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Introduction to Logic:
The Logic refers to both the study of modes of reasoning that are valid and which are untrue and the use of valid reasoning. In another words, logic is used in nearly all intellectual activities, involving science and philosophy, however in initial sense it is studied mainly in the disciplines of mathematics, philosophy, and computer science. It examines common forms which arguments may take. In the stream of mathematics it is the study of valid inferences in some formal language. It is also studied in the argumentation theory.
The Logic was studied in numerous ancient civilizations which include India, China and Greece. In West, the logic was established as a formal discipline by Aristotle who gave it a primary place in philosophy. The study of logic is a section of the classical trivium that also involved rhetoric and grammar.
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Informal logic:
This kind of logic is the study of natural language arguments. The study of fallacy is a major branch of informal logic. The dialogues of Plato are very good illustrations of informal logic.
Formal logic:
This kind of logic is the study of inference with purely formal content. An inference possessed simply formal content if it can be expressed as a specific application of an entirely abstract rule, which is, a rule that is not about any particular thing or property. The work of Aristotle consists of the earliest known formal study of logic. The modern formal logic enlarges and follows on Aristotle. In different definitions of logic logical inference and inference with purely formal content are alike. This does not render the notion of informal logic vacuous, as of no formal logic captures the entire nuance of natural language.
Symbolic logic:
This kind of logic is the study of symbolic abstractions which capture the formal features of logical inference. The symbolic logic is sub-divided into two branches: propositional logic and predicate logic.
Mathematical logic:
This kind of logic is an extension of symbolic logic into other regions, in specific to the study of proof theory, model theory, set theory, and recursion theory.
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