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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. [1]

## A Greek–English Lexicon

A Greek–English Lexicon, often referred to as Liddell & Scott, Liddell–Scott–Jones, or LSJ, is a standard lexicographical work of the Ancient Greek language.

## Abductive reasoning

Abductive reasoning (also called abduction,For example: abductive inference, or retroduction) is a form of logical inference which starts with an observation or set of observations then seeks to find the simplest and most likely explanation.

## ACM Computing Classification System

The ACM Computing Classification System (CCS) is a subject classification system for computing devised by the Association for Computing Machinery (ACM).

## Alan Turing

Alan Mathison Turing (23 June 1912 – 7 June 1954) was an English computer scientist, mathematician, logician, cryptanalyst, philosopher, and theoretical biologist.

Alfred North Whitehead (15 February 1861 – 30 December 1947) was an English mathematician and philosopher.

## Alfred Tarski

Alfred Tarski (January 14, 1901 &ndash; October 26, 1983), born Alfred Teitelbaum,School of Mathematics and Statistics, University of St Andrews,, School of Mathematics and Statistics, University of St Andrews.

## Ammonius Saccas

Ammonius Saccas (Ἀμμώνιος Σακκᾶς; fl. 3rd century AD) was a Greek philosopher from Alexandria who was often referred to as one of the founders of Neoplatonism.

## An Essay Concerning Human Understanding

An Essay Concerning Human Understanding is a work by John Locke concerning the foundation of human knowledge and understanding.

## Analytic philosophy

Analytic philosophy (sometimes analytical philosophy) is a style of philosophy that became dominant in the Western world at the beginning of the 20th century.

## Annals of Mathematics

The Annals of Mathematics is a bimonthly mathematical journal published by Princeton University and the Institute for Advanced Study.

## Anti-realism

In analytic philosophy, anti-realism is an epistemological position first articulated by British philosopher Michael Dummett.

## Antoine Arnauld

Antoine Arnauld (6 February 16128 August 1694) was a French Roman Catholic theologian, philosopher and mathematician.

## Anviksiki

Ānvīkṣikī is a term in Sanskrit denoting roughly the "science of inquiry" and it should have been recognized in India as a distinct branch of learning as early as 650 BCE.

## Arend Heyting

__notoc__ Arend Heyting (9 May 1898 &ndash; 9 July 1980) was a Dutch mathematician and logician.

## 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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## Argumentation theory

Argumentation theory, or argumentation, is the interdisciplinary study of how conclusions can be reached through logical reasoning; that is, claims based, soundly or not, on premises.

## Aristotle

Aristotle (Ἀριστοτέλης Aristotélēs,; 384–322 BC) was an ancient Greek philosopher and scientist born in the city of Stagira, Chalkidiki, in the north of Classical Greece.

## 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.

## Arithmetic logic unit

An arithmetic logic unit (ALU) is a combinational digital electronic circuit that performs arithmetic and bitwise operations on integer binary numbers.

## Arthur Prior

Arthur Norman Prior (4 December 1914 – 6 October 1969), usually cited as A. N. Prior, was a noted logician and philosopher.

## Artificial intelligence

Artificial intelligence (AI, also machine intelligence, MI) is intelligence demonstrated by machines, in contrast to the natural intelligence (NI) displayed by humans and other animals.

## Atomic sentence

In logic, an atomic sentence is a type of declarative sentence which is either true or false (may also be referred to as a proposition, statement or truthbearer) and which cannot be broken down into other simpler sentences.

## Augustus De Morgan

Augustus De Morgan (27 June 1806 – 18 March 1871) was a British mathematician and logician.

## Automated theorem proving

Automated theorem proving (also known as ATP or automated deduction) is a subfield of automated reasoning and mathematical logic dealing with proving mathematical theorems by computer programs.

## Avicenna

Avicenna (also Ibn Sīnā or Abu Ali Sina; ابن سینا; – June 1037) was a Persian polymath who is regarded as one of the most significant physicians, astronomers, thinkers and writers of the Islamic Golden Age.

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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 of choice

In mathematics, the axiom of choice, or AC, is an axiom of set theory equivalent to the statement that the Cartesian product of a collection of non-empty sets is non-empty.

Barry Smith (born June 4, 1952) is an academic working in the fields of ontology and biomedical informatics.

## Begriffsschrift

Begriffsschrift (German for, roughly, "concept-script") is a book on logic by Gottlob Frege, published in 1879, and the formal system set out in that book.

## Bertrand Russell

Bertrand Arthur William Russell, 3rd Earl Russell, (18 May 1872 &ndash; 2 February 1970) was a British philosopher, logician, mathematician, historian, writer, social critic, political activist, and Nobel laureate.

## Boethius

Anicius Manlius Severinus Boëthius, commonly called Boethius (also Boetius; 477–524 AD), was a Roman senator, consul, magister officiorum, and philosopher of the early 6th century.

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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.

## Cambridge University Press

Cambridge University Press (CUP) is the publishing business of the University of Cambridge.

## Cantor's theorem

In elementary set theory, Cantor's theorem is a fundamental result that states that, for any set A, the set of all subsets of A (the power set of A, denoted by \mathcal(A)) has a strictly greater cardinality than A itself.

