Jerusalem) is an Israeli mathematician. ... The title given to this article is incorrect due to technical limitations. ... Giuseppe Peano Giuseppe Peano (August 27, 1858 â€“ April 20, 1932) was an Italian mathematician and philosopher best known for his contributions to set theory. ... Charles Sanders Santiago Peirce (pronounced purse), (September 10, 1839, Cambridge MA â€“ April 19, 1914, Milford PA) was an American polymath. ... W. V. Quine Willard Van Orman Quine (June 25, 1908 - December 25, 2000) was one of the most influential American philosophers and logicians of the 20th century. ... Frank Plumpton Ramsey (February 22, 1903 – January 19, 1930) was a British mathematician, philosopher and economist. ... Wikisource has original works written by or about: Bertrand Russell Writings available online A Free Mans Worship (1903) Am I an Atheist or an Agnostic? Icarus: The Future of Science Has Religion Made Useful Contributions to Civilization? Ideas that Have Harmed Mankind In Praise of Idleness (1932) Nobel Lecture... Alfred North Whitehead, OM (February 15, 1861, Ramsgate, Kent, UK â€“ December 30, 1947, Cambridge, MA) was a British philosopher, physicist, and mathematician who worked in logic, mathematics, philosophy of science and metaphysics. ...

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Alphabetical list