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Logic
Logic

Logic (from the Ancient Greek: , logikḗ), originally meaning "the word" or "what is spoken" (but coming to mean "thought" or "reason"), is generally held to consist of the systematic study of the form of arguments. A valid argument is one where there is a specific relation of logical support between the assumptions of the argument and its conclusion. (In ordinary discourse, the conclusion of such an argument may be signified by words like therefore, hence, ergo and so on.)
There is no universal agreement as to the exact scope and subject matter of logic (see § Rival conceptions, below), but it has traditionally included the classification of arguments, the systematic exposition of the 'logical form' common to all valid arguments, the study of inference, including fallacies, and the study of semantics, including paradoxes. Historically, logic has been studied in philosophy (since ancient times) and mathematics (since the mid1800s), and recently logic has been studied in computer science, linguistics, psychology, and other fields.
The concept of logical form is central to logic. The validity of an argument is determined by its logical form, not by its content. Traditional Aristotelian syllogistic logic and modern symbolic logic are examples of formal logic.
However, agreement on what logic is has remained elusive, and although the field of universal logic has studied the common structure of logics, in 2007 Mossakowski et al. commented that "it is embarrassing that there is no widely acceptable formal definition of 'a logic'".
Logic is generally considered formal when it analyzes and represents the form of any valid argument type. The form of an argument is displayed by representing its sentences in the formal grammar and symbolism of a logical language to make its content usable in formal inference. Simply put, formalising simply means translating English sentences into the language of logic.
 Informal logic is the study of natural language arguments. The study of fallacies is an important branch of informal logic. Since much informal argument is not strictly speaking deductive, on some conceptions of logic, informal logic is not logic at all. See 'Rival conceptions', below.
 Formal logic is the study of inference with purely formal content. An inference possesses a purely formal content if it can be expressed as a particular application of a wholly abstract rule, that is, a rule that is not about any particular thing or property. The works of Aristotle contain the earliest known formal study of logic. Modern formal logic follows and expands on Aristotle. In many definitions of logic, logical inference and inference with purely formal content are the same. This does not render the notion of informal logic vacuous, because no formal logic captures all of the nuances of natural language.
 Symbolic logic is the study of symbolic abstractions that capture the formal features of logical inference. Symbolic logic is often divided into two main branches: propositional logic and predicate logic.
 Mathematical logic is an extension of symbolic logic into other areas, in particular to the study of model theory, proof theory, set theory, and recursion theory.
 Consistency, which means that no theorem of the system contradicts another.
 Validity, which means that the system's rules of proof never allow a false inference from true premises.
 Completeness, which means that if a formula is true, it can be proven, i.e. is a theorem of the system.
 Soundness, meaning that if any formula is a theorem of the system, it is true. This is the converse of completeness. (Note that in a distinct philosophical use of the term, an argument is sound when it is both valid and its premises are true).
 Section F.3 on Logics and meanings of programs and F.4 on Mathematical logic and formal languages as part of the theory of computer science: this work covers formal semantics of programming languages, as well as work of formal methods such as Hoare logic;
 Boolean logic as fundamental to computer hardware: particularly, the system's section B.2 on Arithmetic and logic structures, relating to operatives AND, NOT, and OR;
 Many fundamental logical formalisms are essential to section I.2 on artificial intelligence, for example modal logic and default logic in Knowledge representation formalisms and methods, Horn clauses in logic programming, and description logic.
 Digital electronics (also known as digital logic or logic gates)
 Fallacies
 List of logicians
 List of logic journals
 List of logic symbols
 Logic puzzle
 Mathematics
 Metalogic
 Outline of logic
 Philosophy
 Reason
 Truth
 Vector logic
 Barwise, J. (1982). Handbook of Mathematical Logic. Elsevier. .
 Belnap, N. (1977). "A useful fourvalued logic". In Dunn & Eppstein, Modern uses of multiplevalued logic. Reidel: Boston.
 Bocheński, J. M. (1959). A précis of mathematical logic. Translated from the French and German editions by Otto Bird. D. Reidel, Dordrecht, South Holland.
 Bocheński, J. M. (1970). A history of formal logic. 2nd Edition. Translated and edited from the German edition by Ivo Thomas. Chelsea Publishing, New York.
 Brookshear, J. Glenn (1989). Theory of computation: formal languages, automata, and complexity. Redwood City, Calif.: Benjamin/Cummings Pub. Co. ISBN .
 Cohen, R.S, and Wartofsky, M.W. (1974). Logical and Epistemological Studies in Contemporary Physics. Boston Studies in the Philosophy of Science. D. Reidel Publishing Company: Dordrecht, Netherlands. .
 Finkelstein, D. (1969). "Matter, Space, and Logic". in R.S. Cohen and M.W. Wartofsky (eds. 1974).
 Gabbay, D.M., and Guenthner, F. (eds., 2001–2005). Handbook of Philosophical Logic. 13 vols., 2nd edition. Kluwer Publishers: Dordrecht.
 Hilbert, D., and Ackermann, W, (1928). Grundzüge der theoretischen Logik (Principles of Mathematical Logic). SpringerVerlag. OCLC 2085765
 Susan Haack (1996). Deviant Logic, Fuzzy Logic: Beyond the Formalism, University of Chicago Press.
 Hodges, W. (2001). Logic. An introduction to Elementary Logic, Penguin Books.
 Hofweber, T. (2004), Logic and Ontology. Stanford Encyclopedia of Philosophy. Edward N. Zalta (ed.).
 Hughes, R.I.G. (1993, ed.). A Philosophical Companion to FirstOrder Logic. Hackett Publishing.
 Kline, Morris (1972). Mathematical Thought From Ancient to Modern Times. Oxford University Press. ISBN .
 Kneale, William, and Kneale, Martha, (1962). The Development of Logic. Oxford University Press, London, UK.
 Liddell, Henry George; Scott, Robert. "Logikos". A GreekEnglish Lexicon. Perseus Project.
 Mendelson, Elliott, (1964). Introduction to Mathematical Logic. Wadsworth & Brooks/Cole Advanced Books & Software: Monterey, Calif. OCLC 13580200
 Harper, Robert (2001). "Logic". Online Etymology Dictionary.
 Smith, B. (1989). "Logic and the Sachverhalt". The Monist 72(1):52–69.
 Whitehead, Alfred North and Bertrand Russell (1910). Principia Mathematica. Cambridge University Press: Cambridge, England. OCLC 1041146
 Logic at PhilPapers
 Logic at the Indiana Philosophy Ontology Project
 "Logic". Internet Encyclopedia of Philosophy.
 Hazewinkel, Michiel, ed. (2001), "Logical calculus", Encyclopedia of Mathematics, Springer, ISBN
 An Outline for Verbal Logic
 Introductions and tutorials
 An Introduction to Philosophical Logic, by Paul Newall, aimed at beginners.
 forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic.