## Charles Babbage

Charles Babbage (26 December 1791 – 18 October 1871) was an English polymath.

## 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".

## Christian

A Christian is a person who follows or adheres to Christianity, an Abrahamic, monotheistic religion based on the life and teachings of Jesus Christ.

## Church–Turing thesis

In computability theory, the Church–Turing thesis (also known as computability thesis, the Turing–Church thesis, the Church–Turing conjecture, Church's thesis, Church's conjecture, and Turing's thesis) is a hypothesis about the nature of computable functions.

## 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.

## Classical logic

Classical logic (or standard logic) is an intensively studied and widely used class of formal logics.

## 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.

## Complexity class

In computational complexity theory, a complexity class is a set of problems of related resource-based complexity.

## Computability theory

Computability theory, also known as recursion theory, is a branch of mathematical logic, of computer science, and of the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees.

## Computational linguistics

Computational linguistics is an interdisciplinary field concerned with the statistical or rule-based modeling of natural language from a computational perspective, as well as the study of appropriate computational approaches to linguistic questions.

## Computer science

Computer science deals with the theoretical foundations of information and computation, together with practical techniques for the implementation and application of these foundations.

## Consequent

A consequent is the second half of a hypothetical proposition.

## Consistency

In classical deductive logic, a consistent theory is one that does not contain a contradiction.

## Continuum hypothesis

In mathematics, the continuum hypothesis (abbreviated CH) is a hypothesis about the possible sizes of infinite sets.

## Cooperative principle

In social science generally and linguistics specifically, the cooperative principle describes how effective communication in conversation is achieved in common social situations, that is, how listeners and speakers must act cooperatively and mutually accept one another to be understood in a particular way.

## Critical thinking

Critical thinking is the objective analysis of facts to form a judgment.

## Curry–Howard correspondence

In programming language theory and proof theory, the Curry–Howard correspondence (also known as the Curry–Howard isomorphism or equivalence, or the proofs-as-programs and propositions- or formulae-as-types interpretation) is the direct relationship between computer programs and mathematical proofs.

## David Hilbert

David Hilbert (23 January 1862 – 14 February 1943) was a German mathematician.

## De Interpretatione

De Interpretatione or On Interpretation (Greek: Περὶ Ἑρμηνείας, Peri Hermeneias) is the second text from Aristotle's Organon and is among the earliest surviving philosophical works in the Western tradition to deal with the relationship between language and logic in a comprehensive, explicit, and formal way.

## Decision tree

A decision tree is a decision support tool that uses a tree-like graph or model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility.

## Deductive reasoning

Deductive reasoning, also deductive logic, logical deduction is the process of reasoning from one or more statements (premises) to reach a logically certain conclusion.

## Default logic

Default logic is a non-monotonic logic proposed by Raymond Reiter to formalize reasoning with default assumptions.

## Defeasible reasoning

In logic, defeasible reasoning is a kind of reasoning that is rationally compelling, though not deductively valid.

## Deontic logic

Deontic logic is the field of philosophical logic that is concerned with obligation, permission, and related concepts.

## Description logic

Description logics (DL) are a family of formal knowledge representation languages.

## Dialectic

Dialectic or dialectics (διαλεκτική, dialektikḗ; related to dialogue), also known as the dialectical method, is at base a discourse between two or more people holding different points of view about a subject but wishing to establish the truth through reasoned arguments.

## Dialectical logic

Dialectical logic is the system of laws of thought, developed within the Hegelian and Marxist traditions, which seeks to supplement or replace the laws of formal logic.

## Dialetheism

Dialetheism is the view that there are statements which are both true and false.

## Digital electronics

Digital electronics or digital (electronic) circuits are electronics that operate on digital signals.

## Domain of discourse

In the formal sciences, the domain of discourse, also called the universe of discourse, universal set, or simply universe, is the set of entities over which certain variables of interest in some formal treatment may range.

## Dov Gabbay

Dov M. Gabbay (born October 23, 1945) is a British logician.

## Dynamic logic (modal logic)

Dynamic logic is an extension of modal logic originally intended for reasoning about computer programs and later applied to more general complex behaviors arising in linguistics, philosophy, AI, and other fields.

## Edward N. Zalta

Edward N. Zalta (born March 16, 1952) is a senior research scholar at the Center for the Study of Language and Information.

## Elliott Mendelson

Elliott Mendelson (born 1931) is an American logician.

## Encyclopædia Britannica

The Encyclopædia Britannica (Latin for "British Encyclopaedia"), published by Encyclopædia Britannica, Inc., is a general knowledge English-language encyclopaedia.

## Entscheidungsproblem

In mathematics and computer science, the Entscheidungsproblem (German for "decision problem") is a challenge posed by David Hilbert in 1928.

## Epistemic modal logic

Epistemic modal logic is a subfield of modal logic that is concerned with reasoning about knowledge.

## Epistemology

Epistemology is the branch of philosophy concerned with the theory of knowledge.

## Erasmus Montanus

Erasmus Montanus is a satirical play about academic conceit in rural Denmark, written by Ludvig Holberg in 1722.

## Euclid

Euclid (Εὐκλείδης Eukleidēs; fl. 300 BC), sometimes given the name Euclid of Alexandria to distinguish him from Euclides of Megara, was a Greek mathematician, often referred to as the "founder of geometry" or the "father of geometry".

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## Europe

Europe is a continent located entirely in the Northern Hemisphere and mostly in the Eastern Hemisphere.

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## Fallacy

A fallacy is the use of invalid or otherwise faulty reasoning, or "wrong moves" in the construction of an argument.

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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.

## Formal methods

In computer science, specifically software engineering and hardware engineering, formal methods are a particular kind of mathematically based techniques for the specification, development and verification of software and hardware systems.

## Formal system

A formal system is the name of a logic system usually defined in the mathematical way.

## Formula

In science, a formula is a concise way of expressing information symbolically, as in a mathematical formula or a chemical formula.

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## Foundations of mathematics

Foundations of mathematics is the study of the philosophical and logical and/or algorithmic basis of mathematics, or, in a broader sense, the mathematical investigation of what underlies the philosophical theories concerning the nature of mathematics.

## Free logic

A free logic is a logic with fewer existential presuppositions than classical logic.

## Friedrich Nietzsche

Friedrich Wilhelm Nietzsche (15 October 1844 – 25 August 1900) was a German philosopher, cultural critic, composer, poet, philologist and a Latin and Greek scholar whose work has exerted a profound influence on Western philosophy and modern intellectual history.

## Fuzzy logic

Fuzzy logic is a form of many-valued logic in which the truth values of variables may be any real number between 0 and 1.

## Game semantics

Game semantics (dialogische Logik, translated as dialogical logic) is an approach to formal semantics that grounds the concepts of truth or validity on game-theoretic concepts, such as the existence of a winning strategy for a player, somewhat resembling Socratic dialogues or medieval theory of Obligationes.

## Garrett Birkhoff

Garrett Birkhoff (January 19, 1911 – November 22, 1996) was an American mathematician.

## Gödel's completeness theorem

Gödel's completeness theorem is a fundamental theorem in mathematical logic that establishes a correspondence between semantic truth and syntactic provability in first-order logic.

## Gödel's incompleteness theorems

Gödel's incompleteness theorems are two theorems of mathematical logic that demonstrate the inherent limitations of every formal axiomatic system containing basic arithmetic.

## General relativity

General relativity (GR, also known as the general theory of relativity or GTR) is the geometric theory of gravitation published by Albert Einstein in 1915 and the current description of gravitation in modern physics.

## Geometry

Geometry (from the γεωμετρία; geo- "earth", -metron "measurement") is a branch of mathematics concerned with questions of shape, size, relative position of figures, and the properties of space.

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## Georg Cantor

Georg Ferdinand Ludwig Philipp Cantor (– January 6, 1918) was a German mathematician.

## Georg Wilhelm Friedrich Hegel

Georg Wilhelm Friedrich Hegel (August 27, 1770 – November 14, 1831) was a German philosopher and the most important figure of German idealism.

## 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.

## George Boolos

George Stephen Boolos (September 4, 1940 – May 27, 1996) was an American philosopher and a mathematical logician who taught at the Massachusetts Institute of Technology.

## Gerhard Gentzen

Gerhard Karl Erich Gentzen (November 24, 1909 – August 4, 1945) was a German mathematician and logician.

## Gongsun Long

Gongsun Long (BC) was a member of the School of Names (Logicians) of ancient Chinese philosophy.

## 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.

## Gottlob Frege

Friedrich Ludwig Gottlob Frege (8 November 1848 – 26 July 1925) was a German philosopher, logician, and mathematician.

## Graham Priest

Graham Priest (born 1948) is Distinguished Professor of Philosophy at the CUNY Graduate Center, as well as a regular visitor at the University of Melbourne where he was Boyce Gibson Professor of Philosophy and also at the University of St Andrews.

## Graph theory

In mathematics, graph theory is the study of graphs, which are mathematical structures used to model pairwise relations between objects.

## György Lukács

György Lukács (also Georg Lukács; born György Bernát Löwinger; 13 April 1885 – 4 June 1971) was a Hungarian Marxist philosopher, aesthetician, literary historian, and critic.

## Han Feizi

The Han Feizi is an ancient Chinese text attributed to foundational political philosopher, "Master" Han Fei.

## Harvard University Press

Harvard University Press (HUP) is a publishing house established on January 13, 1913, as a division of Harvard University, and focused on academic publishing.

## High Middle Ages

The High Middle Ages, or High Medieval Period, was the period of European history that commenced around 1000 AD and lasted until around 1250 AD.

## Hilary Putnam

Hilary Whitehall Putnam (July 31, 1926 – March 13, 2016) was an American philosopher, mathematician, and computer scientist, and a major figure in analytic philosophy in the second half of the 20th century.

## Hilbert's program

In mathematics, Hilbert's program, formulated by German mathematician David Hilbert in the early part of the 20th century, was a proposed solution to the foundational crisis of mathematics, when early attempts to clarify the foundations of mathematics were found to suffer from paradoxes and inconsistencies.