Logic SelfTaught: A Workbook (originally prepared for online logic instruction).
 Nicholas Rescher. (1964). Introduction to Logic, St. Martin's Press.
 Essays
 "Symbolic Logic" and "The Game of Logic", Lewis Carroll, 1896.
 Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
 Online Tools
 Interactive Syllogistic Machine A web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.
 Reference material
 Translation Tips, by Peter Suber, for translating from English into logical notation.
 Ontology and History of Logic. An Introduction with an annotated bibliography.
 Reading lists
 The London Philosophy Study Guide offers many suggestions on what to read, depending on the student's familiarity with the subject:
 An Introduction to Philosophical Logic, by Paul Newall, aimed at beginners.
 forall x: an introduction to formal logic, by P.D. Magnus, covers sentential and quantified logic.

Logic SelfTaught: A Workbook (originally prepared for online logic instruction).
 Nicholas Rescher. (1964). Introduction to Logic, St. Martin's Press.
 Nicholas Rescher. (1964). Introduction to Logic, St. Martin's Press.
 "Symbolic Logic" and "The Game of Logic", Lewis Carroll, 1896.
 Math & Logic: The history of formal mathematical, logical, linguistic and methodological ideas. In The Dictionary of the History of Ideas.
 Interactive Syllogistic Machine A web based syllogistic machine for exploring fallacies, figures, terms, and modes of syllogisms.
 Translation Tips, by Peter Suber, for translating from English into logical notation.
 Ontology and History of Logic. An Introduction with an annotated bibliography.
 The London Philosophy Study Guide offers many suggestions on what to read, depending on the student's familiarity with the subject:

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Logic