## Hoare logic

Hoare logic (also known as Floyd&ndash;Hoare logic or Hoare rules) is a formal system with a set of logical rules for reasoning rigorously about the correctness of computer programs.

## Horn clause

In mathematical logic and logic programming, a Horn clause is a logical formula of a particular rule-like form which gives it useful properties for use in logic programming, formal specification, and model theory.

## Human, All Too Human

Human, All Too Human: A Book for Free Spirits (Menschliches, Allzumenschliches: Ein Buch für freie Geister) is a book by 19th-century philosopher Friedrich Nietzsche, originally published in 1878.

## 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.

## 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.

## Immanuel Kant

Immanuel Kant (22 April 1724 – 12 February 1804) was a German philosopher who is a central figure in modern philosophy.

## Indian logic

The development of Indian logic dates back to the anviksiki of Medhatithi Gautama (c. 6th century BCE) the Sanskrit grammar rules of Pāṇini (c. 5th century BCE); the Vaisheshika school's analysis of atomism (c. 6th century BCE to 2nd century BCE); the analysis of inference by Gotama (c. 6th century BC to 2nd century CE), founder of the Nyaya school of Hindu philosophy; and the tetralemma of Nagarjuna (c. 2nd century CE).

## Individual

An individual is that which exists as a distinct entity.

## Inductive reasoning

Inductive reasoning (as opposed to ''deductive'' reasoning or ''abductive'' reasoning) is a method of reasoning in which the premises are viewed as supplying some evidence for the truth of the conclusion.

## Inference

Inferences are steps in reasoning, moving from premises to logical consequences.

## Infinitary logic

An infinitary logic is a logic that allows infinitely long statements and/or infinitely long proofs.

## Informal logic

Informal logic, intuitively, refers to the principles of logic and logical thought outside of a formal setting.

## Intuitionism

In the philosophy of mathematics, intuitionism, or neointuitionism (opposed to preintuitionism), is an approach where mathematics is considered to be purely the result of the constructive mental activity of humans rather than the discovery of fundamental principles claimed to exist in an objective reality.

## 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.

## Is Logic Empirical?

"Is Logic Empirical?" is the title of two articles (one by Hilary Putnam and another by Michael Dummett) that discuss the idea that the algebraic properties of logic may, or should, be empirically determined; in particular, they deal with the question of whether empirical facts about quantum phenomena may provide grounds for revising classical logic as a consistent logical rendering of reality.

## 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.

## Józef Maria Bocheński

Józef Maria Bocheński (Czuszów, Congress Poland, Russian Empire, 30 August 1902 – 8 February 1995, Fribourg, Switzerland) was a Polish Dominican, logician and philosopher.

## Jürgen Habermas

Jürgen Habermas (born 18 June 1929) is a German sociologist and philosopher in the tradition of critical theory and pragmatism.

## John Locke

John Locke (29 August 1632 – 28 October 1704) was an English philosopher and physician, widely regarded as one of the most influential of Enlightenment thinkers and commonly known as the "Father of Liberalism".

## John von Neumann

John von Neumann (Neumann János Lajos,; December 28, 1903 – February 8, 1957) was a Hungarian-American mathematician, physicist, computer scientist, and polymath.

## Jon Barwise

Kenneth Jon Barwise (June 29, 1942 – March 5, 2000) was an American mathematician, philosopher and logician who proposed some fundamental revisions to the way that logic is understood and used.

## Joseph Goguen

Joseph Amadee Goguen (28 June 1941 – 3 July 2006) was a US computer scientist.

## Karl Marx

Karl MarxThe name "Karl Heinrich Marx", used in various lexicons, is based on an error.

## Knowledge representation and reasoning

Knowledge representation and reasoning (KR, KR², KR&R) is the field of artificial intelligence (AI) dedicated to representing information about the world in a form that a computer system can utilize to solve complex tasks such as diagnosing a medical condition or having a dialog in a natural language.

## Kripke semantics

Kripke semantics (also known as relational semantics or frame semantics, and often confused with possible world semantics) is a formal semantics for non-classical logic systems created in the late 1950s and early 1960s by Saul Kripke and André Joyal.

## Kurt Gödel

Kurt Friedrich Gödel (April 28, 1906 – January 14, 1978) was an Austrian, and later American, logician, mathematician, and philosopher.

## L. E. J. Brouwer

Luitzen Egbertus Jan Brouwer (27 February 1881 – 2 December 1966), usually cited as L. E. J. Brouwer but known to his friends as Bertus, was a Dutch mathematician and philosopher, who worked in topology, set theory, measure theory and complex analysis.

## Large cardinal

In the mathematical field of set theory, a large cardinal property is a certain kind of property of transfinite cardinal numbers.

## Law

Law is a system of rules that are created and enforced through social or governmental institutions to regulate behavior.

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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.

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.

## Lewis Carroll

Charles Lutwidge Dodgson (27 January 1832 – 14 January 1898), better known by his pen name Lewis Carroll, was an English writer, mathematician, logician, Anglican deacon, and photographer.

## Linguistic modality

In linguistics, modality is a feature of language that allows for communicating things about, or based on, situations which need not be actual.

## Linguistics

Linguistics is the scientific study of language, and involves an analysis of language form, language meaning, and language in context.

## List of logic journals

This is a list of academic journals in logic.

## List of logic symbols

In logic, a set of symbols is commonly used to express logical representation.

## List of logicians

A logician is a person whose topic of scholarly study is logic.

## Logic gate

In electronics, a logic gate is an idealized or physical device implementing a Boolean function; that is, it performs a logical operation on one or more binary inputs and produces a single binary output.

## Logic in China

Formal logic in China has a special place in the history of logic due to its repression and abandonment—in contrast to the strong ancient adoption and continued development of the study of logic in Europe, India, and the Islamic world.

## Logic programming

Logic programming is a type of programming paradigm which is largely based on formal logic.

## Logic puzzle

A logic puzzle is a puzzle deriving from the mathematics field of deduction.

## Logica Universalis

Logica Universalis is a peer-reviewed academic journal which covers research related to Universal logic.

## Logical biconditional

In logic and mathematics, the logical biconditional (sometimes known as the material biconditional) is the logical connective of two statements asserting "P if and only if Q", where P is an antecedent and Q is a consequent.

## 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.

## 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.

## 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.

## 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.

## Logical form

In philosophy and mathematics, a logical form of a syntactic expression is a precisely-specified semantic version of that expression in a formal system.

## Logical truth

Logical truth is one of the most fundamental concepts in logic, and there are different theories on its nature.

## Logicism

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.

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## Logos

Logos (lógos; from λέγω) is a term in Western philosophy, psychology, rhetoric, and religion derived from a Greek word variously meaning "ground", "plea", "opinion", "expectation", "word", "speech", "account", "reason", "proportion", and "discourse",Henry George Liddell and Robert Scott,: logos, 1889.

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## Ludvig Holberg

Ludvig Holberg, Baron of Holberg (3 December 1684 – 28 January 1754) was a writer, essayist, philosopher, historian and playwright born in Bergen, Norway, during the time of the Dano-Norwegian dual monarchy.

## 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.

## Many-sorted logic

Many-sorted logic can reflect formally our intention not to handle the universe as a homogeneous collection of objects, but to partition it in a way that is similar to types in typeful programming.

## 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.

## 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 "→".

## Material inference

In logic, inference is the process of deriving logical conclusions from premises known or assumed to be true.

## Mathematical logic

Mathematical logic is a subfield of mathematics exploring the applications of formal logic to mathematics.

## Mathematical model

A mathematical model is a description of a system using mathematical concepts and language.

## Mathematical notation

Mathematical notation is a system of symbolic representations of mathematical objects and ideas.

## Mathematics

Mathematics (from Greek μάθημα máthēma, "knowledge, study, learning") is the study of such topics as quantity, structure, space, and change.

## Mechanics

Mechanics (Greek μηχανική) is that area of science concerned with the behaviour of physical bodies when subjected to forces or displacements, and the subsequent effects of the bodies on their environment.

## Metalogic

Metalogic is the study of the metatheory of logic.

## Metaphysics

Metaphysics is a branch of philosophy that explores the nature of being, existence, and reality.

## Michael Dummett

Sir Michael Anthony Eardley Dummett, FBA (27 June 192527 December 2011) was an English philosopher, described as "among the most significant British philosophers of the last century and a leading campaigner for racial tolerance and equality." He was, until 1992, Wykeham Professor of Logic at the University of Oxford.

## Modal fallacy

The formal fallacy of the modal fallacy is a special type of fallacy that occurs in modal logic.

## 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.

## Model theory

In mathematics, model theory is the study of classes of mathematical structures (e.g. groups, fields, graphs, universes of set theory) from the perspective of mathematical logic.

## 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.

## Monotonicity of entailment

Monotonicity of entailment is a property of many logical systems that states that the hypotheses of any derived fact may be freely extended with additional assumptions.

## Natural language

In neuropsychology, linguistics, and the philosophy of language, a natural language or ordinary language is any language that has evolved naturally in humans through use and repetition without conscious planning or premeditation.

## Navya-Nyāya

The Navya-Nyāya or Neo-Logical darśana (view, system, or school) of Indian logic and Indian philosophy was founded in the 13th century CE by the philosopher Gangeśa Upādhyāya of Mithila and continued by Raghunatha Siromani.

## Necessity and sufficiency

In logic, necessity and sufficiency are terms used to describe an implicational relationship between statements.

## 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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## Nicholas Rescher

Nicholas Rescher (born 15 July 1928) is a German-American philosopher at the University of Pittsburgh.

## Nicolai A. Vasiliev

Nicolai Alexandrovich Vasiliev (Николай Александрович Васильев), also Vasil'ev, Vassilieff, Wassilieff (– December 31, 1940), was a Russian logician, philosopher, psychologist, poet.

## Non-classical logic

Non-classical logics (and sometimes alternative logics) are formal systems that differ in a significant way from standard logical systems such as propositional and predicate logic.

## Nuel Belnap

Nuel D. Belnap Jr. (born 1930) is an American logician and philosopher who has made contributions to the philosophy of logic, temporal logic, and structural proof theory.

## Nyaya

(Sanskrit: न्याय, ny-āyá), literally means "rules", "method" or "judgment".

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## On Truth and Lies in a Nonmoral Sense

On Truth and Lies in a Nonmoral Sense (Über Wahrheit und Lüge im aussermoralischen Sinne, also called On Truth and Lie in an Extra-Moral SenseWalter Kaufmann's translation, appearing in The Portable Nietzsche, 1976 edition. Viking Press.) is a philosophical essay by Friedrich Nietzsche.

## Online Etymology Dictionary

The Online Etymology Dictionary is a free online dictionary written and compiled by Douglas Harper that describes the origins of English-language words.

## Organon

The Organon (Greek: Ὄργανον, meaning "instrument, tool, organ") is the standard collection of Aristotle's six works on logic.

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## Outline of logic

Logic is the formal science of using reason and is considered a branch of both philosophy and mathematics.

## Outline of mathematics

Mathematics is a field of study that investigates topics including number, space, structure, and change.

## Outline of philosophy

The following outline is provided as an overview of and topical guide to philosophy: Philosophy &ndash; study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

## Paraconsistent logic

A paraconsistent logic is a logical system that attempts to deal with contradictions in a discriminating way.

A paradox is a statement that, despite apparently sound reasoning from true premises, leads to an apparently self-contradictory or logically unacceptable conclusion.

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The paradoxes of material implication are a group of formulae that are truths of classical logic but are intuitively problematic.

## Perseus Project

The Perseus Project (version 4 also known as "Perseus Hopper") is a digital library project of Tufts University, which is located in Medford and Somerville, near Boston, in the U.S. state of Massachusetts.

## Philo the Dialectician

Philo the Dialectician (Φίλων; fl. 300 BC) was a dialectic philosopher of the Megarian school.

## Philosophical logic

Philosophical logic refers to those areas of philosophy in which recognized methods of logic have traditionally been used to solve or advance the discussion of philosophical problems.

## Philosophical realism

Realism (in philosophy) about a given object is the view that this object exists in reality independently of our conceptual scheme.

## Philosophical skepticism

Philosophical skepticism (UK spelling: scepticism; from Greek σκέψις skepsis, "inquiry") is a philosophical school of thought that questions the possibility of certainty in knowledge.

## Philosophy

Philosophy (from Greek φιλοσοφία, philosophia, literally "love of wisdom") is the study of general and fundamental problems concerning matters such as existence, knowledge, values, reason, mind, and language.

## Philosophy of mathematics

The philosophy of mathematics is the branch of philosophy that studies the assumptions, foundations, and implications of mathematics, and purports to provide a viewpoint of the nature and methodology of mathematics, and to understand the place of mathematics in people's lives.

## Philosophy of mind

Philosophy of mind is a branch of philosophy that studies the nature of the mind.

## Plato

Plato (Πλάτων Plátōn, in Classical Attic; 428/427 or 424/423 – 348/347 BC) was a philosopher in Classical Greece and the founder of the Academy in Athens, the first institution of higher learning in the Western world.

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## Port-Royal Logic

Port-Royal Logic, or Logique de Port-Royal, is the common name of La logique, ou l'art de penser, an important textbook on logic first published anonymously in 1662 by Antoine Arnauld and Pierre Nicole, two prominent members of the Jansenist movement, centered on Port-Royal.

## Posterior Analytics

The Posterior Analytics (Ἀναλυτικὰ Ὕστερα; Analytica Posteriora) is a text from Aristotle's Organon that deals with demonstration, definition, and scientific knowledge.

## Potentiality and actuality

In philosophy, potentiality and actuality are principles of a dichotomy which Aristotle used to analyze motion, causality, ethics, and physiology in his Physics, Metaphysics, Nicomachean Ethics and De Anima, which is about the human psyche.

## Pragma-dialectics

Pragma-dialectics, or pragma-dialectical theory, developed by Frans H. van Eemeren and Rob Grootendorst (see 1984; 1992; 2004) at the University of Amsterdam, is an argumentation theory that is used to analyze and evaluate argumentation in actual practice.

## Predicable

Predicable (Lat. praedicabilis, that which may be stated or affirmed, sometimes called quinque voces or five words) is, in scholastic logic, a term applied to a classification of the possible relations in which a predicate may stand to its subject.

## Principia Mathematica

The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913.

## Principle of bivalence

In logic, the semantic principle (or law) of bivalence states that every declarative sentence expressing a proposition (of a theory under inspection) has exactly one truth value, either true or false.

## Principle of distributivity

The principle of distributivity states that the algebraic distributive law is valid for classical logic, where both logical conjunction and logical disjunction are distributive over each other so that for any propositions A, B and C the equivalences and hold.

## Principle of explosion

The principle of explosion (Latin: ex falso (sequitur) quodlibet (EFQ), "from falsehood, anything (follows)", or ex contradictione (sequitur) quodlibet (ECQ), "from contradiction, anything (follows)"), or the principle of Pseudo-Scotus, is the law of classical logic, intuitionistic logic and similar logical systems, according to which any statement can be proven from a contradiction.

## Principles of Mathematical Logic

Principles of Mathematical Logic is the 1950 American translation of the 1938 second edition of David Hilbert's and Wilhelm Ackermann's classic text Grundzüge der theoretischen Logik, on elementary mathematical logic.

## Prior Analytics

The Prior Analytics (Ἀναλυτικὰ Πρότερα; Analytica Priora) is Aristotle's work on deductive reasoning, which is known as his syllogistic.

## Problem of future contingents

Future contingent propositions (or simply, future contingents) are statements about states of affairs in the future that are contingent: neither necessarily true nor necessarily false.

## Problem of multiple generality

The problem of multiple generality names a failure in traditional logic to describe certain intuitively valid inferences.

## Programming language

A programming language is a formal language that specifies a set of instructions that can be used to produce various kinds of output.

## Prolog

Prolog is a general-purpose logic programming language associated with artificial intelligence and computational linguistics.

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## Proof calculus

In mathematical logic, a proof calculus or a proof system is built to prove statements.

## Proof theory

Proof theory is a major branchAccording to Wang (1981), pp.

## Proof-theoretic semantics

Proof-theoretic semantics is an approach to the semantics of logic that attempts to locate the meaning of propositions and logical connectives not in terms of interpretations, as in Tarskian approaches to semantics, but in the role that the proposition or logical connective plays within the system of inference.

## Proposition

The term proposition has a broad use in contemporary analytic philosophy.

## Propositional calculus

Propositional calculus is a branch of logic.

## Psychologism

Psychologism is a philosophical position, according to which psychology plays a central role in grounding or explaining some other, non-psychological type of fact or law.

## Psychology

Psychology is the science of behavior and mind, including conscious and unconscious phenomena, as well as feeling and thought.

## Qin dynasty

The Qin dynasty was the first dynasty of Imperial China, lasting from 221 to 206 BC.

## Quantifier (logic)

In logic, quantification specifies the quantity of specimens in the domain of discourse that satisfy an open formula.

## Quantum logic

In quantum mechanics, quantum logic is a set of rules for reasoning about propositions that takes the principles of quantum theory into account.

## Rationality

Rationality is the quality or state of being rational – that is, being based on or agreeable to reason.

## Real number

In mathematics, a real number is a value of a continuous quantity that can represent a distance along a line.

## Reason

Reason is the capacity for consciously making sense of things, establishing and verifying facts, applying logic, and changing or justifying practices, institutions, and beliefs based on new or existing information.

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## Relevance logic

Relevance logic, also called relevant logic, is a kind of non-classical logic requiring the antecedent and consequent of implications to be relevantly related.

## Rhetoric

Rhetoric is the art of discourse, wherein a writer or speaker strives to inform, persuade, or motivate particular audiences in specific situations.

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## Rival conceptions of logic

The history of logic as a subject has been characterised by many disputes over what the topic deals with, and the main article 'Logic' has as a result been hesitant to commit to a particular definition of logic.

## Robert Brandom

Robert Boyce Brandom (born March 13, 1950) is an American philosopher who teaches at the University of Pittsburgh.

## Routledge

Routledge is a British multinational publisher.

## Rule induction

Rule induction is an area of machine learning in which formal rules are extracted from a set of observations.

## 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).

In the foundations of mathematics, Russell's paradox (also known as Russell's antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction.

## Saul Kripke

Saul Aaron Kripke (born November 13, 1940) is an American philosopher and logician.

## Scholasticism

Scholasticism is a method of critical thought which dominated teaching by the academics ("scholastics", or "schoolmen") of medieval universities in Europe from about 1100 to 1700, and a program of employing that method in articulating and defending dogma in an increasingly pluralistic context.

## 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.

## Semantic theory of truth

A semantic theory of truth is a theory of truth in the philosophy of language which holds that truth is a property of sentences.

## Semantics

Semantics (from σημαντικός sēmantikós, "significant") is the linguistic and philosophical study of meaning, in language, programming languages, formal logics, and semiotics.

## Semantics (computer science)

In programming language theory, semantics is the field concerned with the rigorous mathematical study of the meaning of programming languages.

## Set theory

Set theory is a branch of mathematical logic that studies sets, which informally are collections of objects.

## Sextus Empiricus

Sextus Empiricus (Σέξτος Ἐμπειρικός; c. 160 – c. 210 CE, n.b., dates uncertain), was a physician and philosopher, who likely lived in Alexandria, Rome, or Athens.

## 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.

## Southern Illinois University Press

Southern Illinois University Press or SIU Press, founded in 1956, is a university press located in Carbondale, Illinois, owned and operated by Southern Illinois University.

## Stanford Encyclopedia of Philosophy

The Stanford Encyclopedia of Philosophy (SEP) combines an online encyclopedia of philosophy with peer-reviewed publication of original papers in philosophy, freely accessible to Internet users.

## Stephen Toulmin

Stephen Edelston Toulmin (25 March 1922 – 4 December 2009) was a British philosopher, author, and educator.

## Stewart Shapiro

Stewart Shapiro (born 1951) is O'Donnell Professor of Philosophy at the Ohio State University.

## Stoic logic

Stoic logic is the system of propositional logic developed by the Stoic philosophers in ancient Greece.

## 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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## Strict conditional

In logic, a strict conditional is a conditional governed by a modal operator, that is, a logical connective of modal logic.

## Structural proof theory

In mathematical logic, structural proof theory is the subdiscipline of proof theory that studies proof calculi that support a notion of analytic proof.

## Structure (mathematical logic)

In universal algebra and in model theory, a structure consists of a set along with a collection of finitary operations and relations that are defined on it.

## Sum of Logic

The Summa Logicae ("Sum of Logic") is a textbook on logic by William of Ockham.

## Supervaluationism

In philosophical logic, supervaluationism is a semantics for dealing with irreferential singular terms and vagueness.

## Supposition theory

Supposition theory was a branch of medieval logic that was probably aimed at giving accounts of issues similar to modern accounts of reference, plurality, tense, and modality, within an Aristotelian context.

## Susan Haack

Susan Haack (born 1945) is Distinguished Professor in the Humanities, Cooper Senior Scholar in Arts and Sciences, Professor of Philosophy, and Professor of Law at the University of Miami.

## 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.

## Tautology (logic)

In logic, a tautology (from the Greek word ταυτολογία) is a formula or assertion that is true in every possible interpretation.

## Temporal logic

In logic, temporal logic is any system of rules and symbolism for representing, and reasoning about, propositions qualified in terms of time.

## 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.

## Terminology

Terminology is the study of terms and their use.

## Tetralemma

The tetralemma is a figure that features prominently in the logic of India.

## The Gay Science

The Gay Science (Die fröhliche Wissenschaft) or The Joyful Wisdom is a book by Friedrich Nietzsche, first published in 1882 and followed by a second edition, which was published after the completion of Thus Spoke Zarathustra and Beyond Good and Evil, in 1887.

## The Laws of Thought

An Investigation of the Laws of Thought on Which are Founded the Mathematical Theories of Logic and Probabilities by George Boole, published in 1854, is the second of Boole's two monographs on algebraic logic.

## Three-valued logic

In logic, a three-valued logic (also trinary logic, trivalent, ternary, or trilean, sometimes abbreviated 3VL) is any of several many-valued logic systems in which there are three truth values indicating true, false and some indeterminate third value.

## Topics (Aristotle)

The Topics (Τοπικά; Topica) is the name given to one of Aristotle's six works on logic collectively known as the Organon: The Topics constitutes Aristotle's treatise on the art of dialectic—the invention and discovery of arguments in which the propositions rest upon commonly held opinions or endoxa (ἔνδοξα in Greek).

## 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 value

In logic and mathematics, a truth value, sometimes called a logical value, is a value indicating the relation of a proposition to truth.

## Turing degree

In computer science and mathematical logic the Turing degree (named after Alan Turing) or degree of unsolvability of a set of natural numbers measures the level of algorithmic unsolvability of the set.

## Universal logic

Universal logic is the field of logic that studies the common features of all logical systems, aiming to be to logic what universal algebra is to algebra.

## Universal quantification

In predicate logic, a universal quantification is a type of quantifier, a logical constant which is interpreted as "given any" or "for all".

## University of California Press

University of California Press, otherwise known as UC Press, is a publishing house associated with the University of California that engages in academic publishing.

## 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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## Vector logic

Vector logicMizraji, E. (1992).

## 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.

## Wilfrid Hodges

Wilfrid Augustine Hodges, FBA (born 27 May 1941) is a British mathematician, known for his work in model theory.

## Wilfrid Sellars

Wilfrid Stalker Sellars (May 20, 1912 – July 2, 1989) was an American philosopher and prominent developer of critical realism, who "revolutionized both the content and the method of philosophy in the United States".

## Wilhelm Ackermann

Wilhelm Friedrich Ackermann (29 March 1896 – 24 December 1962) was a German mathematician best known for the Ackermann function, an important example in the theory of computation.

## Willard Van Orman Quine

Willard Van Orman Quine (known to intimates as "Van"; June 25, 1908 – December 25, 2000) was an American philosopher and logician in the analytic tradition, recognized as "one of the most influential philosophers of the twentieth century." From 1930 until his death 70 years later, Quine was continually affiliated with Harvard University in one way or another, first as a student, then as a professor of philosophy and a teacher of logic and set theory, and finally as a professor emeritus who published or revised several books in retirement.

## William Kneale

William Calvert Kneale (22 June 1906 &ndash; 24 June 1990) was an English logician best known for his 1962 book The Development of Logic, a history of logic from its beginnings in Ancient Greece written with his wife Martha.

## William of Ockham

William of Ockham (also Occam, from Gulielmus Occamus; 1287 – 1347) was an English Franciscan friar and scholastic philosopher and theologian, who is believed to have been born in Ockham, a small village in Surrey.

## William Wallace (philosopher)

William Wallace (11 May 1844 &ndash; 18 February 1897) was a Scottish philosopher and academic who became fellow of Merton College and White's Professor of Moral Philosophy at Oxford University.

## References

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